Vibration analysis of symmetrically laminated rectangular plates with intermediate line supports

In this paper, a computationally efficient and highly accurate numerical method is proposed to analyze the vibrations of symmetrically laminated rectangular composite plates with intermediate line supports. A set of admissible functions are developed from the static solutions of a beam with intermediate point supports under a series of sinusoidal loads, in which the beam may be considered to be a unit width strip taken from the plate in a direction parallel to the edges of the plate. In addition to satisfying both the geometric boundary conditions of the plate and the zero deflection conditions at the line supports, this set of static beam functions, being different from the existing admissible functions, can also properly describe the discontinuity of the shear forces at the line supports, so that more accurate results can be expected for the dynamic analysis of laminated rectangular plates with intermediate line supports. The governing eigenfrequency equation of the plates is derived by using the Rayleigh–Ritz approach. Several test problems are solved to demonstrate the accuracy and the convergency of the proposed method. The effects of the location and number of line supports, the material properties, the number of layers and the fiber orientations on the vibration behavior of the plates are studied in detail. Some data known for the first time are given and can serve as the benchmark for future research on the aforementioned problem. Moreover, two examples of the dynamic responses of line-supported laminated rectangular plates are also given as an extending application of the present method.