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Dynamic Response Of A Vibrating Structure To Sinusoidal Excitation

This is a presentation that I gave to the engineering department as part of a semester-long lab course.

Chapter 2 lecture 1 mechanical vibration

This document summarizes key concepts in vibration of single-degree-of-freedom (SDOF) systems. It discusses the generalized model of SDOF systems and provides examples. It then covers the differential equations of motion for SDOF systems using Newton's law and the energy method in the time domain. Specific examples are given for mass-spring, simple pendulum, and cantilever beam systems. Considerations for equivalent mass and stiffness of springs are also addressed.

DOMV No 8 MDOF LINEAR SYSTEMS - RAYLEIGH'S METHOD - FREE VIBRATION.pdf

This document discusses free vibration analysis of linear multi-degree-of-freedom (MDOF) systems. It introduces Rayleigh's method, an approximate technique to determine natural frequencies of MDOF systems by assuming harmonic motion. Rayleigh's method equates maximum kinetic energy to maximum potential energy to derive an expression for natural frequencies in terms of mass and stiffness matrices and an assumed mode shape. The document also discusses exact calculation of natural frequencies and mode shapes by solving the eigenvalue problem of the dynamic matrix. It states that natural frequencies and mode shapes, known as normal modes, are important for qualitative analysis and solving forced vibration problems of MDOF systems.

Undamped vibration absorber

This document provides a theory and experimental procedure for demonstrating an undamped vibration absorber. The theory section explains how attaching an auxiliary mass-spring system to a vibrating object can reduce vibrations by extracting the energy that causes them. If the absorber's natural frequency matches the object's frequency, the object's amplitude can be reduced to zero. The experiment uses a beam with a motor to induce vibrations, and an absorber attached below to reduce the beam's amplitude at different motor speeds by adjusting the absorber's mass positions. The goal is to determine the absorber configuration that minimizes the beam's vibrations.

Design of Tuned Mass Vibration Absorber - Case Stude

This document discusses the design of a tuned mass vibration absorber to reduce vibrations in a primary system. It begins by providing an overview of vibration and its causes. It then discusses the effects of vibration, both desirable and undesirable. Several methods for reducing vibration are presented, with the tuned mass vibration absorber being selected due to advantages like ease of design. The objective and working principle of a tuned mass vibration absorber are explained. The design procedure involves calculating the natural frequencies of the primary and absorber systems. Experimental validation was performed using equipment like an FFT analyzer and accelerometer. Applications include reciprocating machines and transmission lines. ANSYS was used to analyze balanced vs unbalanced masses. The conclusion is that a tuned mass vibration absor

Design of Tuned Mass Vibration Absorber - Case Stude

By www.Fastrackengine.com- Complete case study for design of tuned mass vibration absorber along with mathematical and practical validation.

Ijetr021232

Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org

Ijetr021232

ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,

Dynamic Response Of A Vibrating Structure To Sinusoidal Excitation

This is a presentation that I gave to the engineering department as part of a semester-long lab course.

Chapter 2 lecture 1 mechanical vibration

This document summarizes key concepts in vibration of single-degree-of-freedom (SDOF) systems. It discusses the generalized model of SDOF systems and provides examples. It then covers the differential equations of motion for SDOF systems using Newton's law and the energy method in the time domain. Specific examples are given for mass-spring, simple pendulum, and cantilever beam systems. Considerations for equivalent mass and stiffness of springs are also addressed.

DOMV No 8 MDOF LINEAR SYSTEMS - RAYLEIGH'S METHOD - FREE VIBRATION.pdf

This document discusses free vibration analysis of linear multi-degree-of-freedom (MDOF) systems. It introduces Rayleigh's method, an approximate technique to determine natural frequencies of MDOF systems by assuming harmonic motion. Rayleigh's method equates maximum kinetic energy to maximum potential energy to derive an expression for natural frequencies in terms of mass and stiffness matrices and an assumed mode shape. The document also discusses exact calculation of natural frequencies and mode shapes by solving the eigenvalue problem of the dynamic matrix. It states that natural frequencies and mode shapes, known as normal modes, are important for qualitative analysis and solving forced vibration problems of MDOF systems.

Undamped vibration absorber

This document provides a theory and experimental procedure for demonstrating an undamped vibration absorber. The theory section explains how attaching an auxiliary mass-spring system to a vibrating object can reduce vibrations by extracting the energy that causes them. If the absorber's natural frequency matches the object's frequency, the object's amplitude can be reduced to zero. The experiment uses a beam with a motor to induce vibrations, and an absorber attached below to reduce the beam's amplitude at different motor speeds by adjusting the absorber's mass positions. The goal is to determine the absorber configuration that minimizes the beam's vibrations.

