Modal analysis methods can be performed in either the time domain or frequency domain. Time domain methods analyze time response data while frequency domain methods analyze frequency response functions. Some popular time domain modal analysis methods include the Ibrahim time domain method, random decrement method, ARMA time series method, least-squares time domain method, and least-squares complex exponential method. These methods identify modal parameters by fitting a mathematical model to measured time response data.

1. Modal Analysis Methods
Time Domain
Submitted To
Respected Sir Dr Saeed Badshah
Submitted By
Mohsin Iftikhar
Qamar Ud Din Abid
Zia Ur Rehman

2. Modal Analysis
• Modal analysis is the process of determining the inherent dynamic characteristics of a system in forms
of natural frequencies, damping factors and mode shapes, and using them to formulate a mathematical model
for its dynamic behavior.
• Experimental modal analysis can be carried out in two step.
• The first step consists of data acquisition of frequency response
functions.
• The second step consists of modal parameter identification and
visualization using a geometry model of the structure.
• The modal frequencies, damping coefficients, and mode shapes
identified, can be used for the structure modification for vibration
suppression, or to avoid the resonance situation

3. Modal analysis methods –time domain
Time domain methods belong to another category of modal
analysis methods.
• Frequency domain modal analysis relies on measured
frequency response function (FRF) data.
• Time domain modal analysis uses time response data.
The methods were developed on the advances of modern
control theory and computer technology.

4. Frequency domain modal analysis
• Frequency domain modal analysis is a technique used to identify the natural frequencies, damping
ratios, and mode shapes of a structure by analyzing the frequency-domain response of the structure to
a known input.
• Frequency domain modal analysis is based on the principle of superposition. This principle states that
the response of a structure to a complex excitation can be represented as a sum of the responses to a
series of simple harmonic excitations. The natural frequencies of a structure are the frequencies of the
simple harmonic excitations that will cause the structure to vibrate with the greatest amplitude.
• Frequency domain modal analysis is performed by exciting the structure with a known frequency and
amplitude. The response of the structure is then measured and analyzed.
• The natural frequencies, damping ratios, and mode shapes of the structure can then be determined by
fitting the measured response to a mathematical model of the structure.

5. Time domain modal analysis
• Time domain modal analysis is a technique used to identify the natural frequencies, damping
ratios, and mode shapes of a structure by analyzing the time-domain response of the structure to
a known input.
• Time domain modal analysis is based on the principle of superposition. This principle states that
the response of a structure to a complex excitation can be represented as a sum of the responses
to a series of simple harmonic excitations. The natural frequencies of a structure are the
frequencies of the simple harmonic excitations that will cause the structure to vibrate with the
greatest amplitude.

6. Time vs Frequency Domain Modal analysis
Advantages
Frequency Domain
• It is a quick and efficient way.
• It can be used to analyze a wide variety of structures, including complex structures
• It can be used to analyze structures that are difficult to access, such as aircraft and spacecraft.
• Time Domain
• It is a more accurate way to identify the natural frequencies, damping ratios, and mode shapes of a structure
than frequency domain modal analysis.
• It is less sensitive to noise and vibration than frequency domain modal analysis.
• It is easier to interpret the results of time domain modal analysis than the results of frequency domain
modal analysis.

7. Time vs Frequency Domain Modal analysis
Disadvantages
Frequency Domain
• It can be sensitive to noise and vibration.
• It can be difficult to interpret the results of frequency domain modal analysis if the structure is complex.
• It can be difficult to identify the natural frequencies and damping ratios of structures with low damping.
• Time Domain
• It can be more time-consuming and expensive than frequency domain modal analysis.
• It can be difficult to excite a structure with a known input, especially if the structure is large or complex.
• It can be difficult to measure the response of a structure, especially if the structure is vibrating in a noisy
environment.

8. How we will do it
• We have physical system, We don’t know exact properties of system, we may want to identify exact properties, so
we that we can use that identified properties in modal of system to predict responses of system.
• WE have measurements from physical system Y and U
• We build model in computer
• Excite system with same input force U
• Get its response, this is simulated response from model.
• Compare measured response with simulated response.
• SM is function f(f, DR, Mass) of model
• Since these are not same as in true system in general, the responses will not match, we compute some error, we
minimize that error to find that set of frequency, Damping Ratio and mass which best fit our measured response
that’s

9. Various Methdos of Modal analysis–time domain
• Ibrahim time domain (ITD) method
• Random decrement method
• ARMA time series method
• Least-squares time domain method
• Least-squares complex exponential (LSCE) method

10. Least-squares time domain method
Least-squares complex exponential (LSCE) method
• The Least-squares time domain (LSTDM) and Least-squares complex exponential (LSCE) methods are
two of the most popular time-domain modal analysis methods. Both methods are based on the
principle of superposition, which states that the response of a structure to a complex excitation can be
represented as a sum of the responses to a series of simple harmonic excitations.
• The LSCE method is a more accurate method than the LSTD method, especially for structures with high
damping ratios. However, the LSCE method can be more difficult to implement, and it can be more
computationally expensive.
• In general, the LSTD method is a good choice for structures with low damping ratios, and the LSCE
method is a good choice for structures with high damping ratios.

11. ARMA time series modal
• The ARMA time series modal analysis method works by first converting the time-
domain response of the structure into the frequency domain. This is done using a
Fourier transform. The frequency-domain response is then decomposed into a
sum of simple harmonic excitations. The natural frequencies, damping ratios, and
mode shapes of the structure can then be determined by fitting the decomposed
response to an ARMA model.

12. Ibrahim time domain (ITD) method
• The Ibrahim time domain (ITD) method is a modal identification technique that
uses the time-domain response of a structure to identify its natural frequencies,
damping ratios, and mode shapes. The ITD method was developed by Sherif
Ibrahim in the early 1980s.
• The ITD method is based on the principle of superposition. This principle states
that the response of a structure to a complex excitation can be represented as a
sum of the responses to a series of simple harmonic excitations.

13. Modal analysis methods –time domain

14. Modal analysis methods –time domain