echo off
%	tdof_modal_time.m	hand solution of modal equations
%	Plots displacements versus time in principal and physical coordinates.

	clf;

	clear all;

%	define time vector for plotting responses

	t = linspace(0,10,50);

%	solve for and plot the modal displacements

	zp1 = (-t.^2/(2*sqrt(3))) - sqrt(3)*t/3;

	zp2 = 3*sqrt(2)/2 - (3*sqrt(2)/2)*cos(t) - (sqrt(2)/2)*cos(t) + (sqrt(2)/2)*sin(t);

	zp3 = (sqrt(6)/6)*((-1/3) + (1/3)*cos(sqrt(3)*t) + 3*cos(sqrt(3)*t) - (7/sqrt(3))*sin(sqrt(3)*t));

	plot(t,zp1,'k+-',t,zp2,'kx-',t,zp3,'k-')
	title('Displacements in Principal Coordinate System')
	xlabel('Time, sec')
	ylabel('Displacements')
	legend('zp1','zp2','zp3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause

	axis([0 1 -2 2])

	disp('execution paused to display figure, "enter" to continue'); pause

%	define the normalized modal matrix, m = 1

	zn = [1/sqrt(3)  1/sqrt(2)  1/sqrt(6)
		  1/sqrt(3)     0	   -2/sqrt(6)
		  1/sqrt(3) -1/sqrt(2)  1/sqrt(6)];

%	define the principal displacement matrix, column vectors of principal displacements
%	at each time step

	zp = [zp1; zp2; zp3];

%	multiply zn times zp to get z

	z = zn*zp;

	z1 = z(1,:);
	z2 = z(2,:);
	z3 = z(3,:);

	plot(t,z1,'k+-',t,z2,'kx-',t,z3,'k-')
	title('Displacements in Physical Coordinate System')
	xlabel('Time, sec')
	ylabel('Displacements')
	legend('z1','z2','z3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause

%	define the motion of each each dof for each mode, zij below refers to the
%	motion of dof "i" due to mode "j"

	z11 = zn(1,1)*zp1;

	z12 = zn(1,2)*zp2;

	z13 = zn(1,3)*zp3;

	z21 = zn(2,1)*zp1;

	z22 = zn(2,2)*zp2;

	z23 = zn(2,3)*zp3;

	z31 = zn(3,1)*zp1;

	z32 = zn(3,2)*zp2;

	z33 = zn(3,3)*zp3;

	plot(t,z11,'k+-',t,z12,'kx-',t,z13,'k-')
	title('Displacement of dof 1 for Modes 1, 2 and 3')
	xlabel('Time, sec')
	ylabel('Displacements')
	legend('Mode 1','Mode 2','Mode 3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause

	plot(t,z21,'k+-',t,z22,'kx-',t,z23,'k-')
	title('Displacement of dof 2 for Modes 1, 2 and 3')
	xlabel('Time, sec')
	ylabel('Displacements')
	legend('Mode 1','Mode 2','Mode 3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause

	plot(t,z31,'k+-',t,z32,'kx-',t,z33,'k-')
	title('Displacement of dof 3 for Modes 1, 2 and 3')
	xlabel('Time, sec')
	ylabel('Displacements')
	legend('Mode 1','Mode 2','Mode 3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause

%	define the motion of each each dof with the rigid body motion for that
%	mode subtracted

	z1vib = z1 - z11;

	z2vib = z2 - z21;

	z3vib = z3 - z31;

	plot(t,z1vib,'k+-',t,z2vib,'kx-',t,z3vib,'k-')
	title('Displacements of dof 1, 2 and 3 with Rigid Body Removed')
	xlabel('Time, sec')
	ylabel('Vibration Displacements')
	legend('dof 1','dof 2','dof 3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause
	
	tplot = t;

	plot(tplot,z1,'k+-',t,z2,'kx-',t,z3,'k-')
	title('Displacements of dof 1, 2 and 3')
	xlabel('Time, sec')
	ylabel('Vibration Displacements')
	legend('dof 1','dof 2','dof 3',3)
	grid

	disp('execution paused to display figure, "enter" to continue'); pause

	save tdof_modal_time_z1z2z3  tplot z1 z2 z3