带有５次非线性项的非线性振动问题的讨论
问题的相关计算程序
%状态方程%给程序中的参数赋值
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
l=1;b=0.05;h=0.05;%梁的尺寸
a1=523.29;a2=1.868*10^7;a3=2.186*10^9;%本构方程中的材料参数
tm=15;%相变温度
i1=b*h^3/12;i2=b*h^5/80;i3=b*h^7/448;%梁的截面矩
%给无量纲量赋值
arf2=a2/(a1*tm);arf3=a3/(a1*tm);
c2=arf2*i2/(i1*l^2);c3=arf3*i3/(i1*l^4);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ctd无量纲温度，v无量纲速度
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
global ctd v k d q;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%b1,b2,b3为状态方程中的系数
%%%%%%%%%%%%%%%%%%%%%%%%%
b1=pi^4*(ctd-1)-pi^2*v^2;
b2=3/4*pi^8*c2;
b3=5/8*pi^12*c3;
%%%%%%%%%%%%%%%%%%%%%%%%%
dy=zeros(3,1);
dy(1)=y(2);
dy(2)=-k*y(2)-b1*y(1)+b2*y(1)^3-b3*y(1)^5+d*sin(y(3));
dy(3)=q;
%相图及时域图
%ctd无量纲温度，v无量纲速度,k无量纲阻尼比,d无量纲激振力幅值,q无量纲激振力频率
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
global ctd v k d q;
ctd=1.7;v=0;k=0.05;d=0.02;q=0.5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
tspan=;
y0=;
=ode45('movingbeamforce',tspan,y0);
figure(1)
hold on
plot(y(end-1000:end,1),y(end-1000:end,2))
xlabel('无量纲位移'),ylabel('无量纲速度')
hold on
figure(2)
hold on
plot(t(end-1000:end),y(end-1000:end,1))
xlabel('无量纲时间'),ylabel('无量纲位移')
hold on
figure(3)
hold on
plot(t(end-1000:end),y(end-1000:end,2))
xlabel('无量纲时间'),ylabel('无量纲速度')
hold on
%Poincare截面程序
functionmbeamforcepoincare
global ctd v k d q;
ctd=1.7;v=0;k=0.05;d=0.02;q=0.5;
y0=;
tspan=;
=ode45('movingbeamforce',tspan,y0);
m=zeros(790,1);
n=zeros(790,1);
for i=1:790
m(i,1)=y(100*i,1);
n(i,1)=y(100*i,2);
end
plot(m,n,'k.','markersize',1);
问题的控制方程
系统控制方程：其中，b2，b3均为常数， 分别为无量纲阻尼比，激振力幅值，激振力频率，无量纲温度及速度，这几个参数可变 方程粘不上，可打开上面的附件１ 计算图上看，在程序给定的参数下，系统做准周期运动或周期运动．请各位高手指教．
若要讨论这类问题的近似解析解，用什么方法更方便些？
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