Based on the Rayleigh-Love theory, the dynamic stiffness matrix of a conical bar in longitudinal vibration is developed for the investigation of free vibration and response characteristics of such bars and their assemblies. First the governing differential equation of motion in free longitudinal vibration of a conical bar using the Rayleigh-Love theory which accounts for the inertia effects due to transverse or lateral deformations is derived by applying Hamilton's principle. Next, for harmonic oscillation, the governing differential equation is recast in the form of Legendre's equation, providing a series solution connected by integration constants. The expressions for the amplitudes of displacements and forces are then obtained by means of the series solution. Finally, the frequency dependent dynamic stiffness matrix is formulated by relating the amplitudes of forces to those of the corresponding displacements at the ends of the conical bar and thereby eliminating the integration constants. As an established solution technique, the Wittrick-Williams algorithm is applied to the resulting dynamic stiffness matrix when computing the natural frequencies and mode shapes of some illustrative examples. The theory is also applied to investigate the response of a cantilever conical Rayleigh-Love bar with a harmonically varying load applied at the tip. The results computed from the Rayleigh-Love model based dynamic stiffness theory are compared and contrasted with those computed from conventional classical theory with significant conclusions drawn.

基于Rayleigh-Love理论，开发了圆锥形杆在纵向振动中的动态刚度矩阵，以研究这种杆及其组件的自由振动和响应特性。首先，通过应用汉密尔顿原理，推导了使用瑞利-洛夫理论的圆锥形杆自由纵向振动中支配的运动微分方程，该理论解释了由于横向或横向变形而产生的惯性效应。接下来，对于谐波振荡，将控制微分方程以勒让德方程的形式重铸，从而提供由积分常数连接的级数解。然后借助级数解获得位移和力的振幅表达式。最后，通过将力的振幅与圆锥形杆端部的相应位移的振幅相关联，从而消除积分常数，可以得出频率相关的动态刚度矩阵。作为已建立的解决方案技术，在计算一些示例性示例的固有频率和振型时，将Wittrick-Williams算法应用于所得的动态刚度矩阵。该理论还用于研究悬臂圆锥形Rayleigh-Love杆的响应，该杆在尖端施加了谐波变化的载荷。将基于Rayleigh-Love模型的动态刚度理论计算出的结果与常规经典理论计算出的结果进行了比较和对比，得出了重要的结论。