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基于DQM(Differential Quadrature Method,微分求积法),对曲线梁的频率方程和边界条件进行离散,通过采用不等分网点划分和替换法边界处理,求解了单跨圆形曲线梁和单跨回旋缓和曲线梁的平面外固有振动特性,并将结果与精确解进行对比,验证了微分求积法的高效性,讨论了网点数对求解精度的影响。在此基础上,研究了弯扭刚度比、翘曲系数以及边界约束形式等因素对曲线梁振动频率的影响,分析对比了圆形和回旋缓和曲线梁振动特性的参数影响规律。研究表明,采用微分求积法可以方便、高效地求解曲线梁的固有动力特性;弯扭刚度比、翘曲系数以及边界约束条件对曲线梁振动频率有着较为显著的影响,随着边界约束的减少,两种形式曲线梁的基本频率均随之减小,对于多数约束情况,两种形式曲线梁振动特性的参数影响规律相类似,唯有一种悬臂形式下的回旋缓和曲线梁振动特性的参数影响规律表现出与其他约束情况下相反的规律。
Based on the differential quadrature method (DQM), the frequency equations and the boundary conditions of the curved beam are discretized. By using the method of unequal meshing and substitution, the single-span circular curved beam and the single- The out-of-plane natural vibration characteristics of the curve beam are relaxed, and the results are compared with the exact solution. The high efficiency of the differential quadrature method is verified. The influence of the number of outlets on the accuracy of the solution is discussed. Based on this, the influences of bending stiffness ratio, warping coefficient and boundary constraint on the vibration frequency of curved beam were studied. The influence of parameters on the vibration characteristics of circular and swirling curved beam was analyzed and compared. The research shows that the differential quadrature method can be used to solve the inherent dynamic characteristics of curved beam easily and efficiently. The flexural-torsional stiffness ratio, warping coefficient and boundary constraint conditions have a significant impact on the vibration frequency of curved beam. With the reduction of boundary constraints , The basic frequencies of the two types of curved beam decrease with the restraint. For most of the restraint cases, the influence law of the parameters of the two kinds of curved beam is similar, only the parameters of a cantilever beam The law shows the opposite of other constraints.