Abstract
The purpose of this paper is to analyze the nonlinear vibration of composite beams and the stability of the solution by using the reduced-order model and the incremental harmonic balance (IHB) method. Timoshenko beam theory is used to indicate the displacement of the beam element. Each nodal point has three degrees of freedom. Simplified homogenized beam theory is used to calculate the equivalent moduli of each ply of the composite beam. Element matrices are created using the weak form quadrature element method, and the equation of motion at the element is created using Lagrange’s equation. A system matrix is created using the element matrix assemble rule of the finite element method. In order to reduce the calculation time, a reduced-order model is used. The nonlinear forced vibration equation is solved using the IHB method. The results calculated using the non-reduced-order model and the reduced-order model are compared, and the results are very close. Based on this, the reduced-order model is used to analyze the nonlinear vibrations of composite beams at the first resonance point, and stability tests are conducted for the calculated solutions using the multivariable Floquet theory.
Highlights
Composite materials are widely used in industrial fields such as automobile industry and aviation industry because of their light weight and excellent engineering characteristics with high ratios of strength to weight and stiffness to weight
The purpose of this paper is to analyze the nonlinear vibration of composite beams and the stability of the solution by using the reducedorder model and the incremental harmonic balance (IHB) method
Simplified homogenized beam theory is used to calculate the equivalent moduli of each ply of the composite beam
Summary
Composite materials are widely used in industrial fields such as automobile industry and aviation industry because of their light weight and excellent engineering characteristics with high ratios of strength to weight and stiffness to weight. Singh et al used the von Kármán large deflection theory to analyze the nonlinear free vibration of unsymmetrically laminated beams.1 They used the direct numerical integration method to solve the nonlinear motion equation. Ganapathi et al used a cubic B-spline shear flexible curved element to analyze the nonlinear free flexural vibration of straight/curved beams.2 They used Newmark’s numerical integration method to solve the motion equation. Huang et al analyzed the nonlinear forced vibration of a curved beam.7 They used the IHB method to obtain the steady-state response of the curved beam and investigated the stability of periodic solutions using the multi-variable Floquet theory.. The drawback of the HBM in solving nonlinear vibration equations is that it consumes a lot of calculation time. The proposed method can be applied to any structure with periodic forces
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