基于特征值法的矩形薄板的动力稳定性试验研究

对边周期荷载作用下的矩形薄板,当外荷载的激振频率与板的自振频率满足特定的条件时,板发生参数共振失去稳定,其振动幅值迅速增加并在临界频率处产生跳跃式的下降。本文通过设定不同幅值的激振力进行扫频试验,根据参数共振的特点,提出运用时域分析法计算得到了板动力失稳的上下临界频率,验证了特征值法在求解理论不稳定域和非线性响应的正确性。试验结果表明当外荷载的作用频率是板自振频率的两倍时,板发生参数共振失去稳定；板在动力失稳的过程中经历了三个阶段,由稳定的暂态振动过渡至失稳的参数共振最后恢复至稳定的暂态振动；此外,非线性响应结果表明几何非线性限制了板动力失稳时振动幅值无限增长的趋势,并牵引其向大频率方向振动。

Experimental Research of Dynamic Stability on Rectangular Thin Plate Based on The Eigenvalue Method

The parametric resonance and instability of the rectangular thin plate under the action of periodic load along two opposite edges were developed when the excitation frequencies of the external load and the natural frequencies of the plate satisfy specific conditions, the vibration amplitude increases rapidly and decreases with a leap at the critical frequencies. In this paper, the swept frequency tests were carried out by setting the excitation force of different amplitude, the time domain analysis method was presented to obtain the upper and lower critical frequencies of dynamic instability region of the plate according to the characteristics of parametric resonance, the correctness of the eigenvalue method in solving the theoretical instability regions and the nonlinear resonance was verified. The test results show that when the excitation frequencies of external load is twice the natural frequencies of the plate, the parametric resonance and instability of the plate was induced; the plate has experienced three stages in the process of dynamic instability, from the stable stage of transient vibration to the unstable stage of parametric resonance and finally restored to the stable stage of transient vibration; In addition, the nonlinear resonance indicates that the trend of unlimited increasing of the vibration amplitude for the instability plate was limited by the geometrical nonlinearity which induces traction resonance vibration toward to the direction of large frequencies.