Quasi-3D solutions for the vibration of solid and hollow slender structures with general boundary conditions

摘要

In this study, a uniform quasi-three-dimensional solution is presented for the free vibration analysis of solid and hollow slender structures with general boundary conditions. The boundary conditions are simulated by penalty method, which releases the limitation of geometrical boundary restraints on the selection of admissible functions. A combination of the improved Fourier series method (IFSM) and Taylor expansion (TE) is introduced to construct the displacement components of the structures. The nuclear matrices of the stiffness and mass matrices are derived using the energy variational principle. Subsequently, an assembly procedure based on the Carrera unified formulation (CUF) is proposed for the global matrices of higher-order configurations. In the current study, the displacement functions are not dependent on the specific shape of the section, and the proposed method is thus suitable for any uniform slender structure. Herein, different types of standard solid and hollow slender structures are studied. The efficiency and accuracy of the present method are illustrated by comparing the results with the reference data and solutions of the commercial codes. Finally, the effects of the geometrical dimensions and boundary conditions on the vibration characteristics are investigated. (C) 2018 Elsevier Ltd. All rights reserved.