预应力简支梁桥在移动荷载作用下的非线性动力特性分析

Analysis of the nonlinear dynamic behavior of simply supported prestressed beam bridges under moving load

考虑预应力梁的剪切变形和几何非线性,建立梁的动力学基本方程式,应用增量谐波平衡法,分析计算梁在预应力作用下的横向振动问题。通过实例计算,得到梁在移动车辆荷载作用下的幅频响应曲线和力与位移的非线性响应关系,并给出了外激励频率不同且初始预加力变化时动挠度的变化规律。计算结果表明,梁非线性位移明显大于线性位移,且荷载与位移呈明显非线性关系,非线性因素的影响不可忽略;施加预应力可以提高梁的动抗弯刚度,减少梁的动挠度值。为预应力混凝土桥梁的设计和动力特性分析提供一定的理论依据。

Considering geometric nonlinear and transversal shear influences, the basic dynamic equations of forced vibration of the simply supported beam are formuated. The transversal vibration behavior of the prestressed concrete beam are calculated and analyzed. Applying the incremental harmonic balance method, the amplitude- frequency and exciting force-displacement response curves of the beam under moving loads are obtained, and the influence of the prestressed force on the dynamic displacement is revealed through an example. The nonlinear displacement is larger than the linear displacement of the beam. The relationship between dynamic displacement and moving load is non-linear, the dynamic flexural stiffness is improved and the dynamic deformation reduced by increasing the prestressed force.