基于状态空间法的圆弧曲梁面内动力学分析  

IN-PLANE DYNAMIC ANALYSIS OF CIRCULARLY CURVED BEAMS BASED ON THE STATE SPACE METHOD

作　　者：刘兴喜 杨博[1] 徐荣桥[2] LIU Xing-xi;YANG Bo;XU Rong-qiao(Department of Civil Engineering,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]浙江大学土木工程系,浙江杭州310058

出　　处：《工程力学》2023年第S01期19-24,55,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(12272335)。

摘　　要：该文采用状态空间法研究了圆弧曲梁面内动力学特性。通过选择合适的状态变量,建立了相应的状态空间列式,并给出了固有频率和振动模态的求解过程。进一步通过引入辛内积的概念,建立了三种工程常见边界条件(简支、固支和自由)下圆弧曲梁面内振动模态关于质量和旋转惯量的正交关系式。在此基础上,运用模态叠加法给出了非齐次状态方程的解析解,并得到了圆弧曲梁在竖向移动集中荷载作用下的瞬态响应。数值算例结果表明该文方法是十分精确和可靠的。The state space method is adopted to study the in-plane dynamic behavior of circularly curved beams.By selecting appropriate state variables,the state space formula is properly set up.The frequencies and corresponding modal shapes of circularly curved beams are then obtained on the basis of state-space formulae.By utilizing the conception of symplectic inner product,the mode orthogonality with respect to the mass and rotary inertia properties for curved beams under three common boundary conditions in engineering(simply-supported,clamped and free)is established.Based on the orthogonality relation,the mode superposition method is utilized to obtain the solution of the inhomogeneous equation for forced vibration and dynamic response of curved beams subjected to a vertical moving constant force.The numerical results show that the proposed method is very accurate and reliable.

关 键 词：圆弧曲梁 自由振动 强迫振动 状态空间法 辛内积 模态正交性 

分 类 号：TB122[理学—工程力学]