Design of Tuned Mass Vibration Absorber - Case Stude

This document discusses the design of a tuned mass vibration absorber to reduce vibrations in a primary system. It begins by providing an overview of vibration and its causes. It then discusses the effects of vibration, both desirable and undesirable. Several methods for reducing vibration are presented, with the tuned mass vibration absorber being selected due to advantages like ease of design. The objective and working principle of a tuned mass vibration absorber are explained. The design procedure involves calculating the natural frequencies of the primary and absorber systems. Experimental validation was performed using equipment like an FFT analyzer and accelerometer. Applications include reciprocating machines and transmission lines. ANSYS was used to analyze balanced vs unbalanced masses. The conclusion is that a tuned mass vibration absor

Design of Tuned Mass Vibration Absorber - Case Stude

By www.Fastrackengine.com- Complete case study for design of tuned mass vibration absorber along with mathematical and practical validation.

Ijetr021232

Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org

Ijetr021232

ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,

Lecture3_Mech_SU.pptx

The lecture discusses measurement system behavior and modeling. It aims to understand how systems respond to different input signals and how instruments modify measurements. Models of zero-order, first-order, and second-order systems are presented. A first-order model is developed to simulate a thermometer's temperature response over time. Second-order systems can oscillate at their natural frequency depending on damping. Characterizing system order, time constants, damping, and frequency response allows predicting instrument behavior.

12 l1-harmonic methodology

Structural harmonic analysis is a technique used to determine the steady-state response of a linear structure to loads that vary sinusoidally over time. Any sustained cyclic load will produce a sustained cyclic response in the structural system. Harmonic response analysis allows predicting the sustained dynamic behavior of structures to verify designs can overcome resonance, fatigue, and other harmful effects of forced vibrations. The analysis calculates the structure's response at different frequencies to identify peak responses and review stresses at peak frequencies.

What is the likely future of real-time transient stability?

Transient stability refers to the ability of synchronous generators in a power system to remain in synchronism after a disturbance. Simulation of system dynamics is the benchmark method to analyze transient stability but requires significant computation time. Many methods have attempted to reduce this time using concepts like Lyapunov analysis or machine learning, but few have been applied in practice. Emerging power system changes like renewable generation and HVDC transmission present new challenges for transient stability analysis and control that require novel approaches beyond just time-domain simulations.

Me330 lecture5

This document discusses modeling mechanical systems for control systems. It covers:
1) Newton's second law governs mechanical systems and results in equations of motion describing dynamical systems. These equations can be represented using block diagrams and Laplace transforms.
2) Modeling involves determining the equation of motion using free body diagrams and summing the forces. Mechanical components like springs, dampers and masses have characteristic force-velocity, force-displacement and impedance relationships.
3) Systems with multiple degrees of freedom require equations of motion equal to the number of independent motions. Transfer functions can be derived from the Laplace transform of the equations of motion.

Structural Dynamics

The document discusses structural dynamics and analysis of multi-degree of freedom systems. It covers key concepts such as dynamic differential equations, natural frequencies, damping, modal analysis, and different analysis methods including direct integration and frequency-based approaches. Linear dynamics allows use of natural modes of vibration while nonlinear dynamics accounts for large motions and changing geometry. Damping dissipates energy through velocity-dependent forces. Analysis can be performed via direct time integration or modal superposition depending on the problem characteristics and dominant frequencies.

Vibration analysis and modelling of cantilever beam

Vibration analysis of cantilever beam with different computational techniques as a single degree of freedom system

Presentation3.ppt

This document discusses measurement system behavior and characterization. It aims to understand terminology like amplitude, frequency, and phase response. It also aims to understand how instruments modify signals and characterize systems by order. First order systems have a time constant that describes their response. Harmonic excitation of first order systems produces amplitude and phase responses that depend on the ratio of excitation frequency to time constant. The behavior of complete measuring systems and their components is determined by mechanical and electrical elements.

Vibtraion notes

This document summarizes key terms and concepts related to dynamics of machines including:
1. Basic terms like time period, frequency, angular frequency, and phase of vibration.
2. Classifications of vibration such as free vs forced, damped vs undamped, linear vs non-linear, and deterministic vs random vibration.
3. Components of vibrating systems including springs, masses, and dampers. Equations of motion and natural frequency are derived using various methods.
4. Types of damping and classifications of damped systems based on damping ratio are discussed.

CS Mod1AzDOCUMENTS.in.pptx

This document contains a lesson plan for Module 1 of a control systems course. The module covers topics such as introduction to control systems, types of control systems, effect of feedback systems, and differential equations of physical, mechanical, and electrical systems. Examples of various control systems like thermostats, traffic signals, and aircraft are provided. Terminology used in control systems like command input, reference input, and disturbance are defined. The types of control systems - open loop and closed loop - are described along with their characteristics. General considerations for designing control systems like stability, accuracy, and speed of response are also outlined.

Instrumentation Lab. Experiment #12 Report: Lateral Beam Vibration

This file contains a report for the 12th experiment in the Lab "Instrumentation and Dynamic Systems", taken by mechanical engineering students.

Fondasi Untuk Mesin Pembuat Kertas

1) The document discusses dynamic analysis of paper machine foundations to reduce vibrations from high-speed machines.
2) Accurate dynamic models from manufacturers are important for determining natural frequencies and performing force-response analyses.
3) Foundations must be designed to meet static load requirements while ensuring the system's natural frequencies satisfy manufacturers' vibration criteria.

