%周期支撑梁色散关系
%弹性支撑(广义状态向量传递矩阵法)
clc
clear
for n=1:1:1000
w=n*10;
wb(n)=w/(2*pi);
E=2.1e11;
I0=3217e-8;
A=77.45e-4;
dens=7850;
m=dens*A;
kn=2e6; %纵向弹簧
l=0.625; %轨枕间距
lam5=w*(dens/E)^0.5; %纵波 波数公式
TM=[1 0
kn 1]; %扣件两段传递矩阵
TM0=[1 0
kn 1];
TL=[cos(lam5*l) sin(lam5*l)/(E*A*lam5)
-lam5*E*A*sin(lam5*l) cos(lam5*l)]; %传递L距离的状态向量传递矩阵
I=eye(2);
T=TM*TL; %相邻周期的传递矩阵
TT=T;
t1(:,n)=eigs(TT); %特征向量特征值
k(:,n)=((log(t1(:,n))*i/l)); %T-EXP(-ikl）=0公式的解
end
figure1 = figure('Color',[1 1 1]);
plot(abs(real(k(2,:))),wb,'-',abs(real(k(1,:))),wb,'-');
title('弹性点支撑模型');
legend('色散曲线');
grid on;
ylabel('频率w');
xlabel('波数k');
figure1 = figure('Color',[1 1 1]);
plot(wb,abs(imag(k(2,:))),'-',wb,abs(imag(k(1,:))),'-');
title('弹性点支撑模型');
legend('衰减曲线');
grid on;
ylabel('衰减率');
xlabel('频率w');
%坐标轴上点连线程序（两条）
x=[0.00,0.02,0.04,0.06,0.08,0.10];
y=[70,71.6,73.2,74.8,76.4,76.4];
plot(x,y,'-ks','MarkerFaceColor','b','MarkerSize',10)
axis([0,0.10,65,80]);
hold on;
u=[1,2,3,4,5];
v=[187.35,219.4,244.8,267.1,286.2];
plot(u,v,'-ks','MarkerFaceColor','r','MarkerSize',10)
axis([0,6,50,300]);
grid on;
%三条 一阶 二阶起始or截止频率
%坐标轴上点连线程序（两条）
x=[0.00,0.02,0.04,0.06,0.08,0.10];
y=[165,168.07,168.7,171.9,175.1,178.3];
plot(x,y,'-ks','MarkerFaceColor','b','MarkerSize',5)
axis([0,0.12,100,1800]);
hold on;
u=[0.00,0.02,0.04,0.06,0.08,0.10];
v=[1047,1106,1170,1238,1313,1396];
plot(u,v,'-ks','MarkerFaceColor','r','MarkerSize',5)
axis([0,0.12,100,1800]);
hold on;
m=[0.00,0.02,0.04,0.06,0.08,0.10];
n=[1112,1170,1233,1302,1375,1456];
plot(m,n,'-ks','MarkerFaceColor','y','MarkerSize',5)
axis([0,0.12,100,1800]);
grid on;
xlabel('扣件宽度（m）');
ylabel('频率（Hz)');
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