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

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

Explain D'Alembert's principle and its applications.

Derive the equation of motion for free torsional vibration of a rigid disc mounted on a flexible shaft.

Set up the equation of motion of a single-degree-of-freedom system using Newton's second law of motion.

Explain how the equation of motion is modified for horizontal earthquake ground acceleration $u_g$.

Starting from the basic definition of stiffness, determine the effective stiffness $k$ of the spring mass system shown in Fig.3

What is damping? Discuss the critical damping with example.

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

Explain logarithmic decrement and Duhamel's integral method for an undamped system.

Write short notes on viscous dampers.

Define logarithmic decrement and sketch its variation with damping ratio.

A single degree of system consists of a mass 20 kg, spring of stiffness 2200N/m and a dashpot with a damping coefficient of 60 N-s/m is subjected to a harmonic excitation of $F = 200\sin 5t$ Newton's. Determine the steady state of response and write the solution of equation of motion.

Find the Laplace transform of a rectangular pulse of height $A$ and duration $\tau$, and hence obtain the response / 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 and the methods used for solving eigenvalue problems.

Discuss the methods of matrix iteration.

Determine the natural frequencies and mode shapes of vibration for a given system and normalize the modes.

Determine the equation of motion of the beam shown in Fig. 6 (a) expressed in terms of Displacements $u_1$ and $u_2$ shown in Fig.6 (b). Hence deduce natural frequencies and mode shapes.

Derive equation of natural frequency for axial vibration of bar and bending vibration of beam as continuous system.

Write note on any four of the followings :

Discuss Newmark's method for numerical evaluation of dynamic response of single degree of freedom system.

Describe the dynamic analysis procedure as per IS 1893:2002 for a high rise building with 4 stories. Indicate how the mass is lumped and the seismic force is distributed along the height. Distinguish between CQC and SRSS procedures given in the code.

Find the first three vibration frequencies and modes of an uniform beam clamped at one end and free at the other. Sketch the mode shapes.

Write Short Notes on: