How to convert SDOF system to MDOF system of Nonlinear Dynamic analysis of a building

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Please, anyone help me.
  4 comentarios
Alan Stevens
Alan Stevens el 19 de Abr. de 2022
You need to provide more detail! Upload your code for the SDOF building. Specify exactly how you want to extend it - for example: to lateral as well as vertical movement? - for extra floors? - etc.

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Sam Chak
Sam Chak el 21 de Abr. de 2022
I'm not a certified Building Dynamicist. But if the equations of motion of a 4-storey building can described like this:
, with , such that
, where
function dxdt = f(t, x)
dxdt = zeros(8,1);
m1 = 4000; % kg
m2 = m1;
m3 = m2;
m4 = m3;
k1 = 5000; % N/m
k2 = k1;
k3 = k2;
k4 = k3;
% Mass matrix
M = diag([m1, m2, m3, m4]);
% Stiffness matrix
K = [k1+k2 -k2 0 0; -k2 k2+k3 -k3 0; 0 -k3 k3+k4 -k4; 0 0 -k4 k4];
% Viscous damping matrix
C = K/1e1;
% State Matrix
A = [zeros(length(M)) eye(length(M)); -M\K -M\C];
dxdt = A*x;
end
then you can solve the system using ode45 solver
tspan = [0 30]; % time span of simulation
x0 = [0.01 0.1 0.2 0.25 0 0 0 0]; % initial displacement with zero velocity
[t, x] = ode45(@(t,x) f(t, x), tspan, x0);
plot(t, x(:, 1:4), 'linewidth', 1.5)
grid on
xlabel('Time, t [sec]')
ylabel({'$x_{1},\; x_{2},\; x_{3},\; x_{4}$'}, 'Interpreter', 'latex')
title('Displacements of the building storeys')
legend({'$x_{1}$', '$x_{2}$', '$x_{3}$', '$x_{4}$'}, 'Interpreter', 'latex', 'location', 'best')
Results:
  1 comentario
Chaudhary P Patel
Chaudhary P Patel el 21 de Abr. de 2022
thank you so much@Sam Chak sir,
but sir i want to nonlinear analysis of MDOF system, for that the SDOF system i already shared.
i just want to know how can i convert it into MDOF system.
Please help me if possible or refers me to some building experts.

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