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针对磁电弹性薄板,结合大挠度板理论,考虑几何非线性,建立了非线性无阻尼强迫振动的数学模型,应用改进的L-P法,对非线性无阻尼强迫振动问题进行求解,得到薄板稳定状态下的幅频响应方程,数值模拟了不同情况下系统的幅频响应曲线图。通过比较分析得出:板的厚度、外激励力、参数ε的不同取值以及压电材料BaT iO 3、压磁材料Co Fe2O4及磁电弹材料BaT iO 3/Co Fe2O4与Terfenol-D/PZT均会对系统的幅频响应曲线产生影响,主要表现为对系统主共振区间,弹簧软硬特性,幅值跳跃现象的影响。这些结论在理论上可以更好地指导工程结构的设计。
Considering the geometrical nonlinearity, a mathematical model of nonlinear undamped forced vibration is established for the magneto-electro-elastic thin plate with the theory of large deflection plate. The improved LP method is used to solve the nonlinear undamped forced vibration problem, and the steady state of the plate is obtained Under the amplitude-frequency response equation, numerical simulation of the system under different conditions amplitude-frequency response curve. Through the comparison and analysis, it is concluded that the thickness of the plate, the external excitation force, the different values of the parameter ε and the piezoelectric material BaTiO 3, the compressive magnetic material Co Fe 2 O 4 and the magnetoelectric elastic material BaTiO 3 / Co Fe 2 O 4 and Terfenol-D / PZT Will have an impact on the amplitude-frequency response curve of the system, mainly showing the influence on the main resonance range, the spring-and-hardware characteristics of the system and the amplitude jump phenomenon. These conclusions can theoretically better guide the design of engineering structure.