螺旋形弹簧拉扭耦合自由振动的解析解

摘要

螺旋形弹簧的拉伸/压缩变形总是伴随着扭转变形。首先通过直接求解螺旋形弹簧单元自由振动的控制运动微分方程，推导了螺旋形弹簧单元拉扭耦合振动的精确的传递矩阵，然后采用二分法求解频率特征方程来得到固有特性。数值结果验证了本文方法的精确性和有效性。%The extensional and/or compressive deformation of the helical springs is always accompanied by the torsional deformation. The exact transfer matrix of the coupled extensional-torsional helical spring element is derived firstly through solving the governing differential equation of motion of the element directly. Then the frequency equation is solved by the bisect method to obtain natural characteristics. Numerical results verified the effectiveness of the proposed method.