Natural vibration analysis of stiffened panels with arbitrary edge constraints using the assumed mode method

Natural vibration analysis of stiffened panels represents an important issue in different kinds of engineering applications. In this article, a procedure for the vibration analysis of stiffened panels with arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equations of motion. The Mindlin thick plate theory is applied for a plate, while the effect of stiffeners having the properties of Timoshenko beams is accounted for by adding their strain and kinetic energies to the corresponding plate energies. The accuracy of the proposed procedure is justified by several numerical examples which include the natural vibration analysis of stiffened panels with different framing sizes, their lengths and orientations, plate thicknesses and different combinations of boundary conditions. A comparison of results with those obtained by the finite element method is provided, and good agreement is achieved.