Three-Dimensional Vibration Analysis of Fiber-Plain-Woven Composite Beams with General Boundary Conditions

Abstract

A three-dimensional differential quadrature model is developed to study the free vibration of fiber plane-woven composite beams with arbitrary combinations of boundary conditions. The fiber-plain-woven composite material is assumed to be a three-dimensional orthotropic anisotropic material. The vibration model for the fiber-plain-woven composite beam is formulated by the three-dimensional elasticity theory combined with the differential quadrature method (DQM), where various boundary conditions (including free, clamped, simply-supported as well as elastic constraints etc.) are flexibly simulated by boundary springs with variable stiffness. In order to clarify the accuracy of the developed model and methodology, some free vibration solutions for isotropic, composite beams in different boundary combinations of free, simply-supported, clamped and elastic constraints are given, where the current solutions are in good agreement with the literature solutions and finite element numerical results. After that, some parameter investigations are carried out to explore the impact of boundary stiffness, volume fraction and geometric dimensions on the vibration properties. Additionally, the obtained new benchmark solutions for fiber-plain-woven composite beams may be used to check the accuracy of other simplified beam theories.