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1. A comparison is made with available simplified theories such as that corresponding to plane strain model . the comparison involves many aspects such as the soil resistance factor , the soil complex local stiffness and the pile complex stiffness at the level of the pile head . the applicability of the other two models is analyzed and checked
   3 、將本文嚴格解與其它簡化解(如基于平面應(yīng)變假定的解等)從土層阻抗因子、土層局部復(fù)剛度和樁頂復(fù)剛度等方面進行了對比分析，檢驗和校核了簡化解的適用性。
2. Based on the solutions proposed herein , the longitudinal vibration properties of an integral pile in a uniform soil or layered soil , a pile with variable sections or variable modulus in a uniform soil are discussed respectively . the influence on the curves of complex stiffness , mobility and reflection wave of pile caused by soil modulus , the degree of pile defects , and the length and location of pile defects are emphatically discussed . 3
   利用所得解分別對均質(zhì)土中完整樁、成層土中完整樁、均質(zhì)土中變截面樁和均質(zhì)土中變模量樁的縱向振動特性進行了分析，重點討論了土層模量變化、樁身缺陷程度、缺陷段位置、缺陷段長度等因素對樁頂復(fù)剛度、速度導(dǎo)納和反射波曲線的影響。
3. A state space model for parts of non - linear oscillation systems is put forward , and the concealed analytical solution for the systems is deduced . a numerical calculation method is presented and the calculation precision is improved greatly through using iterative method . finally the presented numerical method is extended to solve differential equations with complex stiffness matrix
   導(dǎo)出了一類非線性振動系統(tǒng)的狀態(tài)空間模型，在此模型中給出了非線性振動系統(tǒng)的隱式解析解，提出了相應(yīng)的數(shù)值計算方法，并利用迭代法有效地提高了計算精度，最后將該數(shù)值方法推廣應(yīng)用到復(fù)剛度振動方程的數(shù)值求解計算中。
4. 2 . the complex stiffness corresponding to three bearing conditions of semi - infinite elastic subgrade , finite elastic soil layer and end bearing at the pile bottom are theoretically investigated , and analytical expression of the complex stiffness corresponding to finite elastic soil layer bearing condition is obtained . the special influence of bearing conditions on dynamic response at pile head is then discussed
   2 、對剛性支承、有限厚度土層支承和半無限空間支承三種樁底部支承情況下樁底支承復(fù)剛度和樁周土底分布支承復(fù)剛度的解析表達及其特性進行了推導(dǎo)論證，通過假定樁底土為與樁等截面的土柱推導(dǎo)求得有限厚土層支承條件下樁底支承復(fù)剛度的解析解，并據(jù)此分析了不同底部支承邊界對樁頂響應(yīng)的影響。
5. 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 、在考慮樁周土三維波動條件下，對滯回阻尼、粘性阻尼單層均質(zhì)土中樁土縱向耦合振動問題進行了解析研究，分別得到樁頂位移、速度頻域響應(yīng)以及復(fù)剛度的嚴格解析表達，以及半正弦脈沖激振力作用下樁頂時域響應(yīng)半解析解。