Three-dimensional vibration analysis of prisms with isosceles triangular cross-section

Abstract

This paper studies the three-dimensional (3-D) free vibration of uniform prisms with isosceles triangular cross-section, based on the exact, linear and small strain elasticity theory. The actual triangular prismatic domain is first mapped onto a basic cubic domain. Then the Ritz method is applied to derive the eigenfrequency equation from the energy functional of the prism. A set of triplicate Chebyshev polynomial series, multiplied by a boundary function chosen to, a priori, satisfy the geometric boundary conditions of the prism is developed as the admissible functions of each displacement component. The convergence and comparison study demonstrates the high accuracy and numerical robustness of the present method. The effect of length-thickness ratio and apex angle on eigenfrequencies of the prisms is studied in detail and the results are compared with those obtained from the classical one-dimensional theory and the 3-D finite element method. Sets of valuable data known for the first time are reported, which can serve as benchmark values in applying various approximate beam and rod theories.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

“…Typically, Liew et al [7] investigated the 3D vibration of thick prismatic columns with L, C, and I shaped cross sections using the orthogonal polynomials as the admissible functions. Zhou et al [8] studied the 3D vibration of prisms with triangular cross section using the Chebyshev polynomials as the admissible functions. Lim [9] and Leissa and Zhang [10] analyzed the 3D vibration of parallelepipeds using the simple polynomials as the admissible functions.…”