行波效应下黏弹性地基梁动力响应解析解

弹性地基梁动力问题通常采用解析法和数值法进行分析,当可以应用解析法计算时效率更高。采用Laplace和Fourier变换,推导得出了黏弹性地基上受恒定轴向压力和横向行波作用下的无限长Euler-Bernoulli梁的解析解。经与数值模拟结果对比,验证了解答的正确性;并以长隧道为应用实例,分析对比了行波频率、波速、轴力和地基刚度对长隧道动力响应的影响,并得出了隧道内力响应受行波频率影响,频率越低,隧道内力响应越大,以及隧道内力响应受行波波速影响,当行波波速接近临界波速时,隧道内力响应明显增大等结论。

Dynamic response of viscoelastic foundation beams under traveling wave effect

The dynamic problem of elastic foundation beams is usually analyzed by using the analytical and numerical methods, but the numerical method has a large amount of calculation, and the analytical method is usually more efficient. The analytic solution of infinite length Euler-Bernoulli beam on viscoelastic foundation subjected to constant axial pressure and transverse traveling wave is obtained by the Laplace and Fourier transforms. Compared with the numerical simulation results, the correctness of the solution is verified. Taking a long tunnel as an example, the influences of wave frequency, wave velocity and axial force and foundation stiffness on the dynamic response of the long tunnel are analyzed, and its internal force response affected by the wave frequency is obtained. The lower the frequency, the greater the internal force response of the tunnel. The internal force response is affected by the travelling wave velocity. When the travelling wave velocity is close to the critical velocity, the internal force response of the tunnel significantly increases.