XUE Chun-xia, REN Xiu-juan
(School of Science, North University of China, Taiyuan 030051, China)
Abstract： Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use of the improved Lindstedt-Poincare (L-P) method, the undamped forced vibration problem is solved, and the amplitude-frequency response equation of thin plate is obtained. Furthermore, the amplitude frequency response curves of system under different conditions are obtained by numerical simulation. The results show that the thickness of the plate, mechanical excitation, parameter ε, pure piezoelectric material of BaTiO3, pure piezomagnetic material of CoFe2O4, different magneto-electro-elastic materials of BaTiO3/CoFe2O4 and Terfenol-D/PZT will have an impact on the system frequency response. The main effects involve principal resonance interval, spring stiffness characteristic and amplitude jumping phenomena.
Key words： magneto-electro-elastic thin plate; improved Lindstedt-Poincare (L-P) method; principal resonance; amplitude-frequency response curve
CLD number： O322 Document code： A
Article ID： 1674-8042(2014)04-0093-06 doi： 10.3969/j.issn.1674-8042.2014.04.018
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磁电弹薄板的非线性主共振
薛春霞， 任秀娟
(中北大学 理学院， 山西 太原 030051)
摘要: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 BaTiO3、 压磁材料CoFe2O4及磁电弹材料BaTiO3/CoFe2O4 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。
关键词:磁电弹性薄板； 改进的L-P法； 主共振； 幅频响应曲线
引用格式：XUE Chun-xia, REN Xiu-juan. Nonlinear principal resonance of magneto-electro-elastic thin plate. Journal of Measurement Science and Instrumentation, 2014, 5(4): 93-98. [doi: 10.3969/j.issn.1674-8042.2014.04.018]
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