利用杜哈美积分求速度、加速度

assist

请问，怎样利用杜哈美积分求速度、加速度，（求杜哈美积分的导函数）而不是利用v=(s2-s1)/t;a=(v2-v1)/t这样的差分法。

感谢happy上次提供的杜哈美积分的源程序，向具体问问A,B是什么？还有怎样用duhamel积分求速度和加速度。不用差分法。

[ 本帖最后由 ChaChing 于 2010-3-15 15:59 编辑 ]

happy

正弦余弦成分的幅值<BR><BR>已知位移表达式速度加速度表达式你不知道吗？

assist

1. %单自由度系统适用，初始条件任意，比happy提供的适应性强。对于多自由度系统，正
   
2. %则化之后适用，加循环即可（有点修改，for t=0:dTaT end之间的不用改）。
   
3. clc; clear
   
4. n=1000; m=3; T=2; si=0.02; k=2700; w=30;
   
5. dTao=T/n; wD=w*(1-si^2)^0.5;
   
6. p2=[ones(1,333),zeros(1,668)]; % p2=[1000,zeros(1,1000)];
   
7. %%%%%%%%%%%%%%%杜哈美积分开始%%%%%%%%%%%%%%%%
   
8. x0=0; v0=0; j=1;
   
9. for t=0:dTaT
   
10. sysN=0; sysP=0;
    
11. %%%%%%%%%%%%位移\速度\加速度公用部分%%%%%%%%%%%%%%
    
12. for i=0:t/dTao
    
13. sysN=sysN+p2(i+1)*exp(si*i*dTao*w)*cos(wD*i*dTao)*dTao;
    
14. sysP=sysP+p2(i+1)*exp(si*i*dTao*w)*sin(wD*i*dTao)*dTao;
    
15. end
    
16. %%%%%%%%%%%%位移\速度\加速度公用部分%%%%%%%%%%%%%%
    
17. %%%%%%%%%%%%%%%%%求位移%%%%%%%%%%%%%%%%%%%
    
18. sysA=exp(-si*w*t)*(x0*cos(wD*t)+(si*w*x0+v0)/wD*sin(wD*t));
    
19. sysB=exp(-si*w*t)/(m*wD)*(sin(wD*t)*sysN-cos(wD*t)*sysP);
    
20. x(j)=sysA+sysB;
    
21. %%%%%%%%%%%%%%%%%求位移%%%%%%%%%%%%%%%%%%%
    
22. %%%%%%%%%%%%%%%%%%%%%%%%%求速度%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
23. %%%%%%%%%%%%%%%V=C+D+E+F%%%%%%%%%%%%%%%%%%
    
24. sysC=exp(-si*w*t)*(-x0*wD*sin(wD*t)-(si*w)^2*x0*sin(wD*t)/wD);
    
25. sysD=exp(-si*w*t)*(v0*cos(wD*t)-si*w*v0*sin(wD*t)/wD);
    
26. %%%%%%%%%%%%%%%E=G+H%%%%%%%%%%%%%%%%%%%%%%
    
27. sysG=sin(wD*t)*sysN;
    
28. sysH=-cos(wD*t)*sysP;
    
29. sysE=(sysN+sysP)*-si*w*exp(-si*w*t)/(m*wD);
    
30. %%%%%%%%%%%%%%%F=I+J+K+L%%%%%%%%%%%%%%%%%%
    
31. sysI=wD*cos(wD*t)*sysN;
    
32. sysJ=sin(wD*t)*p2(j)*exp(si*w*t)*cos(wD*t);
    
33. sysK=wD*sin(wD*t)*sysP;
    
34. sysL=-cos(wD*t)*p2(j)*exp(si*w*t)*sin(wD*t);
    
35. sysF=(sysI+sysJ+sysK+sysL)*exp(-si*w*t)/(m*wD);
    
36. v(j)=sysC+sysD+sysE+sysF;
    
37. %%%%%%%%%%%%%%%%%%%%%%%%%求速度%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
38. %%%%%%%%%%%%%%%%%%%%%%%%%求加速度%%%%%%%%%%%%%%%%%%%%%%%%%
    
39. %%%%%%%%%%%%%%%%%%%sysdC%%%%%%%%%%%%%%%
    
40. sysdC1=-x0*wD^2*cos(wD*t)-(si*w)^2*x0*cos(wD*t);
    
41. sysdC=-si*w*sysC+exp(-si*w*t)*sysdC1;
    
42. %%%%%%%%%%%%%%%%%%%sysdD%%%%%%%%%%%%%%%
    
43. sysdD1=-v0*wD*sin(wD*t)-si*w*v0*cos(wD*t);
    
44. sysdD=-si*w*sysD+exp(-si*w*t)*sysdD1;
    
45. %%%%%%%%%%%%%%%%%%%sysdE%%%%%%%%%%%%%%%
    
46. sysdG=wD*cos(wD*t)*sysN+sin(wD*t)*p2(j)*exp(si*w*t)*cos(wD*t);
    
