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Structural Dynamics Notes.pdf
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- 9. Chapter 2: FreeVibration Lecture Page 9
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- 12. The vertical suspensionsystem of an automobile is idealized as a viscously damped SDF system. Under the 3000-lb weight of the car the suspension system deflects 2 in. The suspension is designed to be critically damped. (a) Calculate the damping and stiffness coefficients of the suspension. (b) With four 160-lb passengers in the car, what is the effective damping ratio? (c) Calculate the natural vibration frequency for case (b). Lecture Page 12
- 13. The packaging foran instrument can be modeled as shown in Fig. P2.6, in which the instrument of mass m is restrained by springs of total stiffness k inside a container; m = 10 lb/g and k = 50 lb/in. The container is accidentally dropped from a height of 3 ft above the ground. Assuming that it does not bounce on contact, determine the maximum deformation of the packaging within the box and the maximum acceleration of the instrument. Lecture Page 13
- 14. Chapter 3: ForcedVibrations Lecture Page 14
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- 29. In a forcedvibration test under harmonic excitation it was noted that the amplitude of motion at resonance was exactly four times the amplitude at an excitation frequency 20% higher than the resonant frequency. Determine the damping ratio of the system. 1. A machine is supported on four steel springs for which damping can be neglected. The natural frequency of vertical vibration of the machine–spring system is 200 cycles per minute. The machine generates a vertical force p(t) = p0 sin ωt. The amplitude of the resulting steady state vertical displacement of the machine is uo = 0.2 in. when the machine is running at 20 revolutions per minute (rpm), 1.042 in. at 180 rpm, and 0.0248 in. at 600 rpm. Calculate the amplitude of vertical motion of the machine if the steel springs are replaced by four rubber isolators that provide the same stiffness but introduce damping equivalent to ζ = 25% for the system. Comment on the effectiveness of the isolators at various machine speeds. 2. Lecture Page 29
- 30. A one-story reinforcedconcrete building has a roof mass of 500 kips/g, and its natural frequency is 4 Hz. This building is excited by a vibration generator with two weights, each 50 lb, rotating about a vertical axis at an eccentricity of 12 in. When the vibration generator runs at the natural frequency of the building, the amplitude of roof acceleration is measured to be 0.02g. Determine the damping of the structure. 3. Consider an industrial machine of mass m supported on spring-type isolators of total stiffness k. The machine operates at a frequency of f hertz with a force unbalance po. 4. (a) Determine an expression giving the fraction of force transmitted to the foundation as a function of the forcing frequency f and the static deflection δst = mg/k. Consider only the steady-state response. (b) Determine the static deflection δst for the force transmitted to be 10% of po if f = 20 Hz. An automobile is traveling along a multispan elevated roadway supported every 100 ft. Long term creep has resulted in a 6-in. deflection at the middle of each span (Fig. E3.4a). The roadway profile can be approximated as sinusoidal with an amplitude of 3 in. and a period of 100 ft. The SDF system shown is a simple idealization of an automobile, appropriate for a “first approximation” study of the ride quality of the vehicle. When fully loaded, the weight of the automobile is 4 kips. The stiffness of the automobile suspension system is 800 lb/in., and its viscous damping coefficient is such that the damping ratio of the system is 40%. Determine: 5. (a) the amplitude uo t of vertical motion ut(t) when the automobile is traveling at 40 mph (b) the speed of the vehicle that would produce a resonant condition for uo t. (c) the amplitude of the force developed in the spring of the suspension system. Lecture Page 30
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- 32. Chapter 4: Arbitrary Excitations 23August 2018 08:23 Lecture Page 32
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- 38. eq-india Earthquake excitation Equation ofmotion Response Quantities Response history and internal forces Response spectrum concept Deformation, pseudo velocity and pseudo acceleration response spectra Peak structural response from the response spectrum Chapter 5: Earthquake Response of Linear Systems Lecture Page 38
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- 49. Chapter 6: NumericalResponse Lecture Page 49
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- 56. Chapter 7: GeneralizedSDOF Systems Lecture Page 56
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- 67. Chapter 8: MDOFSystems Intro Lecture Page 67
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- 80. Chapter 9 FreeVibration Lecture Page 80
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- 100. Chapter 10 ForcedVibration Lecture Page 100
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- 114. Chapter 11 Base-IsolatedStructures Lecture Page 114
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