Theoretical Derivation on the Fundamental Frequency of Variable-thickness Conical Shells

Abstract

The fundamental frequencies of the variable thickness truncated conical shells with different boundary conditions are studied by combining the vibration theory with the generalized differential quadrature method which is applied to discrete the derivatives in the governing equations. The discretization of the system leads to a standard linear eigenvalue problem. The coefficients of the governing equations are obtained by theoretical derivation and different boundary conditions are considered. The work can provide the theoretical evidences to design the conical shell for good structural performance.