Numerical integration of one DOF discrete gust wind model 1-minus-cosine shape. Time domain

Good morning,

i'm having some difficulties when i try to write a Matlab code for the Numerical integration of one DOF discrete gust wind model 1-minus-cosine shape, time domain.

I found something useful in the image below, i think i need a bit of help to handle the derivative inside the integral.

It's my first time here, i hope my question will respect all the rules and the netiquette of the community.

Thank you very much

Marco Ruggiero

[Benjamin Thompson]

What have you done so far? Please attach samples files to your question.

[MARCO DAVIDE ALFREDO]

I tried to write the convolution with an approximation based on the trapezoidal rule. I had some problems and errors trying to solve the differential equation with ode 45, so i tried and something similar to Euler step-by step method. The code produces some values too distant from the expected ones. Thank you very much for your help.

I posted only the final part of the script.

 % INIZIALIZZAZIONE

    z_sol = zeros(N,1); dz_sol = zeros(N,1); z_ddot = zeros(N,1);
    z_sol(1) = 0; dz_sol(1) = 0;                       

    % INTEGRAZIONE CON EULERO (PASSO PASSO)

    for i=2:N
    s_hist = s_span(1:i-1);
    z_ddot_hist = z_ddot(1:i-1);
    
    if i==2
        conv_Kw = 0;
    else
        integrand = Kw(s_span(i)-s_hist).*z_ddot_hist;
        conv_Kw = trapz(s_hist, integrand);
        if numel(conv_Kw) > 1
            conv_Kw = conv_Kw(1);
        end
    end
    
    Kg_val = Kg(s_span(i));
    if numel(Kg_val) > 1
        Kg_val = Kg_val(1);
    end
    
    acc = -(1/mu)*conv_Kw + (1/mu)*(mac/V)*Kg_val;
    
    dz_sol(i) = dz_sol(i-1) + acc*delta_s;   
    z_sol(i) = z_sol(i-1) + dz_sol(i-1)*delta_s;
    z_ddot(i) = acc;
end

Answer 1

[Supraja]

Hello Marco,

Please refer to the MATLAB documentation for writing code for integrals and differentiation which is given here: Numerical Integration and Differentiation - MATLAB & Simulink

Thanks!