Application of duhamel integral on vehicle vibration 积分在车辆振动中的应用
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U . s . air force master sergeant epps ( tyrese gibson , left ) and special forces army ranger sgt . lennox ( josh duhamel , right ) are on patrol in qatar 美国空军中士爱普斯（泰瑞兹?吉布森饰，居左）和特种兵突击队中士利诺克斯（乔希?杜哈梅尔饰，居右）正在卡塔尔巡逻。
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The thermal process model of imbed pipe floor heating room at intermittent operation was set up by analyzing the thermal storage of enclosure . then , a solution method was give for it basing on duhamel theorem . the calculation results shown a good indoor thermal environment can be hold when the system , which designed on out door temperature for heating basis , operates half day in night under outer door mean temperature in winter 对典型房间的计算结果显示:系统间歇运行时，供暖系统开启和关闭后室内温度呈指数规律变化;当系统按供暖室外计算温度设计，实际运行日的室外平均温度等于供暖期室外日平均温度时，在室外逐时温度较低的时段低温热水地板辐射供暖系统运行半天左右可满足全天供暖室内计算温度要求。
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Based on the unified recursive formula , the four algorithms included in this study are the central difference method , the newrnark ' s method , z - transform method , and duhamel ' s step integral method . the accuracy , the phase and other existent problem are studied in this paper . it is proved in this paper that the recursive parameters b1and b2are relate to the poles of theoretical transfer function 分析中可以发现，中心差分方法， newmark中点加速度方法、 z变换方法及duhamel逐步积分法在精度范围内其计算相位是没有畸变的，中国地震局工程力学研究所顷土学位论文一但是中心差分方法， newmark中点加速度方法随着采样间隔及系统自振频率的增大，系统的固有自振周期被改变，其传递函数的共振区域与理论传递函数的共振区域会发生分离。
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A new step - by - step integral procedure of dynamics equations is presented . the general expression of the solution of dynamics equations is obtained on the basis of the homogenous analytical solutions of dynamics equations and duhamel integration . the explicit analytical integration algorithm , which is characterized by fourth - order accuracy , self - starting and self - correcting , is employed to discretize the equivalent load terms 另外提出了求解动力学方程的一个新型的逐步积分法，基于线性动力学方程的解析齐次解及duhamel积分，构造出适用于非线性动力学方程解的一般积分表达式，对包含非线性项的非齐次项采用插值近似的方法，得到一个单步显式、自起步、预测校正具有四阶精度的解析逐步积分算法。
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The precision duhamel integration solution for the linearization equation is also given from the theory of linear differential equation . the calculating results show that the new method can improve the calculation precision greatly . in fact , the truncation error is not limited by this method , it can arrive the precision according to the requirement 本文的主要工作有以下几个方面: ( 1 )由于非线性项的存在,使得多数情况下难以得到非线性动力方程的解析解表达式,目前常使用数值积分方法来求解非线性动力学方程的解,但常规计算方法的计算精度不很理想,本文提出了含taylor展开项中高阶余项的非线性动力方程的线性化数值计算方法,构造了瞬态线性化方程,给出了duhamel积分的表达式。
