Structural Dynamics (CE-702 (C)) - Important Questions

Explain D'Alembert's principle and its applications to single degree of freedom system.

Define natural frequency, period and amplitude of motion for an undamped single degree of freedom system and derive their inter-relationships.

A damped single degree of freedom system has successive free vibration amplitudes of 50 mm and 20 mm. Determine the logarithmic decrement, damping ratio and damped natural frequency if the undamped natural period is 0.5 sec.

What is damping? Discuss the critical damping with example.

Find the natural frequency for given system in Fig. 1.

Derive the equation of motion for a single degree of freedom damped forced vibration system.

A single degree of freedom system consists of a mass 20 kg, spring of stiffness 2200 N/m and a dashpot with a damping coefficient of 60 N-s/m subjected to a harmonic excitation of F = 200 sin 5t Newton. Determine the steady state response, magnification factor and phase angle.

Find the Laplace transform of a rectangular pulse of height A and duration tau, and hence obtain the Laplace transform of a unit impulse.

Indicate how Duhamel integral can be used to find the response of system shown in Fig. 4 (a) for unit impulse?

Discuss in detail the eigenvalue problem for multi degree of freedom system. Explain normal modes and their properties and the methods used for solving eigenvalue problems.

Discuss the methods of matrix iteration for determination of natural frequencies and mode shapes.

Determine the natural frequencies and mode shapes of vibration for the system shown in Fig. 5. Normalize the modes to have unit vertical deflection at the free end.

Determine the equation of motion of the beam shown in Fig. 6 (a) expressed in terms of displacements u1 and u2 shown in Fig. 6 (b). Hence deduce natural frequencies and mode shapes.