【摘要】 多层建筑振动时,沿竖向的变形以剪切为主。对于层数很多且又不分阶的建筑物,各层质量相差不大,而其刚度每层往往不同,因此可将多层建筑作为等质量变刚度的多层建筑。只考虑等质量变刚度的多层建筑剪切变形,由弹性振动理论得到其剪切固有振动微分方程,采用改进的摄动法研究多层建筑剪切固有振动。对求解变系数二阶齐次微分方程的摄动法进行改进,求得等质量变刚度多层建筑剪切固有振动的振型函数,得到确定等质量变刚度多层建筑剪切固有振动频率的特征方程。将分析结果与其他文献分析结果进行对比,算例表明改进摄动法不但计算过程简便,而且计算精度与Bessel函数法的计算精度非常接近。更多还原

【Abstract】 The vertical deformation of multi-story building vibration is main shear deformation.As the quality of each layer has little difference for multi-story building with the same global dimension,the stiffness,however,is variable,the multi-story building is regarded as equal mass and variable stiffness model.Only taking shear deformation into consideration,the shear natural vibration equation of multi-story building with equal mass was derived with elastic vibrate theory,which was solved with improved perturbation.Perturbation for variable coefficient second order homogeneous differential equation was improved.Meanwhile its mode shape function and characteristic equation was obtained.A thorough comparison with well-known published results is presented for the examples analysis that the improved perturbation not only simplified the calculation process but also got a calculation accuracy quite close to Bessel function method.更多还原