带集中质量复合材料层合屈曲梁参激振动的研究

RESEARCH ON THE PARAMETRICALLY EXCITED VIBRATIONS OF A COMPOSITE LAMINATED BUCKLED BEAM WITH A LUMPED MASS

基于欧拉梁理论,运用Reissner变分原理,导出了轴向周期激励下一端固定一端夹支,带集中质量的复合材料层合屈曲梁的非线性动力学控制方程.利用模态截断,对系统非线性偏微分控制方程进行Galerkin积分,并用四阶龙格-库塔法数值研究了主共振下梁随激励幅值变化的分岔图,讨论了集中质量大小和位置对系统一阶频率和倍周期分叉的影响,结果表明,外激励幅值及集中质量的大小和位置会对带集中质量的屈曲梁的动力学行为产生重要影响.

Based on the Euler-Bernoulli beam theory and Reissner principle, the equations of the non-linear re- sponse of a composite laminated buckled beam with clamped ends and a lumped mass to an axial periodic excita- tion were obtained. By using the single-mode approximation and Galerkin＇s method, the differential equation was derived, and the bifurcation diagram of displacement varying with the excitation amplitude was obtained by using the fourth-order Runga-Kutta algorithm. Moreover, the effect of size and locations of the concentrated mass on the natural frequency and period-doubling bifurcation was discussed. The numerical simulation indicates that the excitation amplitudes and the sizes and locations of the concentrated mass have significant impact on the non-linear response of the buckled beam.