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This investigation proposes a series solution method for free and forced vibration analysis of T-shaped plate structure with general elastic supports, arbitrary coupling angles and elastically coupled conditions. The present solution framework can be readily utilized for various boundary or coupling conditions without modifying the solution algorithms or procedures. The general boundary and coupling conditions are considered with artificial spring method and can be easily achieved with assigning the restraining springs with specified values. In the current approach, the displacement functions for in-plane and bending vibration are expressed as a new form of trigonometric series expansion. The sine terms are introduced to eliminate the discontinuity along the boundary edge or coupling edge. Rayleigh–Ritz method is employed to determine the series expansion coefficients, which are treated as the generalized coordinates. Numerous numerical examples are carried out to verify the accuracy and reliability of the present method. The present method can be directly extended to more complicated structures with any number of plates.

Free and forced vibration analysis of T-shaped plates with general elastic boundary supports