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Nonlinear damping and quasi-linear modelling.

S J Elliott¹, M Ghandchi Tehrani², R S Langley³

¹Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK s.j.elliott@soton.ac.uk.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|August 26, 2015

Summary

This summary is machine-generated.

Nonlinear damping significantly impacts mechanical systems. This study models nonlinear damping using an equivalent linear system, simplifying analysis for various excitations and providing physical insight.

Keywords:

nonlinear damping quasi-linear statistical linearization

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Area of Science:

Mechanical Engineering
Nonlinear Dynamics
Vibration Analysis

Background:

Nonlinear damping is a primary source of nonlinearity in many mechanical systems.
Analysis of these systems is often simplified by representing them with a quasi-linear model.
The nonlinear damping force is assumed to be proportional to the nth power of velocity.

Purpose of the Study:

To review diverse sources of nonlinear damping.
To analyze systems with nonlinear damping under sinusoidal and random excitation.
To present methods for calculating system response and equivalent linear damping parameters.

Main Methods:

Harmonic balance method (related to describing function method) for sinusoidal excitation.
Equivalent linear damper calculation for random excitation, often requiring iterative methods.
Analysis of power dissipation for validation of the quasi-linear model.

Main Results:

System response to sinusoidal excitation is often nearly sinusoidal.
Equivalent linear damper values depend on system response and require iterative calculation for random excitation.
Power dissipation of the equivalent linear damper accurately matches that of the nonlinear damper.

Conclusions:

The quasi-linear model provides a theoretically sound and physically insightful approach to analyzing systems with nonlinear damping.
This modeling simplifies the analysis of complex mechanical systems.
Applications include microspeakers, vibration isolation, energy harvesting, and the cochlea's mechanical response.