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求解移动荷载作用下黏弹性半空间体的响应,是研究交通荷载引起的环境振动问题的基础。移动荷载作用下半空间体响应的积分形式解不难得出,但当荷载移动速度接近或大于瑞利波速时,被积函数往往具有奇异性和高振荡性,这就使得数值计算相当困难。该文研究了移动随机线源荷载作用下黏弹性半空间体的响应问题。利用虚拟激励法,将系统的随机振动分析转化为确定性分析,然后通过广义Duhamel积分得到了响应的积分形式解。将被积函数图形化确定了函数的积分限,通过自适应数值积分算法解决了被积函数的振荡性,最终得出了黏弹性半空间体动力响应的数值结果。为确保数值计算结果的正确性,同样计算了确定性荷载作用下半空间体的响应,并与已有文献结果进行了对比。在验证了数值算法正确性的基础上,计算了随机荷载作用下半空间体的响应,荷载移动速度涵盖了亚音速、跨音速和超音速三种情形。通过具体算例,分析了响应的时间和空间分布规律,并对荷载移动速度对响应的影响进行了分析。
Solving the response of viscoelastic half-space body under moving loads is the basis of studying the environmental vibration problems caused by traffic load. It is not hard to draw an integral form solution of the half-space response under the action of moving loads. However, when the moving velocity of the load is close to or greater than the Rayleigh wave velocity, the integrand is often singular and highly oscillatory, which makes numerical calculation quite difficult. In this paper, we study the response of viscoelastic half-space body under moving stochastic source. Using the virtual excitation method, the stochastic vibration analysis of the system is transformed into a deterministic analysis, and then the integral form solution of the response is obtained through the generalized Duhamel integral. The integrator limit is defined by plotting the integrand function, and the oscillatory property of the integrand is solved by the adaptive numerical integration algorithm. Finally, the numerical results of the viscoelastic half-space dynamic response are obtained. In order to ensure the correctness of the numerical calculation, the response of the half-space body under the deterministic load is also calculated and compared with the existing literature results. After verifying the correctness of the numerical algorithm, the response of the half-space body under random loading is calculated. The load moving speed covers three subsonic, transonic and supersonic velocities. Through concrete example, the time and space distribution of response are analyzed, and the influence of load moving speed on response is analyzed.