求曲线箱梁桥自振频率的精细传递矩阵法
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摘要
将高精度的精细积分法和力学概念清晰的传递矩阵法结合起来,以微分方程和矩阵分析理论为基础,提出了一种新的精细传递矩阵形式,推导了该方法的计算公式,并用于求解曲线箱形梁桥的自振频率.与传统的传递矩阵法相比,无需对微分方程组进行求解,只需按照迭代公式进行计算,就可以得到所需要的传递矩阵.根据边界条件,运用频率搜索方法便可得到结构的自振频率.提出的方法虽然是条件稳定的,但是稳定性条件极易满足.算例表明本文方法的有效性.
Based on the theory of differential equations and matrix analysis,a new precise transfer matrix form is provided by combining the high-precision precise integration and the clear concept transfer matrix method.The calculation formulas of the method are derivated.The natural frequencies of the curved box bridge are solved with the method.Compared with the traditional transfer matrix method,there is no need to solve the differential equations,Just by following the iterative formula,the necessary transfer matrixes can be obtained.According to the boundary condition,the natural frequency of the structure can be got by the searching method of the frequency.The stable condition of the method is met easily.Example shows that the method is effective.
Based on the theory of differential equations and matrix analysis,a new precise transfer matrix form is provided by combining the high-precision precise integration and the clear concept transfer matrix method.The calculation formulas of the method are derivated.The natural frequencies of the curved box bridge are solved with the method.Compared with the traditional transfer matrix method,there is no need to solve the differential equations,Just by following the iterative formula,the necessary transfer matrixes can be obtained.According to the boundary condition,the natural frequency of the structure can be got by the searching method of the frequency.The stable condition of the method is met easily.Example shows that the method is effective.
引文
[1]魏双科.曲线梁桥的固有振动特性及地震反应分析[D].南京:南京工业大学,2006.WEI Shuang-ke.Natural dynamic characteristics and seismic response analysis of curved girder bridges[D].Nanjing:NanJing University of Technology,2006.
[2]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(4):131-136.ZHONG Wan-xie.Precise time-intergration method for structural dynarnics[J].Journal of Dalian University ofTechnology,1994,34(2):131-136.
[3]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,5(1):18-23.LI Qing-ning.The transfer matrix method of bar elements with variable cross-section[J].J.Xi′an Univ.of Arch.&Tech.(Natural Science Edition)2001,5(1):18-23.
[4]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.LI U Qing-tan,NI Guo-rong.The transfer matrix method used in structure analysis[M].Beijing:China Rail way Press,1997.
[5]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191-195.WANG Meng-fu,ZHOU Xi-yuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191-195.
[6]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增刊):554-566.WANG Yi-fa.Solving structural dynamic equation using combination of the precise integraton method and direct precise integraton method[J].Industrial Architecture2006,36(S):554-566.
[7]王梦甫,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191-195.WANG Meng-fu,ZHOU Xi-yuan.Renewal precise time step integration method of structural dynamic analysis[J].Mechanica Sinica,2004,36(2):191-195.
[8]张晓志,程岩,谢礼立.结构动力反应分析的三阶显式方法[J].地震工程与工程振动,2002,21(3):1-8.Zhang Xiao-zhi,CHENG Yan,XIE Li-li.Anewexplicit solution of dynamic response analysis[J].Journal of Earth-quake Engineering and Engineering Vibration,2002,21(3):1-8.
[9]郭泽英,李青宁.动力反应分析的显式积分方法及其稳定性[J].地震工程与工程振动,2008,28(2):15-19.GUO Ze-ying,LI Qing-ning.An explicit integral method and the stability of dynamic response analysis[J].Journal of Earthquake Engineering and Engineering Vibration,2008,28(2):15-19.
[2]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(4):131-136.ZHONG Wan-xie.Precise time-intergration method for structural dynarnics[J].Journal of Dalian University ofTechnology,1994,34(2):131-136.
[3]李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报:自然科学版,2001,5(1):18-23.LI Qing-ning.The transfer matrix method of bar elements with variable cross-section[J].J.Xi′an Univ.of Arch.&Tech.(Natural Science Edition)2001,5(1):18-23.
[4]刘庆潭,倪国荣.结构分析中的传递矩阵法[M].北京:中国铁道出版社,1997.LI U Qing-tan,NI Guo-rong.The transfer matrix method used in structure analysis[M].Beijing:China Rail way Press,1997.
[5]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191-195.WANG Meng-fu,ZHOU Xi-yuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191-195.
[6]王一凡.直接积分法与精细积分法结合求解结构动力方程[J].工业建筑,2006,36(增刊):554-566.WANG Yi-fa.Solving structural dynamic equation using combination of the precise integraton method and direct precise integraton method[J].Industrial Architecture2006,36(S):554-566.
[7]王梦甫,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191-195.WANG Meng-fu,ZHOU Xi-yuan.Renewal precise time step integration method of structural dynamic analysis[J].Mechanica Sinica,2004,36(2):191-195.
[8]张晓志,程岩,谢礼立.结构动力反应分析的三阶显式方法[J].地震工程与工程振动,2002,21(3):1-8.Zhang Xiao-zhi,CHENG Yan,XIE Li-li.Anewexplicit solution of dynamic response analysis[J].Journal of Earth-quake Engineering and Engineering Vibration,2002,21(3):1-8.
[9]郭泽英,李青宁.动力反应分析的显式积分方法及其稳定性[J].地震工程与工程振动,2008,28(2):15-19.GUO Ze-ying,LI Qing-ning.An explicit integral method and the stability of dynamic response analysis[J].Journal of Earthquake Engineering and Engineering Vibration,2008,28(2):15-19.
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