Mechanical Vibrations Answer these true and false questions

Mechanical Vibrations

Answer these true and false questions: If the time duration of a general loading, say a shock pad, is very small, Duhamel integral con not be used for evaluating the response True False If a system is damped, a general periodic but non-harmonic input force cannot be modelled and represented by Fourier series for response analysis. True False Dynamic stresses developed in a beam subjected to a harmonic load are more several than dynamic stresses due an impact load in general. True False As a system yields and becomes weaker, the domping will decrease True False For a champed system as and increases, the free vibration response shows a higher period. True False

Solution

a) FALSE.

For suddenly applied load, If the time period is small, Duhamel integral can be used.

if the time period is large then e^-at become very small and system vibrate with steady state amplitude, Duhamel integral cannot be used.

b) False

Input force can be modeled and represented by Fourier analysis with the aid of Fourier functions.

c) True

harmonic loads, which vary according to the sinusoidal law are very dangerous because stress reversal takes place. This gives rise to cracks and system eventually fail. Hence they are more dangerous than impact loading

d) False

As the system yields, the damping or energy dissipation increases. metallic yield dampers are most widely used in energy dissipation purpose.

e) false

As the damping ratio increases, the vibration response shows lower period as the energy dissipation increases.