Winkler地基上材料非线性矩形薄板的主共振

为了研究Winkler地基上材料非线性矩形薄板受简谐激励的非线性振动,应用弹性力学理论,建立了其动力学方程,并用Galerkin方法将其转化为非线性振动方程.应用非线性振动的多尺度法,求得系统主共振的近似解,并进行了数值计算.研究表明,随着阻尼系数、几何参数和激励幅值的改变,主共振响应曲线有跳跃和滞后现象,振幅随阻尼系数的增大而减小.此外,还对系统主共振响应方程进行了奇异性分析,得到了开折参数平面的转迁集和分岔图.

Primary Resonance of Thin Rectangular Plate with Material Nonlinearity on Winkler Foundation

Based on the elastic theory,nonlinear dynamical equations for an externally excited thin rectangular plate on the Winkler foundation were established by considering meterial nonlinearity in order to investigate its nonlinear vibration,and the corresponding nonlinear vibration equation was obtained using the Galerkin's method.By means of the method of multiple scales for nonlinear oscillations,the approximate solution of primary resonance of the system was acquired,and a numerical analysis was carried out.The research shows that jump and hysteresis phenomena exist in the amplitude-frequency response curves with the changing of damping factor,geometric parameters and excitation,the amplitude decreases with the increase of damping.In addition,the amplitude-frequency response equation was investigated,and the transition variety and bifurcation diagram of unfolding parameter plane were obtained based on the singularity theory.