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为了研究三跨有粘结预应力连续梁的动力特性,建立了基于Bernoulli-Euler梁理论的有粘结预应力钢筋布置形式的连续梁分析模型。通过建立有粘结预应力与位移的函数关系,将连续梁视为满足弯矩、转角和位移条件的多个单跨梁,采用分段联立法建立三跨预应力连续梁的振动方程组,获得了频率方程的解析解。通过求解频率方程得到自振频率,以三跨有粘结预应力连续梁为例,分别将本文方法计算结果与有限元法计算结果及实桥测试结果进行对比。研究结果表明:本文方法所得预应力梁的基频与有限元法计算结果的相对误差仅为0.6%,与实桥测试结果的误差为-1.18%;前四阶频率与有限元法计算结果的最大误差在3%以内;前三阶自振频率与实桥测试结果的平均误差在3%以内,结果吻合较好。通过本文公式可以较准确地求得三跨有粘结预应力连续梁的自振频率等动力参数。
In order to study the dynamic characteristics of the three-span bonded prestressed continuous beams, a continuous beam analysis model based on the Bernoulli-Euler beam theory is proposed. By establishing a function of prestress and displacement as a function of displacement, the continuous beam is considered as a single span beam satisfying the conditions of bending moment, rotation angle and displacement. The vibration equations of the three-span prestressed continuous beam are established by the piecewise simultaneous method. An analytical solution of the frequency equation is obtained. By solving the frequency equation, the natural frequency is obtained. Taking the three-span bonded prestressed continuous beam as an example, the calculation results of this method are compared with those of the finite element method and the real bridge test results respectively. The results show that the relative error between the fundamental frequency and finite element method of the prestressed beam obtained in this method is only 0.6%, which is -1.18% compared with the actual bridge test results. The results of the first four frequencies and the finite element method The maximum error is within 3%. The average error between the first three natural frequencies and the real bridge test results is within 3%. The result is in good agreement. Through this formula, the dynamic parameters such as natural frequency of three-span bonded prestressed continuous beams can be obtained more accurately.