PPT VIBRATIONS.ppt

This document provides notes for a course on Mechanical Vibrations. It summarizes that the course notes were compiled from several sources including a textbook on mechanical vibrations and technical notes. It then provides an introduction to mechanical vibrations, defining vibration as oscillations about an equilibrium position. It discusses different types of vibration including free vibration, forced vibration, and resonance. It also discusses modeling vibrations using lumped parameter models and numerical methods. Key concepts covered include degrees of freedom, modeling elastic elements as springs, moment of inertia, damping, and an example problem calculating beam stiffness.

Forcedamp2

For a damped spring-mass system undergoing forced vibration by a sinusoidal force or ground excitation, the steady state response is also sinusoidal at the excitation frequency. The maximum response amplitude occurs at a frequency slightly below the natural frequency and decreases with increased damping. Damping reduces the sharpness of resonance and limits the maximum response amplitude reached.

Ch 01, Introduction to Mechanical Vibrations ppt.pdf

This document provides an introduction to mechanical vibration, including definitions, applications, causes, and importance. It discusses elementary parts of vibrating systems like springs, masses, and dampers. Vibration can be classified based on the excitation, such as free or forced vibration. Simple harmonic motion is described as the simplest form of periodic motion. The steps for analyzing vibration are defined as: 1) defining the problem, 2) physical modeling, 3) formulating governing equations, 4) mathematically solving the equations, and 5) physically interpreting the results.

Vibration

The document provides notes for a course on mechanical vibrations. It summarizes that:
1) The course notes were compiled from textbooks, technical notes, and a professor's webpage that are gratefully acknowledged.
2) Vibrations are oscillations of a system about an equilibrium position. Mechanical systems can be modeled using basic components of springs, dampers, and masses.
3) Free vibration occurs when a disturbed system vibrates at its natural frequency and mode shapes. Forced vibration follows an external force frequency, with resonance dangerously increasing amplitudes at the natural frequency.

Sliding Mode Controller

Sliding mode control is a variable structure control method where the control input switches between two or more different structures based on the current position in the state space. There are two main steps: 1) designing a sliding surface that constrains the plant dynamics to achieve the desired response, and 2) constructing switched feedback gains to drive the plant's state trajectory onto the sliding surface. The main advantages are robustness to perturbations or uncertainties and stabilizing some nonlinear systems not possible with continuous feedback. Chattering is the main drawback but can be reduced using techniques like nonlinear gains or higher-order sliding mode control.

Presentation statusmeeting 2017_05

This document discusses vibration isolation of a LEGO platform using a skyhook control solution. It proposes using an active damping system with force proportional to isolated mass speed. Preliminary measurements found the first 8 eigenmodes. A real system uses 4 symmetric actuators and sensors. Decentralized control is effective with minimal performance loss versus MIMO control. Experimental results show reduced transmissibility between base and plate when controlled, though high noise remains an issue. Next steps propose replacing the current system with the SISO isolation demo's lower cost analog PID control approach.

Basics of Electrochemical Impedance Spectroscopy

An introduction to Electrochemical Impedance Spectroscopy (EIS) theory and has been kept as free from mathematics and electrical theory as possible. If you still find the material presented here difficult to understand, don't stop reading. You will get useful information from this application note, even if you don't follow all of the discussions.

Multi degree of freedom systems

The document discusses influence coefficients and approximate methods for determining natural frequencies of multi-degree of freedom systems. It defines influence coefficients as the influence of a unit displacement or force at one point on forces or displacements at other points. Approximate methods like Dunkerley's and Rayleigh's are described to quickly estimate fundamental natural frequencies. Dunkerley's method involves solving a polynomial equation to determine natural frequencies from flexibility influence coefficients of the system.

Lecture3_Mech_SU.pptx

The lecture discusses measurement system behavior and modeling. It aims to understand how systems respond to different input signals and how instruments modify measurements. Models of zero-order, first-order, and second-order systems are presented. A first-order model is developed to simulate a thermometer's temperature response over time. Second-order systems can oscillate at their natural frequency depending on damping. Characterizing system order, time constants, damping, and frequency response allows predicting instrument behavior.

12 l1-harmonic methodology

Structural harmonic analysis is a technique used to determine the steady-state response of a linear structure to loads that vary sinusoidally over time. Any sustained cyclic load will produce a sustained cyclic response in the structural system. Harmonic response analysis allows predicting the sustained dynamic behavior of structures to verify designs can overcome resonance, fatigue, and other harmful effects of forced vibrations. The analysis calculates the structure's response at different frequencies to identify peak responses and review stresses at peak frequencies.

What is the likely future of real-time transient stability?

Transient stability refers to the ability of synchronous generators in a power system to remain in synchronism after a disturbance. Simulation of system dynamics is the benchmark method to analyze transient stability but requires significant computation time. Many methods have attempted to reduce this time using concepts like Lyapunov analysis or machine learning, but few have been applied in practice. Emerging power system changes like renewable generation and HVDC transmission present new challenges for transient stability analysis and control that require novel approaches beyond just time-domain simulations.

