Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation

This paper has studied the effects of in-plane load on the vibration of transversely isotropic annular sector plates resting on the Winkler and Pasternak elastic foundations. The governing coupled partial differential equations are obtained based on the third-order shear deformation plate theory. Based on Levy’s solution, the radial edges are assumed to be simply supported, and various boundary conditions are considered for circular edges. Therefore, nine different boundary conditions are considered here. At first, stability equations are analytically solved, and the critical buckling loads are obtained. Then, the natural frequency is extracted from the governing equations of motion subjected to in-plane loads. The effects of different in-plane loads on first natural frequencies of laminated thick annular sector plates with different aspect ratios, various thickness-length ratios, and some Winkler and Pasternak elastic foundation parameters are investigated. In addition, the effects of in-plane load on mode shape contour plots are presented for various boundary conditions. The obtained results show that the in-plane loads have a significant effect on the natural frequency of transversely isotropic annular sector plates. Also, increasing the in-plane force can affect the natural frequencies of the sector plate. For unique industrial designs, the natural frequency of the plate from the work area can be changed or prevent vibrations. Therefore, the resonance phenomenon can be easily changed and modified.