【作者】 李宏亮； 邵晓华； 杨勇；

【Author】 LI Hong-liang1, SHAO Xiao-hua1, YANG Yong1 (1.Harbin Engineering University, Harbin 150001, China)

【机构】 哈尔滨工程大学建筑工程学院；

【摘要】 本文研究了柔性变速旋转圆板的建模,理论公式推导和动力响应的求解问题。基于Kirchhoff平板理论和von Karman应变理论,推导出变速旋转圆板在位移具有几何非线性项时,柱坐标系下的变形几何关系,物理关系和内力分析。然后考虑转动惯量的影响,通过系统动能和势能的表达式,应用哈密顿原理推导出柔性圆板旋转运动的非线性振动方程。该方程既是受约束柔性多体系统大范围刚体运动和弹性小变形的耦合方程,又是关于轴向,径向位移和横向位移的耦合方程。对非线性微分方程组的求解采用假设模态法。通过边界条件和正规化条件,求得前四阶静态面内振动和横向振动的固有频率及假设模态函数。假设模态函数是贝塞尔函数的线性叠加。更多还原

【Abstract】 The modeling, theoretical formulation and dynamical response of flexible spinning disc are described in this paper. Based on the Kirchhoff plate theory and the von Karman strain theory, considering the angular acceleration of the disc and the geometric nonlinearity of the displacements, the nonlinear displacement-strain relations, strain-stress relations and internal force in circular cylindrical coordinate system are derived. Dynamics stiffening effects are taken into account, from the expressions of potential and kinetic energies of the system, Hamiltion’s principle is employed to obtain non-linear governing partial differential equations of motion, which are not only coupled equations between the large rigid-body motion and small elastic deformation encountered in constrained multibody systems, but also coupled equations between the radial, tangential and transverse displacements. The non-linear governing partial differential equations of motion are discretized by using assumed modes method. By using the boundary conditions and the normalizing conditions, the first four natural frequency and assumed modes functions of radial, tangential and transverse vibration are obtained. Assumed modes functions are linearity superposition of Bessel functions.更多还原