Me330 lecture5

This document discusses modeling mechanical systems for control systems. It covers:
1) Newton's second law governs mechanical systems and results in equations of motion describing dynamical systems. These equations can be represented using block diagrams and Laplace transforms.
2) Modeling involves determining the equation of motion using free body diagrams and summing the forces. Mechanical components like springs, dampers and masses have characteristic force-velocity, force-displacement and impedance relationships.
3) Systems with multiple degrees of freedom require equations of motion equal to the number of independent motions. Transfer functions can be derived from the Laplace transform of the equations of motion.

Structural Dynamics

The document discusses structural dynamics and analysis of multi-degree of freedom systems. It covers key concepts such as dynamic differential equations, natural frequencies, damping, modal analysis, and different analysis methods including direct integration and frequency-based approaches. Linear dynamics allows use of natural modes of vibration while nonlinear dynamics accounts for large motions and changing geometry. Damping dissipates energy through velocity-dependent forces. Analysis can be performed via direct time integration or modal superposition depending on the problem characteristics and dominant frequencies.

Vibration analysis and modelling of cantilever beam

Vibration analysis of cantilever beam with different computational techniques as a single degree of freedom system

Presentation3.ppt

This document discusses measurement system behavior and characterization. It aims to understand terminology like amplitude, frequency, and phase response. It also aims to understand how instruments modify signals and characterize systems by order. First order systems have a time constant that describes their response. Harmonic excitation of first order systems produces amplitude and phase responses that depend on the ratio of excitation frequency to time constant. The behavior of complete measuring systems and their components is determined by mechanical and electrical elements.

Vibtraion notes

This document summarizes key terms and concepts related to dynamics of machines including:
1. Basic terms like time period, frequency, angular frequency, and phase of vibration.
2. Classifications of vibration such as free vs forced, damped vs undamped, linear vs non-linear, and deterministic vs random vibration.
3. Components of vibrating systems including springs, masses, and dampers. Equations of motion and natural frequency are derived using various methods.
4. Types of damping and classifications of damped systems based on damping ratio are discussed.

CS Mod1AzDOCUMENTS.in.pptx

This document contains a lesson plan for Module 1 of a control systems course. The module covers topics such as introduction to control systems, types of control systems, effect of feedback systems, and differential equations of physical, mechanical, and electrical systems. Examples of various control systems like thermostats, traffic signals, and aircraft are provided. Terminology used in control systems like command input, reference input, and disturbance are defined. The types of control systems - open loop and closed loop - are described along with their characteristics. General considerations for designing control systems like stability, accuracy, and speed of response are also outlined.

Instrumentation Lab. Experiment #12 Report: Lateral Beam Vibration

This file contains a report for the 12th experiment in the Lab "Instrumentation and Dynamic Systems", taken by mechanical engineering students.

Fondasi Untuk Mesin Pembuat Kertas

1) The document discusses dynamic analysis of paper machine foundations to reduce vibrations from high-speed machines.
2) Accurate dynamic models from manufacturers are important for determining natural frequencies and performing force-response analyses.
3) Foundations must be designed to meet static load requirements while ensuring the system's natural frequencies satisfy manufacturers' vibration criteria.

PPT VIBRATIONS.ppt

This document provides notes for a course on Mechanical Vibrations. It summarizes that the course notes were compiled from several sources including a textbook on mechanical vibrations and technical notes. It then provides an introduction to mechanical vibrations, defining vibration as oscillations about an equilibrium position. It discusses different types of vibration including free vibration, forced vibration, and resonance. It also discusses modeling vibrations using lumped parameter models and numerical methods. Key concepts covered include degrees of freedom, modeling elastic elements as springs, moment of inertia, damping, and an example problem calculating beam stiffness.

Forcedamp2

For a damped spring-mass system undergoing forced vibration by a sinusoidal force or ground excitation, the steady state response is also sinusoidal at the excitation frequency. The maximum response amplitude occurs at a frequency slightly below the natural frequency and decreases with increased damping. Damping reduces the sharpness of resonance and limits the maximum response amplitude reached.

Ch 01, Introduction to Mechanical Vibrations ppt.pdf

This document provides an introduction to mechanical vibration, including definitions, applications, causes, and importance. It discusses elementary parts of vibrating systems like springs, masses, and dampers. Vibration can be classified based on the excitation, such as free or forced vibration. Simple harmonic motion is described as the simplest form of periodic motion. The steps for analyzing vibration are defined as: 1) defining the problem, 2) physical modeling, 3) formulating governing equations, 4) mathematically solving the equations, and 5) physically interpreting the results.

Vibration

The document provides notes for a course on mechanical vibrations. It summarizes that:
1) The course notes were compiled from textbooks, technical notes, and a professor's webpage that are gratefully acknowledged.
2) Vibrations are oscillations of a system about an equilibrium position. Mechanical systems can be modeled using basic components of springs, dampers, and masses.
3) Free vibration occurs when a disturbed system vibrates at its natural frequency and mode shapes. Forced vibration follows an external force frequency, with resonance dangerously increasing amplitudes at the natural frequency.

