基于状态空间法的平面圆弧曲梁面外动力学分析  

OUT-OF-PLANE DYNAMIC ANALYSIS OF PLANAR CIRCULAR CURVED BEAMS USING THE STATE SPACE METHOD

作　　者：刘兴喜 姚媛 徐荣桥[3] LIU Xing-xi;YAO Yuan;XU Rong-qiao(Department of Civil Engineering,Zhejiang Sci-Tech University,Hangzhou,Zhejiang 310018,China;Library of Zhejiang Sci-Tech University,Hangzhou,Zhejiang 310018,China;Department of Civil Engineering,Zhejiang University,Hangzhou,Zhejiang 310058,China)

机构地区：[1]浙江理工大学土木工程系,浙江杭州310018 [2]浙江理工大学图书馆,浙江杭州310018 [3]浙江大学土木工程系,浙江杭州310058

出　　处：《工程力学》2024年第S01期89-97,共9页Engineering Mechanics

基　　金：国家自然科学基金项目(12272335);浙江理工大学基本科研业务费专项资金项目(23052117-Y)。

摘　　要：该文通过选择广义位移和与其对偶的广义力作为状态变量,建立了平面圆弧曲梁面外动力学问题的状态方程列式,并求解了工程中常见的四种边界条件下圆弧曲梁面外自由振动的频率和模态。利用状态空间列式和辛内积的概念,建立了振动模态关于质量和旋转惯量以及关于刚度的正交关系式。基于建立的振动模态关于质量和旋转惯量的正交关系式,运用模态叠加法得到了非齐次状态方程即面外强迫振动控制方程的解析解,并具体考察了竖向移动荷载作用下圆弧曲梁的动力响应。给出了数值算例,并与已有结果进行了比较,验证了该文方法在进行圆弧曲梁面外自由振动和强迫振动分析时的准确性和可靠性。By selecting the appropriate generalized displacements and their conjugated forces as state variables,the state space formula is properly set up to investigate the out-of-plane dynamic behavior of planar circular curved beams.On the basis of the established state space formula,the out-of-plane natural frequencies and corresponding vibration modes of circular curved beams under four common boundary conditions in engineering practice are then solved.The state space formula and the conception of sympletic inner product are utilized to derive two orthogonality relations of vibration modes.One is with respect to the mass and rotary inertia properties,and another is with respect to the stiffness property.Based on the established orthogonality relation with respect to the mass and rotary inertia properties,the mode superposition method is used to obtain the analytical solution of the inhomogeneous state equation,i.e.the governing equation for out-of-plane forced vibration,and the dynamic responses of circular curved beams under a vertical moving concentrated load are given.Several numerical examples are presented and the results are compared with those available in the literature with good agreement,which demonstrates the accuracy and reliability of the proposed method.

关 键 词：平面圆弧曲梁 面外自由振动 面外强迫振动 状态空间法 辛内积 模态正交性 模态叠加法 

分 类 号：TU311.3[建筑科学—结构工程]