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Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators
Zahra Nourmohammadi1, Surabhi Joshi1, Srikar Vengallatore1
1Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada.
Plos One
|October 14, 2016
Summary
This study explores nonlinear thermoelastic damping (TED) in beams, revealing that thermomechanical nonlinearities significantly impact damping. The finite difference method quantifies these effects, showing variations across materials like quartz, silicon, aluminum, and zinc.
Area of Science:
- Solid Mechanics
- Materials Science
- Thermodynamics
Background:
- Linear theory of thermoelastic damping (TED) is well-established.
- Nonlinearities in TED are not well understood.
- TED arises from thermomechanical coupling within materials.
Purpose of the Study:
- To initiate the study of dissipative nonlinearities in thermoelastic damping.
- To investigate thermomechanical nonlinearities in Euler-Bernoulli beams.
- To quantify nonlinear TED effects and compare them to linear predictions.
Main Methods:
- Developed a nonlinear governing equation for TED.
- Employed the finite difference method for numerical solutions.
- Estimated nonlinear TED in Euler-Bernoulli beams.
Main Results:
- Quantified nonlinear TED for various materials.
- Observed significant differences between nonlinear and linear TED estimates.
- Maximum differences ranged from 0.06% (quartz) to 28% (zinc).
Conclusions:
- Dissipative nonlinearities play a crucial role in thermoelastic damping.
- Material properties significantly influence the magnitude of nonlinear TED effects.
- This research provides a foundation for understanding nonlinear TED in engineering applications.
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