Sliding Mode Controller

Sliding mode control is a variable structure control method where the control input switches between two or more different structures based on the current position in the state space. There are two main steps: 1) designing a sliding surface that constrains the plant dynamics to achieve the desired response, and 2) constructing switched feedback gains to drive the plant's state trajectory onto the sliding surface. The main advantages are robustness to perturbations or uncertainties and stabilizing some nonlinear systems not possible with continuous feedback. Chattering is the main drawback but can be reduced using techniques like nonlinear gains or higher-order sliding mode control.

Presentation statusmeeting 2017_05

This document discusses vibration isolation of a LEGO platform using a skyhook control solution. It proposes using an active damping system with force proportional to isolated mass speed. Preliminary measurements found the first 8 eigenmodes. A real system uses 4 symmetric actuators and sensors. Decentralized control is effective with minimal performance loss versus MIMO control. Experimental results show reduced transmissibility between base and plate when controlled, though high noise remains an issue. Next steps propose replacing the current system with the SISO isolation demo's lower cost analog PID control approach.

Basics of Electrochemical Impedance Spectroscopy

An introduction to Electrochemical Impedance Spectroscopy (EIS) theory and has been kept as free from mathematics and electrical theory as possible. If you still find the material presented here difficult to understand, don't stop reading. You will get useful information from this application note, even if you don't follow all of the discussions.

Multi degree of freedom systems

The document discusses influence coefficients and approximate methods for determining natural frequencies of multi-degree of freedom systems. It defines influence coefficients as the influence of a unit displacement or force at one point on forces or displacements at other points. Approximate methods like Dunkerley's and Rayleigh's are described to quickly estimate fundamental natural frequencies. Dunkerley's method involves solving a polynomial equation to determine natural frequencies from flexibility influence coefficients of the system.

Lecture3_Mech_SU.pptx

Lecture3_Mech_SU.pptx

12 l1-harmonic methodology

12 l1-harmonic methodology

What is the likely future of real-time transient stability?

What is the likely future of real-time transient stability?

