Vibration & Dynamics

Modal Analysis Simulators

A focused Vibration & Dynamics hub for modal analysis tools, keeping related formulas, assumptions, and engineering checks together.

17 simulators

Adjacent categories

Structural Analysis Mechanical Engineering Acoustics Controls & Robotics

Simulator list

Accelerometer Frequency Response Simulator
Modal Analysis
An accelerometer is itself a tiny spring-mass-damper system.
Beam Vibration Modes — Natural Frequencies & Mode Shapes
Modal Analysis
Visualize and animate natural vibration modes for beams. Superimpose modes to see combined effects and explore natural frequencies.
Chladni Figures Simulator — Vibration Modes of a Square Plate
Modal Analysis
Builds the vibration mode φ_mn(x,y) on a square plate by Ritz combination and renders Chladni nodal lines with the relative eigenfrequency. Sweep mode (m,n), mix α, and …
Damped Natural Frequency Simulator
Modal Analysis
Explore the damped free vibration of a single-degree-of-freedom mass-spring-damper system when it is displaced and released.
Drumhead Vibration Simulator — Bessel Modes of a Circular Membrane
Modal Analysis
Drumhead vibration simulator. Vary radius R, tension T, surface density ρ_s, and mode index to compute eigenfrequencies f_mn from the Bessel-zero α_mn in real time.
Eigenvalue Analysis
Modal Analysis
Interactive simulator for multi-DOF spring-mass systems. Calculate natural frequencies, visualize mode shapes with animation, and explore real-time frequency response.
Natural Frequency & Vibration Mode Calculator — Beams & Strings
Modal Analysis
Calculate beam or string natural frequencies and vibration modes. Select boundary conditions, enter properties, and view animated results instantly.
Frequency Response Function (FRF) Calculator — Bode Plot, Resonance, Damping
Modal Analysis
Calculate Frequency Response Function (FRF) Bode plots in real-time. Input natural frequency & damping ratio to get resonance, Q factor, and half-power bandwidth.
Lamb Wave Dispersion Simulator — Plate S_0/A_0 Modes
Modal Analysis
Lamb wave dispersion simulator: real-time S_0 and A_0 phase velocity and wavelength for thin plates, with adjustable Young's modulus, density, frequency and thickness.
Logarithmic Decrement Damping Simulator
Modal Analysis
Strike an object once, let it ring freely, and measure how its motion dies away. Enter the first peak amplitude and the peak n cycles later to see the logarithmic decrem…
1D FEM Modal Analysis Simulator — Natural Frequencies & Mode Shapes
Modal Analysis
Simulate 1D rod vibration modes. Assemble stiffness & mass matrices, solve eigenvalue problems, and animate mode shapes with this FEM modal analysis tool.
Modal Analysis Simulator — 2-DOF Spring-Mass System
Modal Analysis
Explore natural frequencies, mode shapes, and FRF in real time. Adjust mass and stiffness in a 2-DOF spring-mass simulator with live animations.
Parametric Oscillator Simulator — Mathieu Equation, Stability Diagram
Modal Analysis
Simulate parametric resonance with the Mathieu equation. Adjust modulation to explore stability diagrams, time-domain responses, and phase portraits.
Rayleigh-Ritz Method Natural Frequency Estimator
Modal Analysis
Visualize the Rayleigh-Ritz method: adjust an assumed mode shape and see the frequency converge. Understand the upper-bound theorem for natural vibration analysis.
Spring Constant Calculator — Coil Spring, Leaf Spring & Natural Frequency
Modal Analysis
Calculate spring constant, solid length, index, and frequency for helical and leaf springs with our free real-time calculator.
String Vibration Frequency Simulator
Modal Analysis
Find the pitch of a plucked, struck or bowed string from its length, tension and linear density. The simulator shows the fundamental frequency, mode shape, wavelength, p…
Torsional Pendulum Simulator — Natural Frequency & Period Calculator
Modal Analysis
Simulate torsional pendulums. Adjust shaft & disk parameters to instantly compute natural frequency, stiffness, and period. Visualize oscillations.

How to Use

  1. Select structural component type (beam, plate, shell, or assembled frame) from the category filter dropdown
  2. Input material properties: Young's modulus (GPa), density (kg/m³), and damping ratio (%). For steel, use E=210 GPa and ρ=7850 kg/m³
  3. Define geometry: span length (m), cross-sectional dimensions, boundary conditions (fixed-free, simply-supported, clamped-clamped), and mesh density
  4. Run simulation to compute natural frequencies (Hz), mode shapes, and participate mass percentages for the first 12 modes
  5. Export mode data as CSV for harmonic response or random vibration follow-on analysis

Worked Example

Steel cantilever beam: L=1.5 m, rectangular section 50×10 mm, E=210 GPa, ρ=7850 kg/m³, damping=2%. Fixed-free boundary yields first mode at 8.7 Hz (transverse bending), second mode at 54.3 Hz (first overtone). Participating mass for mode 1 is 73% of total beam mass in vertical direction. If excitation occurs at 8.7 Hz with 0.5g amplitude, resonant amplification factor Q ≈ 25 in low-damping regime, producing displacement peaks around 12 mm at mid-span.

Practical Notes

  1. Always validate first three natural frequencies against hand-calculation formulas (Rayleigh, Dunkerley) before trusting complex geometry results; discrepancies >5% signal meshing or material input errors
  2. For welded structures, reduce effective Young's modulus by 8–12% and increase damping to 3–5% to account for joint compliance and weld discontinuities
  3. Rotating machinery excitation typically couples to 1× and 2× running speed; use cat-filter to isolate blade-pass frequencies and avoid coincidence with structural modes within ±10%
  4. Modal density increases rapidly above 500 Hz in stamped sheet metal; use frequency range limits to focus on design-critical bands for NVH optimization