Exact solutions for coupled free vibrations of tapered shear-flexible thin-walled composite beams

Abstract

In this paper, analytical solutions for the free vibration analysis of tapered thin-walled laminated-composite beams with both closed and open cross-sections are developed. The present study is based on a recently developed model that incorporates in a full form the shear flexibility. The model considers shear flexibility due to bending as well as warping related to non-uniform torsion. The theory is briefly reviewed with the aim to present the equilibrium equations, the related boundary conditions and the constitutive equations. The stacking sequences in the panels of the cross-sections are selected in order to behave according to certain elastic coupling features. Typical laminations for a box-beam such as circumferentially uniform stiffness (CUS) or circumferentially asymmetric stiffness (CAS) configurations are adopted. For open cross-sections, special laminations behaving elastically like the CAS and CUS configurations of closed sections are also taken into account. The exact values (i.e. with arbitrary precision) of frequencies are obtained by means of a generalized power series methodology. A recurrence scheme is introduced with the aim to simplify the algebraic manipulation by shrinking the number of unknown variables. A parametric analysis for different taper ratios, slenderness ratios and stacking sequences is performed. Numerical examples are also carried out focusing attention in the validation of the present theory with respect to 2D FEM computational approaches, as well as to serve as quality test and convergence test of former finite elements schemes.