Dynamic Vibration Absorber Calculator

• •Use the Dynamic Vibration Absorber Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Dynamic Vibration Absorber Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Design a tuned mass damper: optimal absorber tuning, anti-resonance frequency, and primary system response All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

A dynamic vibration absorber (also called tuned mass damper, TMD) is a secondary mass-spring system added to a primary structure to reduce its vibration at a specific frequency. The absorber consists of a mass m_a, stiffness k_a, and sometimes damping c_a. The absorber is 'tuned' to match the problem frequency: ω_a = √(k_a/m_a) = ω_problem. At the tuned frequency, the absorber oscillates out of phase with the primary structure, exerting an opposing force that cancels the excitation. The result is that the primary structure has near-zero amplitude at the tuned frequency, while the absorber experiences large motion that is confined to it. For undamped absorbers, two new natural frequencies emerge on either side of the original (split by the absorber mass ratio μ = m_a/m_primary); the primary structure has high amplitude at these new frequencies, so the absorber is effective only over a narrow range around ω_a. Adding damping to the absorber broadens the effective range but reduces the maximum attenuation. Optimal damping balances the two new peaks and gives the lowest maximum amplitude. Den Hartog's optimal tuning: ω_a/ω_n = 1/(1 + μ) and ζ_a = √(3μ/(8(1+μ)³)). Typical mass ratios μ are 2-10% of the primary structure mass. Applications include skyscraper sway reduction (Taipei 101 has a 660-ton TMD), bridge deck vibration control, helicopter rotor vibration absorbers, and automotive crankshaft dampers.

• •Tall building wind-induced sway control: massive tuned mass dampers on top floors of skyscrapers reduce motion for occupant comfort during high winds.
• •Bridge vibration absorption: tuned mass dampers on pedestrian bridges prevent 'synchronous footfall' induced vibration (Millennium Bridge London).
• •Helicopter rotor vibration: tuned absorbers on rotor hubs cancel characteristic blade-passage vibration transmitted to the fuselage.
• •Automotive torsional vibration dampers: crankshaft dampers absorb torsional vibration from firing pulses, protecting timing gears and chain.
• •Rotating machinery isolation: secondary mass-spring absorbers reduce vibration at specific orders of shaft rotation.