Question

Which form of a periodic solution is sought for the natural vibration study of plane elastic bodies?

(a) {Δ}={Δ0}e^iωt

(b) {Δ}={Δ0}e^-iω

(c) {Δ}={Δ0}e^-iωt

(d) {Δ}={Δ0}e^-iω/t

I had been asked this question in class test.

The query is from Plane Elasticity topic in portion Plane Elasticity of Finite Element Method

Answer 1

Correct option is (c) {Δ}={Δ0}e^-iωt

For explanation I would say: For natural vibration study of plane elastic bodies, we seek a periodic solution of the form {Δ}={Δ0}e^-iωt, where Δ denotes the displacements, ω is the frequency of natural vibration and i=\(\sqrt{-1}\). With this, the finite element models of plane elastic problems reduce to an eigen value problem (-ω^2M^e+K^e)\(\Delta_0^e\)=Q^e.