弹性支撑条件下分段轴压阶梯梁自由振动及稳定性分析

分析了在各种经典及其派生弹性支撑边界条件下任意多段分段常轴压阶梯梁的自由振动和稳定问题，得到了形式统一的封闭解析解。首先采用分布传递函数方法，得到了轴压等截面梁在各种边界条件下自由振动及稳定性分析的解析解，然后根据分段轴压阶梯梁横截面弯曲刚度和轴向压力沿轴线的变化情况，将梁分成多段子梁，再利用各子梁的解析解以及各子梁间的位移连续和力平衡条件，得到粱的各阶自由振动频率和失稳载荷及其相应的模态形状。最后通过三阶梯梁的三个算例验证了本文方法的正确性，并针对各种边界条件，计算了各种边界条件下分段轴压四阶梯梁自由振动的前三阶固有频率和失稳载荷参数，分析了固有频率和失稳载荷与其模态形状的关系，探讨了弹性支撑条件下轴压阶梯梁固有频率随弹簧常数的变化趋势。

Free vibration and stability of multiple-step beams on elastic end supports and under stepped axial pressure

An exact and closed-form solution was obtained for free vibration and stability of a beam with multiple-step changes in flexural rigidity and in axial pressure on the classical boundary conditions or their degenerated elastic end supports.Firstly,the analytic solution was presented for free vibration and stability of a uniform beam under axial pressure and on different boundary conditions with the distributed transfer function method.Then,according to variations of flexural rigidity and axial pressure in ax...