Free in-plane vibration analysis of rotating annular panels with elastic boundary restraints

Abstract

In this paper, an accurate solution for the in-plane vibration analysis of rotating circular panels with general edge restraints is established by solving the governing equations and boundary conditions, simultaneously. Two coupled in-plane displacement fields are constructed as Fourier series with smoothed supplementary polynomials to remove the relevant differential discontinuities associated with the original radial component at inner and/or outer edges. Any type of boundary conditions can be easily achieved by setting the boundary restraining stiffness accordingly. System characteristic matrix is obtained through the comparison of all expanded Fourier series coefficients. Numerical examples are then presented to validate the correctness and reliability of the proposed solution by comparing them with those solved from other approaches. Based on the model established, significant influence of elastic boundary condition on the in-plane modal characteristics of rotating annular panel is investigated and addressed. This work represents the first time that analytical solution for the in-plane vibration of rotating circular panel with general boundary conditions is derived, and can also shed some new light on the understanding of complex dynamic behavior of such structural system.