Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators

• Published in: PloS one Vol. 11; no. 10; p. e0164669
• Main Authors: Nourmohammadi, Zahra, Joshi, Surabhi, Vengallatore, Srikar
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 13.10.2016; Public Library of Science (PLoS)
• Subjects: Algorithms; Aluminum; Aluminum - chemistry; Boundary conditions; Carbon - chemistry; Damping; Dissipation; Elasticity; Euler-Bernoulli beams; Finite difference method; Friction; Heat; Mechanical engineering; Micro-Electrical-Mechanical Systems; Microelectromechanical systems; Nonlinear analysis; Nonlinear systems; Nonlinearity; Numerical analysis; Partial differential equations; Physical Sciences; Quartz - chemistry; Resonators; Silicon - chemistry; Temperature; Zinc; New York; Canada; Montreal Quebec Canada; Quebec Canada
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0164669

The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.