47. sysdH=wD*sin(wD*t)*sysP-cos(wD*t)*p2(j)*exp(si*w*t)*sin(wD*t);
    
48. sysdE=(si*w)^2*exp(-si*w*t)*(sysG+sysH)/(m*wD)-si*w*exp(-si*w*t)*(sysdG+sysdH)/(m*wD);
    
49. %%%%%%%%%%%%%%%%%%%sysdF%%%%%%%%%%%%%%%
    
50. sysdI=-wD^2*sin(wD*t)*sysN+wD*cos(wD*t)*p2(j)*exp(si*w*t)*cos(wD*t);
    
51. %%%%%%%%%%%%怎样考虑dP2,暂时取0%%%sysdJ%%%%%%%%%%
    
52. sysdJ1=wD*cos(wD*t)^2*p2(j)*exp(si*w*t);
    
53. sysdJ2=sin(wD*t)*0*exp(si*w*t)*cos(wD*t);
    
54. sysdJ3=sin(wD*t)*p2(j)*si*w*exp(si*w*t)*cos(wD*t);
    
55. sysdJ4=-wD*sin(wD*t)^2*p2(j)*exp(si*w*t);
    
56. sysdJ=sysdJ1+sysdJ2+sysdJ3+sysdJ4;
    
57. %%%%%%%%%%%%%%%%%%%sysdK%%%%%%%%%%%%%%%
    
58. sysdK=wD^2*cos(wD*t)*sysP+wD*sin(wD*t)*p2(j)*exp(si*w*t)*sin(wD*t);
    
59. %%%%%%%%%%%%怎样考虑dP2,暂时取0%%%sysdL%%%%%%%%%%
    
60. sysdL1=wD*sin(wD*t)^2*p2(j)*exp(si*w*t);
    
61. sysdL2=cos(wD*t)*0*exp(si*w*t)*sin(wD*t);
    
62. sysdL3=-cos(wD*t)*p2(j)*si*w*exp(si*w*t)*sin(wD*t);
    
63. sysdL4=-wD*cos(wD*t)^2*p2(j)*exp(si*w*t);
    
64. sysdL=sysdL1+sysdL2+sysdL3+sysdL4;
    
65. %%%%%%%%%%%%%%%%%sysdF%%%%%%%%%%%%%%
    
66. sysdF=-si*w*exp(-si*w*t)*(sysI+sysJ+sysK+sysL)/(wD*m)+exp(-si*w*t)*(sysdI+sysdJ+sysdK+sysdL)/(wD*m);
    
67. %%%%%%%%%%%%%%%%%acc%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
68. acc(j)=sysdC+sysdD+sysdE+sysdF;
    
69. %%%%%%%%%%%%%%%%%%%%%%%%%求加速度%%%%%%%%%%%%%%%%%%%%%%%%%
    
70. j=j+1;
    
71. end
    
72. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%杜哈美积分完毕%%%%%%%%%%%%%%%%%%%%%%%%%
    
73. figure;
    
74. t=0:dTaT;
    
75. subplot(3,1,1);plot(t,x);grid on;
    
76. subplot(3,1,2);plot(t,v);grid on;
    
77. subplot(3,1,3);plot(t,acc);grid on;

复制代码

[ 本帖最后由 ChaChing 于 2009-4-18 21:28 编辑 ]

realyyy

好东西！我要研究研究！谢了！

lf51999

好东西，收藏

cyk_2006

好东西！我要研究研究！谢了！

hyl2323

杜哈梅积分，求任意激励的响应，振动力学里的，我也编写过，你这个好难看懂！
这是我写的duhamel积分，完全是按照西安交大版《振动力学》上的公式写的，调试无误。
% duhamel        duhamel integral
% y=duhamel(x,h,fs)
% inputs:     x:analysed signal(vector)
%             h:impulse response
%             fs:frequency of sampling
% outputs:    y:duhamel integral of analysed signal x
function y=duhamel(x,h,fs)
    n=length(x);
    for i=1:n
        xx=x(1:i);
        hh=fliplr(h(1:i));
        temp=xx.*hh;
        y(i)=trapz(temp)*(1/fs);
    end

[ 本帖最后由 ChaChing 于 2009-4-18 21:26 编辑 ]

assist

原帖由 hyl2323 于 2007-12-20 13:47 发表

                               
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杜哈梅积分，求任意激励的响应，振动力学里的，我也编写过，你这个好难看懂！

我这个没有使用任何matlab系统函数，完全的一步一步下来的，如果你对duhamel积分公式研究一下是能看懂的。

hyl2323

支持非matlab算法程序！

zeus1208

好好学习一下

laughzha

恩，好东西，楼主新年给大家送好礼啊:lol

上官楼

:@) :@) :@) :@) 经典，就是不出结果啊！

wyx3710

for t=0:dTaT
dTaT是什么意思？提示没定义呀？

liwang11

支持！！！！

liwang11

for t=0:dTaT
dTaT是什么意思？提示没定义呀？