Dynamic stiffness method and CUF-based component-wise theories applied to free vibration analysis of solid beams, thin-walled structures and reinforced panels

Abstract

In this paper, an exact dynamic stiffness formulation using higher-order theories with displacement variables only is presented and subsequently used to investigate the free vibration characteristics of solid beams, thin-walled structures and reinforced panel structures. In essence, higher-order displacement fields are developed by using the Carrera unified formulation (CUF), and by discretizing the cross-section kinematics with bilinear, cubic and fourth-order Lagrange polynomials. In particular, the component-wise (CW) approach based on Lagrange expansion is applied in which the solid part and thin-walled part are considered as two independent components that can be assembled. The principle of virtual displacements is used to derive the governing differential equations and the associated natural boundary conditions. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The explicit terms of the dynamic stiffness matrices are also presented. The Wittrick–Williams algorithm of the dynamic stiffness method (DSM) is applied with the explicit expressions of the J0 count for beam elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. The accuracy and efficiency of the proposed methodology are extensively assessed for different solid beams, thin-walled structures and reinforced panels and the results are compared with those appearing in published literature and also checked by 3D finite element (FE) solutions.