卷积定理 meaning in English

convolution theorem

Thus the resistance factor and vibration modes of the soil layer are obtained and used to analysis the pile response . by considering the interaction between the soil layer and the pile with boundary condition of continuity of displacement and equilibrium of force at the interface of soil layer and pile , the dynamic equilibrium equation of pile is solved and an analytical solution for the pile response in frequency domain is yielded , which is used to define complex stiffness and mobility at the level of the pile head . based on the convolution theorem and inverse fourier transform , a semi - analytical solution of velocity response in time - domain subjected to a semi - sine exciting force is given
首先通过引入势函数方法对土体位移进行分解，从而将土体动力平衡方程解耦，求解得到了土层的振动模态和阻抗因子，然后利用该解以小应变条件下桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用，求解桩的动力平衡方程，得到了桩顶的频域响应解析解、复刚度和速度导纳，利用卷积定理和傅里叶逆变换，求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。