Question

The free vibrations equation after Finite Element discretization of a structure is expressed as Mẍ+Kx=0. Which option is not correct about the free vibration case?

(a) Displacements are harmonic

(b) x=Xe^iωt where X is amplitude

(c) [K-ω^2M]X=0

(d) KX=Mω^2

The question was asked during an internship interview.

The doubt is from Eigen Value and Time Dependent Problems topic in section Single Variable Problems of Finite Element Method

Answer 1

The correct option is (d) KX=Mω^2

Explanation: In a free vibration analysis, the external load vector is zero and the displacements, x are harmonic x=Xe^iωt where X is amplitude, on substituting x in governing equation we get [K-ω^2M]X=0 or  KX=Mω^2X.