求解曲线箱梁空间振动特性的Cayley-Hamilton传递矩阵法  

A Cayley-Hamilton transfer matrix method for solving the vibration characteristics of curved box beams

作　　者：闫仙丽[1] 李青宁[2] 

机构地区：[1]山西大学土木工程系,太原030013 [2]西安建筑科技大学土木工程学院,西安710055

出　　处：《振动与冲击》2017年第8期138-143,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(51078306);国家自然科学基金(51408453);高等学校博士学科点专项科研基金资助项目(20136120120022)

摘　　要：将传递矩阵法与Cayley-Hamilton定理相结合,以微分方程和矩阵分析理论为基础,提出了一种新的Cayley-Hamilton传递矩阵法。应用该方法,考虑曲线箱梁桥的空间弯曲、剪切、扭转、拉压、翘曲及其相互间的耦合作用,推导了曲线箱梁桥离散模型的振动空间传递矩阵。以某单跨简支曲线箱梁桥为例,采用所推导矩阵,对其进行计算机编程运算,得到该桥梁的自振频率与振型,并与有限元法计算结果相比较,二者吻合良好,表明本文方法有效。A new Cayley-Hamilton transfer matrix method was proposed by integrating the Cayley-Hamilton theorem and the transfer matrix method. It was based on the theory of differential equations and matrix analysis. Adopting this method, the space vibration transfer matrix of the discrete curved box girder bridge model was derived taking into account the spatial bending, shear, torsion, tension, compression, warping and their coupling effects. With a simply supported single span curved bridge as an example, a calculation programming was conducted to obtain the vibration frequency and vibration mode of the bridge by using the derived matrix. And compared with the results of the finite element method, the results agree well with each other. It demonstrates that this method is effective. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.

关 键 词：桥梁工程 振动特性 Cayley-Hamilton传递矩阵法 曲线箱梁 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]