Me330 lecture5

Me330 lecture5

Structural Dynamics

Structural Dynamics

Vibration analysis and modelling of cantilever beam

Vibration analysis and modelling of cantilever beam

Mechanical Vibration Ch-1.pptxgygyyyyyygyyy

Mechanical Vibration Ch-1.pptxgygyyyyyygyyy

Presentation3.ppt

Presentation3.ppt

Vibtraion notes

Vibtraion notes

CS Mod1AzDOCUMENTS.in.pptx

CS Mod1AzDOCUMENTS.in.pptx

Instrumentation Lab. Experiment #12 Report: Lateral Beam Vibration

Instrumentation Lab. Experiment #12 Report: Lateral Beam Vibration

Fondasi Untuk Mesin Pembuat Kertas

Fondasi Untuk Mesin Pembuat Kertas

PPT VIBRATIONS.ppt

PPT VIBRATIONS.ppt

Forcedamp2

Forcedamp2

Ch 01, Introduction to Mechanical Vibrations ppt.pdf

Ch 01, Introduction to Mechanical Vibrations ppt.pdf

Vibration

Vibration

Sliding Mode Controller

Sliding Mode Controller

Presentation statusmeeting 2017_05

Presentation statusmeeting 2017_05

Basics of Electrochemical Impedance Spectroscopy

Basics of Electrochemical Impedance Spectroscopy

Multi degree of freedom systems

Multi degree of freedom systems

Poles and Root Locus.pptxjjjjjjjjjjjjjjjjjjjjjjj

Poles and Root Locus.pptxjjjjjjjjjjjjjjjjjjjjjjj

Poles and Root Locus Tutoribbbbbbbal.pptx

Poles and Root Locus Tutoribbbbbbbal.pptx

Multi Degrees of Freedom.pptxjjjjjjjjjjjjjjjjjjjjjj

Multi Degrees of Freedom.pptxjjjjjjjjjjjjjjjjjjjjjj

Matrix Methods.pptxbbbbbbbbbbbbbbbbbbbbb

Matrix Methods.pptxbbbbbbbbbbbbbbbbbbbbb

Forced Vibrations.pptxbbbbbbbbbbbbbbbbbb

Forced Vibrations.pptxbbbbbbbbbbbbbbbbbb

Poles and Root Locus Tutorial.hhhhhhpptx

Poles and Root Locus Tutorial.hhhhhhpptx

Second Order Systems Qhhhhhhhhuestions.pptx

Second Order Systems Qhhhhhhhhuestions.pptx

Second Order Systems.pptxkkkkkkkkkkkkkjj

Second Order Systems.pptxkkkkkkkkkkkkkjj

First and Second Order Systems Questions.pptx

First and Second Order Systems Questions.pptx

First and Second Order Sykkkkkkkkstems.pptx

First and Second Order Sykkkkkkkkstems.pptx

Week 11 Mini Tasks 123.pptxjjjjjjjjjjjjjjj

Week 11 Mini Tasks 123.pptxjjjjjjjjjjjjjjj

Water Tank Model and Feedback Equation.pptx

Water Tank Model and Feedback Equation.pptx

First Order System Time Resphhhonse.pptx

First Order System Time Resphhhonse.pptx

Modelling and simulation diagrams tutorial.pptx

Modelling and simulation diagrams tutorial.pptx

Modelling and Simulation Diajjgrams.pptx

Modelling and Simulation Diajjgrams.pptx

Modelling and Simulation jquestions.pptx

Modelling and Simulation jquestions.pptx

Modelling and Simulation basics.phhhhptx

Modelling and Simulation basics.phhhhptx

Matlab Tasks – Modelling an electronic circuit filter.pptx

Matlab Tasks – Modelling an electronic circuit filter.pptx

Matlab Tasks – Modelling an electronic circuit filter.pptx

Matlab Tasks – Modelling an electronic circuit filter.pptx

Balancing of rotating bodies questions.pptx

Balancing of rotating bodies questions.pptx

Game Concept Presentation for Ukrainian Mythology Based Game With Designs

The Game Concept created as a Final Project piece for college. Creative Media year 2 student

EASY TUTORIAL OF HOW TO USE CAPCUT BY: FEBLESS HERNANE

CapCut is an easy-to-use video editing app perfect for beginners. To start, download and open CapCut on your phone. Tap "New Project" and select the videos or photos you want to edit. You can trim clips by dragging the edges, add text by tapping "Text," and include music by selecting "Audio." Enhance your video with filters and effects from the "Effects" menu. When you're happy with your video, tap the export button to save and share it. CapCut makes video editing simple and fun for everyone!

ARENA - Young adults in the workplace (Knight Moves).pdf

Presentations of Bavo Raeymaekers (Project lead youth unemployment at the City of Antwerp), Suzan Martens (Service designer at Knight Moves) and Adriaan De Keersmaeker (Community manager at Talk to C)
during the 'Arena • Young adults in the workplace' conference hosted by Knight Moves.

Storytelling For The Web: Integrate Storytelling in your Design Process

In this slides I explain how I have used storytelling techniques to elevate websites and brands and create memorable user experiences. You can discover practical tips as I showcase the elements of good storytelling and its applied to some examples of diverse brands/projects..

Branding de la empresa de Bolt- 2024.pdf

Branding de Bolt

Technoblade The Legacy of a Minecraft Legend.

Technoblade, born Alex on June 1, 1999, was a legendary Minecraft YouTuber known for his sharp wit and exceptional PvP skills. Starting his channel in 2013, he gained nearly 11 million subscribers. His private battle with metastatic sarcoma ended in June 2022, but his enduring legacy continues to inspire millions.

一比一原版(UW毕业证)西雅图华盛顿大学毕业证如何办理

UW毕业证学历书【微信95270640】做UW文凭、办UW文凭、买UW文凭Q微信95270640买办国外文凭UW毕业证买学历咨询/代办美国毕业证成绩单文凭、办澳洲文凭毕业证、办加拿大大学毕业证文凭英国毕业证学历认证-毕业证文凭成绩单、假文凭假毕业证假学历书制作仿制、改成绩、教育部学历学位认证、毕业证、成绩单、文 凭、UW学历文凭、UW假学位证书、毕业证文凭、、文凭毕业证、毕业证认证、留服认证、使馆认证、使馆证明 、使馆留学回国人员证明、留学生认证、学历认证、文凭认证、学位认证
(诚招代理)办理国外高校毕业证成绩单文凭学位证,真实使馆公证（留学回国人员证明）真实留信网认证国外学历学位认证雅思代考国外学校代申请名校保录开请假条改GPA改成绩ID卡
1.高仿业务:【本科硕士】毕业证,成绩单（GPA修改）,学历认证（教育部认证）,大学Offer,,ID,留信认证,使馆认证,雅思,语言证书等高仿类证书；
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1客户提供办理信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
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6快递给客户（国内顺丰国外DHLUPS等快读邮寄）
-办理真实使馆公证（即留学回国人员证明）
-办理各国各大学文凭（世界名校一对一专业服务,可全程监控跟踪进度）
-全套服务：毕业证成绩单真实使馆公证真实教育部认证。让您回国发展信心十足！
（详情请加一下 文凭顾问+微信:95270640）欢迎咨询！实伙伴平时山娃上学阿黑也摇头晃脑地跟去暑假用不着上学阿黑更是天天围着山娃转山娃上山除了察看埋下的野兽铁夹子看护早上逐上山的大黄牛外也觅着采草药摘红菇积攒起来拿到镇上卖山娃知道母亲身体不好家里盖新房也欠了不少钱总想趁假期赚点钱在校寄宿时用不着老向爷爷奶奶要盛夏的乡村仍旧清凉清清爽爽的山娃也过得自由自在不知为啥山娃总情不自禁地思念起城里的父亲每年暑假瞅见远乡近邻的小伙伴都争先恐后地往城里跑山娃就更思片

