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

Please, anyone help me.

[Sam Chak]

@Chaudhary P Patel

I tried searching "SDOF()" and "MDOF()" in the Documentation, but there are no such functions.

Are they newly-added functions in the latest MATLAB release? If you wrote those functions and need help for invesgation, please post the MATLAB code so that people understand your question well.

Is your question technically related to MATLAB?

Are you using specific toolboxes to solve the conversion problem in your Nonlinear Dynamical System?

Who are your target specific audiences with your question related to "SDOF" and "MDOF" in MATLAB? For example, are you looking for a Building Dynamicist, who may understand the abbreviations of "SDOF" and "MDOF"?

[Chaudhary P Patel]

SDOF = single degree of freedom system

MDOF= multi-degree of freedom system

The problem is related to the Nonlinear analysis of building.

[Alan Stevens]

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.

[Chaudhary P Patel]

@Alan Stevens sir, please reply me.

@Sam Chak

Answer 1

[Sam Chak]

@Chaudhary P Patel

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:

[Chaudhary P Patel]

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.