Vibration Analysis of Conical Shells by the Improved Fourier Expansion-Based Differential Quadrature Method

Abstract

An improved Fourier expansion-based differential quadrature (DQ) algorithm is proposed to study the free vibration behavior of truncated conical shells with different boundary conditions. The original function is expressed as the Fourier cosine series combined with close-form auxiliary functions. Those auxiliary functions are introduced to ensure and accelerate the convergence of series expansion. The grid points are uniformly distributed along the space. The weighting coefficients in the DQ method are easily obtained by the inverse of the coefficient matrix. The derivatives in both the governing equations and the boundaries are discretized by the DQ method. Natural frequencies and modal shapes can be easily obtained by solving the numerical eigenvalue equations. The accuracy and stability of this proposed method are validated against the results in the literature and a very good agreement is observed. The centrosymmetric properties of these newly proposed weighting coefficients are also validated. Studies on the effects of semivertex angle and the ratio of length to radius are reported.