Abstract
In this paper, a forced vibration model of composite beams under the action of periodic excitation force considering geometric nonlinearity is proposed. For the strain–displacement relationship, Timoshenko beam theory is used, and the element and system matrices are developed using the differential quadrature finite element method. Each node has 3 degrees of freedom. The incremental harmonic balance method is used to solve the nonlinear forced vibration equation. In order to prove the validity of the proposed model, the solution of the Duffing equation is calculated using the analytical method and the proposed method. Next, linear forced vibration analysis of the beam made of isotropic material is performed and compared with the result of ABAQUS. The results are very close. Based on these comparisons, nonlinear vibration phenomena of composite beams are studied under the action of periodic forces.
Highlights
Composite materials have characteristics such as high ratio of strength to weight, high fatigue strength, and light weight, and are widely used in different industries including aerospace, shipbuilding, and automobiles
Singh et al analyzed scitation.org/journal/adv the nonlinear free vibration of composite beams based on von Kármán large deflection theory using the classical lamination theory, one-dimensional and high-dimensional shear-deformation theory.[2]
Malekzadeh and Vosoughi used the differential quadrature method (DQM) to analyze the nonlinear free vibration of composite beams supported on a nonlinear elastic foundation.[5]
Summary
Composite materials have characteristics such as high ratio of strength to weight, high fatigue strength, and light weight, and are widely used in different industries including aerospace, shipbuilding, and automobiles. Kapania and Raciti described the stress–displacement relationship using Timoshenko beam theory and studied the nonlinear vibration characteristics of composite beams by the perturbation method.[1] They used a finite element with 10 degrees of freedom per node. The perturbation method or the numerical integration method is widely used in the nonlinear forced vibration analysis of composite beams, while numbers of the degree of freedom used for analysis are limited. In order to explain these problems, it is necessary to use a multi-degree of freedom system for vibration analysis to accurately understand the dynamic characteristics Considering this point, in this paper, the IHB method is used to analyze the nonlinear forced vibration equation of composite beams with a multi-degree of freedom. The differential quadrature finite element method (DQFEM) and the IHB method are combined to analyze the nonlinear vibration of composite beams with geometric nonlinearity. The simple nonlinear vibration is analyzed, but the proposed method could be extended to periodic nonlinear structural vibrations with arbitrary structures
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