This article investigates the lateral vibration and resonance of bridges, crucial for transportation network integrity and traffic safety. It aims to understand the underlying principles and causes of these vibrations to enhance bridge design and maintenance. Utilizing Euler-Bernoulli beam theory and assumptions like linear elasticity and uniform material, the study simplifies complex bridge dynamics into a manageable model. It explores the bridge's flexural response under static and dynamic loads, focusing on resonance phenomena. Numerical simulations, including the finite difference method and analysis of nonlinear elastic responses, assess the bridge behavior under various load conditions, particularly periodic loads. The findings offer theoretical insights and practical guidelines for vibration control and safe bridge operation.

翻译：本文研究了桥梁的横向振动与共振现象，这对交通网络完整性和行车安全至关重要。旨在理解这些振动的基本原理与成因，从而优化桥梁设计与维护。研究采用欧拉-伯努利梁理论，并基于线弹性与均匀材料等假设，将复杂的桥梁动力学简化为易处理的模型。探讨了桥梁在静载与动载作用下的弯曲响应，重点关注共振现象。通过数值模拟（包括有限差分法与非线性弹性响应分析），评估了桥梁在不同荷载条件（尤其是周期性荷载）下的行为。研究结果为振动控制与桥梁安全运营提供了理论见解与实践指导。