中文摘要：

推导了扬声器辐射体旋转薄壳的离散非线性振动方程。从虚功原理出发，选用扬声器辐射体旋转薄壳的本征模态对连续体进行离散。薄壳的几何非线性采用Sanders非线性薄壳理论的应变一位移关系。方程系数由有限元方法确定。方程表明轴对称模态由驱动力直接激励，非轴对称模态由轴对称模态非线性耦合激励，该耦合激励表现为参数激励。方程揭示了扬声器非线性失真的机制，可用于分析扬声器辐射体薄壳非线性引起的谐波失真、分谐波失真和互调失真。

英文摘要：

Nonlinear discretization vibration equations are derived for loudspeaker revolution shells. The nature modes of loudspeaker revolution shells are chosen to discretize the continuous body according to the virtual work principle. Geometric nonlinearities are accounted for by utilizing the strain-displacement relation of the Sanders nonlinear shell theory. The coefficients of the equations are determined by the finite element method. The equations show that the axisymmetric mode is driven directly, whereas the asymmetric modes are excited by the axisymmetric mode through a parametric excitation. The equations can be used to analyze the subharmonic distortion, harmonic distortion and intermodulation distortion caused by the loudspeaker shell nonlinearity.