Spectral dynamic stiffness theory for free vibration analysis of plate structures stiffened by beams with arbitrary cross-sections

Abstract

A spectral dynamic stiffness (SDS) model for plate assemblies stiffened by beams is proposed. The theory is sufficiently general where the plate assemblies can be subjected to any arbitrary boundary conditions (BCs), but importantly, the beam stiffeners can be of open or closed cross-sections, and maybe connected to plates with or without eccentricity. First, by using modified Fourier series, the SDS formulations for different beam stiffeners are developed based on their equations of motion for the most general case. Then, the beam stiffeners’ SDS matrices are superposed directly onto those of the plate assemblies. Next, the reliable, efficient and robust Wittrick-Williams algorithm is applied for the modal analysis of the overall structure. Representative examples are provided to illustrate the accuracy and versatility of the method, where the proposed theory is extensively validated by the software ANSYS. The proposed method inherits all advantages of the previously developed SDS theory for plate structures, including high computational efficiency, accuracy, robustness in eigenvalue calculation and the versatility in modelling arbitrary BCs. The proposed theory extends the existing SDS theory substantially to cover a wide class of beam stiffened plate structures used in train bodies, ship hulls, aircraft fuselage and wings and many others.