Question

The unsteady natural axial oscillations of a bar are periodic, and they are determined by assuming a solution u(x, t) = U(x) e^-iwt. Which option is not correct about the solution equation?

(a) w denotes the natural frequency

(b) w^2 denotes eigenvalue

(c) U(x) denotes mode shape

(d) u(x, t) denotes transverse displacements

The question was posed to me in an online quiz.

This intriguing question comes from Eigen Value and Time Dependent Problems topic in chapter Single Variable Problems of Finite Element Method

Answer 1

Right option is (d) u(x, t) denotes transverse displacements

Best explanation: The unsteady natural axial oscillations of a bar are periodic. They are measured by assuming a solution u(x, t) = U(x) e^-iwt, where w is natural frequency, w^2 is an eigenvalue, U(x) is mode shape, and u is instantaneous axial displacement. The problem is solved in FEM by employing bar elements and appropriate shape functions.