摘要
根据弹性薄板自由振动问题的基本方程,把问题引入到哈密顿对偶体系中.x方向模拟为时间,选取弯矩,等效剪力,转角和挠度为对偶向量,得到了在不同边界条件时关于x轴对称和反对称时的解析解.算例研究了四边固支薄板的自由振动情形,从而推广了哈密顿体系的应用范围,验证了哈密顿体系求解方法在自由振动问题中的有效性.
Based on the basic equations of free vibration of thin plate, the Hamilton canonical equations were obtained. By variable selection of moment, equivalent shear force, rotation angel and deflection forming dual variables, the analytical solutions for free vibration of thin plate were obtained under different boundary conditions, which were divided into symmetrical and asymmetrical about x-axial. The computational example of a quadrilateral rectangular plate bending was given, which demonstrated the effectiveness of the proposed method, thus extending the application of Hamilton system.
出处
《动力学与控制学报》
2005年第2期10-16,共7页
Journal of Dynamics and Control
基金
国家自然科学基金(10372084)
教育部新世纪优秀人才基金
西北工业大学博士创新基金(CX200314)
大连理工大学工业装备结构分析国家重点实验室开放基金资助项目~~
