中文摘要：

以预应力简支梁为例，分析了预应力在梁的横向振动过程中的变化，建立了预应力梁横向弯曲振动的微分方程。采用模态摄动法，进一步推导出预应力梁模态特性的近似分析方法，把复杂的变系数微分方程的求解转化为线性代数方程组的求解，从而有效地简化了计算过程。最后通过算例，讨论了预应力对梁的横向振动特性的影响。计算结果表明：当施加预应力的位置有较大的偏心距时，预应力对梁的自振特性有较大的影响。

英文摘要：

A simply-supported prestressed beam is studied. The change of the prestress force in the lateral vibration process of the beam is discussed and the differential equation of lateral vibrations for the simply-supported prestressed beam is given. The mode perturbation method is used to establish an approximate analysis technique for the modal characteristics of the prestressed beam in lateral vibrations. As a result, the solution of the complicated differential equation with variable coefficients is obtained approximately by solving the algebraic equations and the computational effort is reduced effectively. The influence of the prestress force on the natural frequencies of the beam is also discussed. Numerical results show that the effect of the prestress force on the first modal frequency is significant when the eccentricity of the prestress force is large.