Analysis of the nonlinear forced vibration and stability of composite beams using the reduced-order model

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.