摘要
研究了在四边简支的边界条件下,正交各向异性矩形叠层板在横向简谐激励作用下的非线性主共振及其稳定性问题.在给出了正交各向异性叠层板的振动微分方程的基础上,利用伽辽金法导出了相应的达芬型非线性强迫振动方程.应用平均法对主共振问题进行求解,得到了系统在稳态运动下的幅频响应方程.基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件.作为算例,分别给出了不同条件下,系统运动的幅频响应曲线图、振幅-激励幅值响应曲线图和动相平面图,并对解的稳定性进行了分析,讨论了各参数对系统非线性振动特性的影响.
The stability and nonlinear principal resonance of rectangular orthotropic thin plate excited by a harmonic force were studied in this paper, under the condition of four sides simply supported. Based on the vibration differential equation of orthotropic laminated plates, the nondimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method. The amplitude frequency response equation of system steady motion under principal resonance was obtained by means of averaging method. Based on Lyapunov stable theory, the critical conditions of steady-state solutions＇ stability were got. By some examples, the amplitude-frequency curves, amplitude-excitation amplitude curves and phase trajectories in moving phase plane were derived under different situations. The stability of solution and the influence of different parameters on nonlinear resonance properties of system were analyzed.
出处
《动力学与控制学报》
2009年第1期35-38,共4页
Journal of Dynamics and Control
关键词
正交各向异性
叠层板
主共振
稳定性
平均法
orthotropic, laminated plate, principal resonance, stability, averaged method
