应用多尺度法得到了超磁致伸缩换能器几何非线性振动系统响应的解析解和频响特性表达式。

Then, the analytic solution of the geometrical nonlinear vibration system and the frequency-response properties of the actuator were analyzed by using multi-scale method.

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应用达朗贝尔原理建立了考虑几何非线性的方形张拉膜结构的离散非线性振动方程组；

D′Alembert′s principle is used to derive an ordinary differential equation set for free vibration of a discretized square tensioned membrane with geometric nonlinearity.

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