Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method

• Simplified procedure for vibration analysis of plate structures is developed.
• Harmonic point excitation force and boundary displacement loading is considered.
• Assumed mode method is used for natural vibration analysis.
• Mode superposition method is used for frequency response analysis.
• The procedure gives very accurate results compared with general purpose FE software.

This paper deals with numerical procedure for the vibration analysis of rectangular plates and stiffened panels subjected to point excitation force and enforced displacement at boundaries. The procedure is based on the assumed mode method, where natural response is determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equation of motion. Mode superposition method is applied to calculate plate/stiffened panel frequency response. The Mindlin plate theory is adopted for a plate, while the effect of stiffeners having the properties of Timoshenko beams is taken into account by adding their potential and kinetic energies to the corresponding plate energies. The accuracy of the proposed procedure is justified by several numerical examples which include forced vibration analysis of plates and stiffened panels with different dimensions and framing sizes and orientations, having various combinations of boundary conditions. The results obtained by the developed in-house code are compared to those obtained by the finite element method (FEM) and experimental results from the relevant literature. The presented procedure is confirmed to be highly accurate.