Two DoF Non linear mass spring damper system with lookup tables, help with ODE

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Paolo 2016-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/279459-two-dof-non-linear-mass-spring-damper-system-with-lookup-tables-help-with-ode

评论： Mischa Kim 2016-7-13

Hi everybody, that's my first time writing here, so I apologize in advance for any mistake.

I'm trying to integrate the mathematical model of a landing gear drop test, modeled as a two dof mass spring damper system. The system and the two free body diagram are the following:

I wrote the system as 4 eq. one order, using some lookup table to solve the non-linearities:

      function [ yp ] = sistema_interpolato( t, y, D, z_s, z_inf, m1, m2, delta_ref, F_el_sa_ref, deltadot_ref, F_damp_sa_ref,delta_tyre_ref, F_el_tyre_ref)
      x1 = y(1);
      x2 = y(2);
      x1dot = y(3);
      x2dot = y(4);
      delta_sa = z_inf - (x1-x2); % with z_inf that's the 0-force distnace between x1 and x2
      F_el_sa = interp1(delta_ref,F_el_sa_ref,delta_sa);
      deltadot_sa = x2dot - x1dot; % compression/extension speed 
      F_damp_sa = interp1(deltadot_ref, F_damp_sa_ref, deltadot_sa); 
      delta_tyre = D/2 - x2; % tyre compression, with D = tyre diameter
      F_el_tyre = interp1(delta_tyre_ref, F_el_tyre_ref, delta_tyre);
      yp(1,1) = x1dot; % x1dot
      yp(2,1) = x2dot; % x2dot
      yp(3,1) = (1/m1) * (-m1*9.81 + F_el_sa + F_damp_sa); % x1dotdot
      yp(4,1) = (1/m2) * (- F_el_sa - F_damp_sa + F_el_tyre); % x2dotdot

then I try to integrate with all ODEs solver in matlab and with an Euler fwd method implemented by me, obtaining always this warning:

Warning: Failure at t=3.909016e-02. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.110223e-16) at time t.

with t variable, depending on the time interval and the initial conditions (5,5,-3.7,-3.7).

Does anyone have any idea?

For this project I cannot use simulink unfortunately.

Thank you very much in advance :)

Grazie Mille!

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Mischa Kim 2016-7-13

Paolo, please attach a copy of the derived differential equations and the entire code. My first guess would be a sign error in your equations that result in an unstable system.

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Two DoF Non linear mass spring damper system with lookup tables, help with ODE

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