Modeling simulation and analysis of engineering system

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Modeling simulation and analysis of engineering system

Hydromechanical systems are created by combining hydraulic and mechanical components, and they are used to convert the energy stored in the pressurized fluid to mechanical energy (motion and displacement).: Figure shows a simple hydraulic actuator with an input low rate Q in to the cylinder and a piston connected to the load mass.

1- Represent the different part of that engineering system and Mechanical model, by naming all the forces acting with their expression.

2- Derive the mathematical model of the hydromechanical system.

3- Write the MATLAB’s command that can help the engineer to solve this differential equation Data: m = 25Kg viscous friction b = 0.25N * m ^ – 1 * s k = 20N / m P = 100Pa Patm-75 Pa; F_{L} = 10N Fe = 15N.

4- Use MATLAB’s command to plot the evolution with time t.

5- Analyse the effect of b on the motion. Write the MATLAB’s command to plot in the same graph the evolution of vibration when b = (0N / m) / s and = (0.25N / m) / s . conclut

6- The vibration of this Hydromechanical systems is function of atmospheric pressure. Use matlab command to plot in the same graph the evolution when P atm =0 ; P atm =25 Pa; and P atm =P=100 Pa. Analyse.

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Desmond 2025-01-30T22:11:35+05:00 1 Answer 24 views Beginner
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  1. Mechanical Engineering Expert
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    2025-01-31T00:17:48+05:00
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    % Given data
    m = 25; % Mass (kg)
    b = 0.25; % Viscous friction coefficient (Nm^-1s)
    k = 20; % Spring constant (N/m)
    P = 100; % Pressure (Pa)
    Patm = 75; % Atmospheric pressure (Pa)
    FL = 10; % External load force (N)
    A = 1; % Cross-sectional area (m^2), assumed for simplicity

    % Time span
    tspan = [0 10]; % Time span for simulation

    % Initial conditions
    x0 = [0; 0]; % Initial displacement and velocity

    % Define the differential equation
    ode = @(t, x) [x(2); ((P – Patm) * A – FL – b * x(2) – k * x(1)) / m];

    % Solve the differential equation
    [t, x] = ode45(ode, tspan, x0);

    % Plot the displacement over time
    figure;
    plot(t, x(:, 1));
    xlabel(‘Time (s)’);
    ylabel(‘Displacement (m)’);
    title(‘Displacement vs Time’);

    % Analyze the effect of b on the motion
    b_values = [0, 0.25]; % Different values of b
    figure;
    hold on;
    for b = b_values
    ode = @(t, x) [x(2); ((P – Patm) * A – FL – b * x(2) – k * x(1)) / m];
    [t, x] = ode45(ode, tspan, x0);
    plot(t, x(:, 1));
    end
    xlabel(‘Time (s)’);
    ylabel(‘Displacement (m)’);
    title(‘Effect of Viscous Friction on Displacement’);
    legend(‘b = 0 N/m/s’, ‘b = 0.25 N/m/s’);
    hold off;

    % Analyze the effect of atmospheric pressure on vibration
    Patm_values = [0, 25, 100]; % Different values of Patm
    figure;
    hold on;
    for Patm = Patm_values
    ode = @(t, x) [x(2); ((P – Patm) * A – FL – b * x(2) – k * x(1)) / m];
    [t, x] = ode45(ode, tspan, x0);
    plot(t, x(:, 1));
    end
    xlabel(‘Time (s)’);
    ylabel(‘Displacement (m)’);
    title(‘Effect of Atmospheric Pressure on Displacement’);
    legend(‘Patm = 0 Pa’, ‘Patm = 25 Pa’, ‘Patm = 100 Pa’);
    hold off;

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