These three criteria are implied in the statement that an acceptable system must have a satisfactory time response to specified inputs and disturbances 在陈述： “一个可接受的系统对指定输入和扰动必须有满意的时域响应”已经包含了这三个指标的含义。
The numerical results show that the time domain response of the laminated plates induced by the in - line force of non - steady component oscillating flow is similar to harmonic motion with certain ribbon which is formed by period motion 计算结果表明，零均值流量脉动流顺流向作用力诱发反对称角铺设层合板的时域响应近似于具有一定带宽的谐波运动，而这一带宽又是由一定周期运动形成的。
3 . by comparing the available theories corresponding to plane strain model and winkler model with the solutions developed in this paper , the applicability of the two models is analyzed and checked . the comparison involves many aspects such as local soil stiffness , dynamic stiffness and time domain response at the pile head , and some important conclusions are made 3 、将基于平面应变简化假定和winkler模型的桩振动理论解与本文严格理论解对比，分析校验了平面应变简化假定和winkler模型在桩基振动理论应用中的适用性，具体比较范围涉及土层对桩的局部复阻抗、桩顶幅频响应、速度导纳、桩顶复刚度、桩顶时域响应等方面，并得到若干重要结论。
With laplace transforms , the question can be solved in laplace domain . with the aid of impedance transmit functions , an analytical solution for the impedance function in laplace domain is yielded , so is the corresponding analytical solution for the impedance function in frequency domain , semi - analytical solution of velocity response in time - domain subjected to a semi - sine exciting force and mobility at the level of the pile head 利用拉普拉斯变换，将定解问题转化到拉普拉斯域内求解，结合阻抗函数的传递性，得到了拉普拉斯域内的桩顶阻抗函数解析解，进而得到了频域内的桩顶阻抗函数解析解、半正弦脉冲激振力作用下的速度时域响应半解析解和速度导纳。
Finally , dynamic compliances of a pile with variable impedance embedded in layered saturated soil are studied . a simplified layered model is put forward on the basis of the single layer elastic bearing model . by using the same method , analytical solutions in frequency domain hence semi - analytical solutions in time domain representing the dynamic responses at pile head are obtained 基于土层层问相互作用，提出了饱和成层土中任意变阻抗桩的纵向振动问题简化层间模型，利用单层土中提出的解析方法，基于这一简化层间模型，求得饱和成层土中任意段变阻抗桩的桩顶频域解析解和时域响应半解析解，并论证了模型的合理性。
As follows are the main contents of this paper : firstly , a matlab program has been worked out according to the response model of integrate and defective pile in time zone ; secondly , the most important factor that affects the curve of velocity is obtained through analyzing the curve of velocity response 主要研究内容如下：首先，针对成层土中完整桩和缺陷桩的时域响应模型编制了matlab程序；其次，通过对成层土中桩的时域速度响应曲线的分析，得到了影响速度响应曲线的主要因素。
The main original work includes : 1 . the interaction between an integral pile and a uniform visco - elastic soil layer with viscous damping or hysteretic damping is theoretically studied , and the pile response to a harmonic load is obtained in a closed form and used to define complex stiffness at the pile head . semi - analytical solution of the velocity response in time domain subjected to a semi - sine wave exciting force is also given 主要工作包括： 1 、在考虑桩周土三维波动条件下，对滞回阻尼、粘性阻尼单层均质土中桩土纵向耦合振动问题进行了解析研究，分别得到桩顶位移、速度频域响应以及复刚度的严格解析表达，以及半正弦脉冲激振力作用下桩顶时域响应半解析解。
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。
