Add example to demonstrate base excitation with multiple TimeFunctions.

examples/dynamics/discretemassspringdamper/example_dynamic_tms4.m

+%% Example Kelvin-Voigt mass system
+% Two masses connected by rheological devices, one mass constrained by Dirichlet
+addpath([ '..' filesep '..' filesep '..' filesep ]);
+%% Definition of sections
+s1 = mafe.Section0D();
+s1.k  =  4.0; % [N/m]
+s1.d  =  0.1; % [Ns/m]
+s2 = mafe.Section0D();
+s2.m  =  1.0; % [Ns^2/m]
+%% Definition of time functions: Omega, factor_cosine, factor_sine
+tfuns = mafe.TimeFunction.empty(0,0);
+% define a spectrum of excitation
+K = 80;
+% chosen frequencies
+Omegas = linspace(0,8,K);
+% chosen amplitudes
+% Amplit = logspace(-2,-6,K); % == 'push over'
+Amplit = 0.5 * [Omegas == 0.5 + min(abs(Omegas-0.5))]; % pronounce single frequency sharply == 'harmonic'
+% Amplit = 1.e-3 * Omegas./((Omegas-0.5).^2 + 0.005); % pronounce single frequency smoothly == 'harmonic'
+% Amplit = 1.e-3 * Omegas./(((Omegas-1.0).*(Omegas-3.0)).^2 + 0.05); % pronounce certain frequencies == 'harmonic'
+% set time functions
+for ii = 1:K
+  tfuns(end+1) = mafe.TimeFunction( Omegas(ii), 0.0, Amplit(ii) ); % time function = A*sin(Omega*t)
+end
+%% Definition of nodes in the system
+% Node 1
+n1 = mafe.Node1D( [0.5] );
+% Node 2
+n2 = mafe.Node1D( [1.5] );
+% Vector of nodes
+nodes = [ n1, n2 ];
+%% Definition of elements in the system
+% Element 1
+e1 = mafe.RheoKelvinVoigt1D( [n1, n2], s1 );
+% Element 2
+e2 = mafe.Point( n2, s2 );
+% vector of elements
+elems = [ e1, e2 ];
+%% Definition of constraints in the system
+const = mafe.Constraint.empty(0,0);
+for tf = tfuns
+  const(end+1) = mafe.ConstraintNode( n1, mafe.DofType.Disp1, mafe.ConstraintType.Dirichlet, 1.0, tf ); % [m]
+end
+%% Setup of the finite element problem
+fep = mafe.FeProblem( nodes, elems, const );
+%% Select an analysis type: dynamic
+ana = mafe.FeAnalysisDynamicFD( fep, tfuns );
+%% Calculate response
+ana.analyse();
+%% Obtain amplification matrix
+V = ana.Z(:,2:end);
+
+%% --- Inspect results
+
+%% Show
+%   - excitation spectrum of the prescibed base displacement u(t) at n1
+%   - response spectrum of the resulting displacement u(t) at n2
+fig = figure(1); clf; subplot('Position',[0.10 0.10 0.80 0.85]); hold on;
+plot(Omegas,[Amplit; abs(Amplit.*V)], '.-');
+xlim([ 0 8]);
+grid;
+legend('|A_k| of u_{n1}(t)', '|A_k| of u_{n2}(t)');
+xlabel('excitation frequency \Omega_k [rad/s]');
+ylabel('amplitude of displacement u_k = A_k * sin(\Omega t) [m]');
+
+%% Show relative amplifications due to forced vibration
+fig = figure(2); clf; subplot('Position',[0.10 0.10 0.80 0.85]); hold on;
+plot(Omegas,abs(V), '.');
+xlim([ 0 8]);
+ylim([-4 4]);
+grid;
+legend('u_{n1} = prescribed', 'u_{n2} = resulting');
+xlabel('excitation frequency \Omega [rad/s]');
+ylabel('amplification of natural coordinate (displacement) [-]');
+
+% Show the system response (total solution for given initial conditions)
+fig = figure(3); clf; subplot('Position',[0.10 0.10 0.80 0.85]); hold on;
+% apply initial conditions
+u0 = zeros(fep.ndofs,1);
+v0 = zeros(fep.ndofs,1);
+ana.applyInitialConditions( u0, v0 );
+% evaluate and plot for given time instants
+u_h = [];
+u_p = [];
+time = 0:0.1:pi*50; % first undamped eigenfrequency is omega = 2 [rad/s] -> T = 2pi/omega = 3.14 [s]
+for tt = time
+    ana.putSolToDof(tt, 'homogeneous');
+    u_h(:,end+1) = [n1.lhs( find( n1.dof == mafe.DofType.Disp1 ) ), n2.lhs( find( n2.dof == mafe.DofType.Disp1 ) )];
+    ana.putSolToDof(tt, 'particular');
+    u_p(:,end+1) = [n1.lhs( find( n1.dof == mafe.DofType.Disp1 ) ), n2.lhs( find( n2.dof == mafe.DofType.Disp1 ) )];
+end
+plot(time,[u_p; u_h+u_p], '-');
+xlim([ time(1) time(end)]);
+grid;
+legend('u_p(t) at n1 = prescribed', 'u_p(t) at n2 = resulting', 'u(t) at n1 = prescribed', 'u(t) at n2 = resulting');
+xlabel('time [s]');
+ylabel('natural coordinate (displacement) [m]');
+
+% % Visualise system response (total solution for given initial conditions)
+% fig = figure(4); clf; subplot('Position',[0.05 0.05 0.90 0.90]); axis equal; hold on;
+% % apply initial conditions
+% u0 = zeros(fep.ndofs,1);
+% v0 = zeros(fep.ndofs,1);
+% ana.applyInitialConditions( u0, v0 );
+% % evaluate and plot for given time instants
+% time = 0:0.1:pi*50; % first undamped eigenfrequency is omega = 2 [rad/s] -> T = 2pi/omega = 3.14 [s]
+% for tt = time
+%     ana.putSolToDof(tt);
+%     fig = figure(4); clf; hold on;
+%     xlim([0 2.5])
+%     ylim([-0.25 0.25])
+%     fep.plotSystem('reference');
+%     fep.plotSystem('deformed');
+%     text(2.0,0.2,sprintf('t = %2.3f s', tt));
+%     drawnow;
+% end