Vibration & Dynamics Simulators

Change the damping ratio and natural frequency to draw resonance curves in real time. Supports overlay of multiple zeta values.

Calculate response sigma_rms and 3-sigma from PSD input using Miles' equation. Display input/response PSDs overlaid on a log-log plot.

Real-time display of frequency response for 2-DOF coupled vibration and the optimal tuning effect of a Tuned Mass Damper (TMD).

Display design response spectra (Sa/Sv/Sd) by damping ratio and soil type. Fundamentals for seismic isolation and vibration control design.

Back-calculate optimal mount stiffness from equipment mass and excitation frequency. Confirm isolation effectiveness on a TR vs. frequency ratio log plot.

Animate single-DOF vibration by adjusting spring constant, mass, and damping coefficient. Experience underdamped, critically damped, and overdamped responses in real time.

Calculate suspension response to road input using a quarter-car model. Visualize the trade-off between ride comfort and handling stability.

Calculate equivalent stiffness and static displacement for series, parallel, and compound spring systems. Simulate free and forced vibration time history.

Numerically solve the eigenvalue problem of multi-DOF systems to find natural frequencies and mode shapes. Animated mode shape display included.

Estimate the lowest natural frequency of multi-DOF systems using the Rayleigh quotient. Select assumed mode shapes and verify accuracy.

Calculate seismic response of structural systems via direct integration. Compute peak response displacement, acceleration, and inter-story drift for design earthquakes.

Compute nonlinear frequency response of the Duffing oscillator. Visualize hardening/softening springs, jump phenomena, and backbone curves.