一比一原版(BU毕业证)波士顿大学毕业证如何办理

BU毕业证学位证【微信95270640】办理BU毕业证【Q微信95270640】波士顿大学毕业证书原版↑制作波士顿大学学历认证文凭办理波士顿大学留信网认证,留学回国办理毕业证成绩单文凭学历认证【Q微信95270640】专业为海外学子办理毕业证成绩单、文凭制作，学历仿制，回国人员证明、做文凭，研究生、本科、硕士学历认证、留信认证、结业证、学位证书样本、美国教育部认证百分百真实存档可查】
【实体公司】办波士顿大学波士顿大学本科毕业证成绩单学历认证学位证文凭认证办留信网认证办留服认证办教育部认证（网上可查实体公司专业可靠）
— — — 留学归国服务中心 — — -
【主营项目】
一.波士顿大学毕业证成绩单使馆认证教育部认证成绩单等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
国外毕业证学位证成绩单办理流程：
1客户提供波士顿大学波士顿大学本科毕业证成绩单办理信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
5成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）。
专业服务请勿犹豫联系我！本公司是留学创业和海归创业者们的桥梁。一次办理终生受用一步到位高效服务。详情请在线咨询办理,欢迎有诚意办理的客户咨询!洽谈。
招聘代理：本公司诚聘英国加拿大澳洲新西兰美国法国德国新加坡各地代理人员如果你有业余时间有兴趣就请联系我们咨询顾问：+微信:95270640知道母亲身体不好家里盖新房也欠了不少钱总想趁假期赚点钱在校寄宿时用不着老向爷爷奶奶要盛夏的乡村仍旧清凉清清爽爽的山娃也过得自由自在不知为啥山娃总情不自禁地思念起城里的父亲每年暑假瞅见远乡近邻的小伙伴都争先恐后地往城里跑山娃就更思念父亲了老想着进父亲的城看看每次从城里洋里洋气地回来小伙伴们总争论着各自到过的城比试比试谁父亲的城最大最美他们大谈城里的新鲜事大谈父亲携他们逛城的快乐事在孩子们幼小的心中地

UNIT IV-VISUAL STYLE AND MOBILE INTERFACES.pptx

Visual Style and Aesthetics: Basics of Visual Design
Visual Design for Enterprise Applications
Range of Visual Styles.
Mobile Interfaces:
Challenges and Opportunities of Mobile Design
Approach to Mobile Design
Patterns

原版定做(penn毕业证书)美国宾夕法尼亚大学毕业证文凭学历证书原版一模一样

原版纸张【微信：741003700 】【(penn毕业证书)美国宾夕法尼亚大学毕业证、文凭学历证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

Top Interior Designers in Bangalore.pdf1

Decormart Studio is widely recognized as one of the best interior designers in Bangalore, known for their exceptional design expertise and ability to create stunning, functional spaces. With a strong focus on client preferences and timely project delivery, Decormart Studio has built a solid reputation for their innovative and personalized approach to interior design.

一比一原版(MMU毕业证书)曼彻斯特城市大学毕业证成绩单如何办理

学校原件一模一样【微信：6496090 】【(MMU毕业证书)曼彻斯特城市大学毕业证成绩单】【微信：6496090 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微6496090
【主营项目】
一.毕业证【q微6496090】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微6496090】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(MMU毕业证书)曼彻斯特城市大学毕业证【微信：6496090 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(MMU毕业证书)曼彻斯特城市大学毕业证【微信：6496090 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(MMU毕业证书)曼彻斯特城市大学毕业证【微信：6496090 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(MMU毕业证书)曼彻斯特城市大学毕业证【微信：6496090 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

SECURING BUILDING PERMIT CITY OF CALOOCAN.pdf

How to apply for building permit in the city of Caloocan?
What is a building permit?
Who applies for building permit?

Mohannad Abdullah portfolio _ V2 _22-24

Mohannad Abdullah
Architecture | Interior Design
portoflio_V2_22-24

一比一原版(NCL毕业证书)纽卡斯尔大学毕业证成绩单如何办理

学校原件一模一样【微信：6496090 】【(NCL毕业证书)纽卡斯尔大学毕业证成绩单】【微信：6496090 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微6496090
【主营项目】
一.毕业证【q微6496090】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微6496090】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(NCL毕业证书)纽卡斯尔大学毕业证【微信：6496090 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(NCL毕业证书)纽卡斯尔大学毕业证【微信：6496090 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(NCL毕业证书)纽卡斯尔大学毕业证【微信：6496090 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(NCL毕业证书)纽卡斯尔大学毕业证【微信：6496090 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

一比一原版(毕业证)长崎大学毕业证成绩单如何办理

一模一样【q/微:1954292140】【(毕业证)长崎大学毕业证成绩单Offer】【q/微:1954292140】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【q/微:1954292140】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【q/微:1954292140】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！

Timeless Principles of Good Design

Timeless Principles of Good Design from my 2015 Presentation at TYPO SF

Impact of Fonts: in Web and Apps Design

Fonts play a crucial role in both User Interface (UI) and User Experience (UX) design. They affect readability, accessibility, aesthetics, and overall user perception.

一比一原版(毕业证)早稻田大学毕业证成绩单如何办理

一模一样【q/微:1954292140】【(毕业证)早稻田大学毕业证成绩单Offer】【q/微:1954292140】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【q/微:1954292140】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【q/微:1954292140】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！

Game Concept Presentation for Ukrainian Mythology Based Game With Designs

Game Concept Presentation for Ukrainian Mythology Based Game With Designs

EASY TUTORIAL OF HOW TO USE CAPCUT BY: FEBLESS HERNANE

EASY TUTORIAL OF HOW TO USE CAPCUT BY: FEBLESS HERNANE

ARENA - Young adults in the workplace (Knight Moves).pdf

ARENA - Young adults in the workplace (Knight Moves).pdf

Storytelling For The Web: Integrate Storytelling in your Design Process

Storytelling For The Web: Integrate Storytelling in your Design Process

Branding de la empresa de Bolt- 2024.pdf

Branding de la empresa de Bolt- 2024.pdf

Technoblade The Legacy of a Minecraft Legend.

Technoblade The Legacy of a Minecraft Legend.

一比一原版(UW毕业证)西雅图华盛顿大学毕业证如何办理

一比一原版(UW毕业证)西雅图华盛顿大学毕业证如何办理

一比一原版(BU毕业证)波士顿大学毕业证如何办理

一比一原版(BU毕业证)波士顿大学毕业证如何办理

UNIT IV-VISUAL STYLE AND MOBILE INTERFACES.pptx

UNIT IV-VISUAL STYLE AND MOBILE INTERFACES.pptx

原版定做(penn毕业证书)美国宾夕法尼亚大学毕业证文凭学历证书原版一模一样

原版定做(penn毕业证书)美国宾夕法尼亚大学毕业证文凭学历证书原版一模一样

Top Interior Designers in Bangalore.pdf1

Top Interior Designers in Bangalore.pdf1

一比一原版(MMU毕业证书)曼彻斯特城市大学毕业证成绩单如何办理

一比一原版(MMU毕业证书)曼彻斯特城市大学毕业证成绩单如何办理

SECURING BUILDING PERMIT CITY OF CALOOCAN.pdf

SECURING BUILDING PERMIT CITY OF CALOOCAN.pdf

Mohannad Abdullah portfolio _ V2 _22-24

Mohannad Abdullah portfolio _ V2 _22-24

一比一原版(NCL毕业证书)纽卡斯尔大学毕业证成绩单如何办理

一比一原版(NCL毕业证书)纽卡斯尔大学毕业证成绩单如何办理

Virtual Tour Application Powerpoint for museum of edinburgh

Virtual Tour Application Powerpoint for museum of edinburgh

一比一原版(毕业证)长崎大学毕业证成绩单如何办理

一比一原版(毕业证)长崎大学毕业证成绩单如何办理

Timeless Principles of Good Design

Timeless Principles of Good Design

Impact of Fonts: in Web and Apps Design

Impact of Fonts: in Web and Apps Design

一比一原版(毕业证)早稻田大学毕业证成绩单如何办理

一比一原版(毕业证)早稻田大学毕业证成绩单如何办理

- 1. Evaluating natural frequencies and mode shapes
- 2. Multi degrees of freedom:
- 3. Multi degrees of freedom: We have already deployed this for 2DOF systems. –Eigenvalues -> Natural Frequencies of modes –Eigenvectors -> Initial Conditions X1,X2 It can be applied to higher order systems –And becomes increasingly tedious (More EoM, Bigger Matrices….) –Needs computational assistance Influence coefficients: -Used in some matrix method calculations -Stiffness Influence Coefficient –The stiffness matrix rewritten as the relation between displacement at point and the forces at other points in a system Flexibility Influence Coefficient –‘flexibility’ or inverse of stiffness
- 4. Dunkerly method: Useful for structures undergoing vibration testing. Attach an eccentric mass exciter to a structure and excite with frequency w22 Note the frequencies of maximum amplitude w1 Calculate w11
- 5. Dunkerly method example: An aircraft rudder tab shows a resonant frequency of 30Hz when vibrated by an eccentric mass shaker mass 1.5kg. By attaching a further 1.5kg to the shaker the frequency is lowered to 24Hz What is the true natural frequency of the tab?
- 6. Holzer method: •A tabular trial-and-error scheme to find natural frequencies and mode shapes of oscillating systems •A trial frequency is first assumed, and a solution is found when the constraints are satisfied. •Requires several trials •Gives node (zero displacement) positions •Used on semi-definite systems (needs a ‘free’ end.)
- 8. Torsional Systems: When the sum of the Torques = 0 • Graph of ST v w will give the modal frequencies • Where the curve passes the w axis • q values for each station will give the mode shapes
- 9. Holzer’s Method for Spring mass systems: