受机械力作用金属／陶瓷功能梯度板主共振奇异性

Singularites of primary resonance of ceramic and metal functionally graded material rectangular plate subjected to mechanical force

研究机械力作用下金属，陶瓷功能梯度薄板主共振奇异性问题。按照功能梯度薄板的非线性动力学方程，得到金属，陶瓷功能梯度薄板受横向机械力作用的非线性振动方程。应用非线性振动的多尺度法得到系统主共振幅频响应分岔方程并进行奇异性分析，求得幅频响应分岔方程在开折参数平面的转迁集和分岔图。

In order to study singularity of primary resonance of ceramic and metal functionally graded material rectangular plate subjected to mechanical force excitation, according to the nonlinear dynamics equation of the functionally graded material rectangular plate, the nonlinear vibration equation of ceramic and metal functionally graded material rectangular plate subjected to mechanical force excitation is obtained. By means of the method of multiple scales the amplitude frequency response bifurcation equation of primary resonance of the system is acquired. Singularities of the primary resonance solution were investigated. The transition variety and bifurcation diagram of unfolding parameter plane are obtained.