Mass-Spring-Damper Simulation of Polymer Viscoelastic Model in Stress Relaxation Tests

Project info

• Field of studyChemistry and Materials
• LevelMaster's thesis (S2)
• Method typeNumerical Simulation
• Estimated build time± 5 working days
• Toolsode45, islocalmax (MATLAB inti)
• PriceUS$28 - US$178

Research goal

Simulate polymer strain as a mass-spring-damper system and assess the influence of spring modulus and damper viscosity.

Variables

Example result

• 8.533Natural freq. (rad/s)
• 0.119Damping ratio
• 0.039Steady amplitude
• 0.058Resonance peak
• 8.405Resonance freq. (rad/s)
• 1.13Energy dissipated

The mass-spring-damper system (natural frequency 8.53 rad/s, damping ratio 0.119) reaches a steady amplitude of 0.039 in Polymer strain under 9.50 rad/s forcing; the resonance peak of 0.06 occurs at 8.40 rad/s.

Computed from illustrative synthetic data, not from a real study.

About Mass-Spring-Damper Simulation

A mass-spring-damper simulation models the vibration of a second-order mechanical system with mass, stiffness, and damping. It is used for vibration analysis, vehicle suspension, and dynamic model validation in mechanical engineering theses.

Steps

1. 1Define mass m, stiffness k, damping c, and external force
2. 2Write the equation of motion as a state system [x; v]
3. 3Simulate with ode45
4. 4Compute natural frequency, damping ratio, and damped frequency
5. 5Verify the oscillation period from the simulation
6. 6Plot displacement, velocity, and the phase portrait

Assumptions to check

• Linear model with constant parameters
• Friction is viscous only
• Parameter units are consistent (SI)

Reading and reporting the results

Report parameters, natural frequency, damping ratio, and simulated versus theoretical oscillation period. Discuss how changes in c and k affect the response.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

m = 2;  k = 200;  c = 6;                            % mass, stiffness, damping
wn = sqrt(k/m);  zeta = c / (2*sqrt(k*m));  wd = wn*sqrt(1 - zeta^2);
fprintf('wn = %.2f rad/s, zeta = %.3f, damped period = %.4f s\n', wn, zeta, 2*pi/wd);

F = @(t) 0;                                         % free vibration
f = @(t, y) [y(2); (F(t) - c*y(2) - k*y(1)) / m];
[spring_modulus, polymer_strain] = ode45(f, [0 3], [0.05; 0], odeset('RelTol', 1e-8));

pk = islocalmax(polymer_strain(:,1));
tp = spring_modulus(pk);
fprintf('Simulated period: %.4f s\n', mean(diff(tp)));

figure;
subplot(1,2,1);
plot(spring_modulus, polymer_strain(:,1), 'LineWidth', 1.2); hold on;
plot(spring_modulus, 0.05*exp(-zeta*wn*spring_modulus), 'r--', spring_modulus, -0.05*exp(-zeta*wn*spring_modulus), 'r--');
xlabel('Time (s)'); ylabel('Displacement (m)');
subplot(1,2,2);
plot(polymer_strain(:,1), polymer_strain(:,2)); xlabel('x'); ylabel('v'); title('Phase portrait');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions