Nonlinear behavior in a piezoelectric resonator: a method of analysis
J E Garcia1, R Perez, A Albareda
1Dept. de Fisica Aplicada, Univ. Politecnica de Catalunya, Barcelona, Spain.
Summary
This study presents a simplified model for analyzing nonlinear piezoelectric resonator behavior across all amplitude ranges. The asymptotic method effectively captures weak nonlinearities, improving theoretical predictions and experimental agreement.
Area of Science:
- Physics
- Materials Science
- Electrical Engineering
Background:
- Existing theories for piezoelectric resonator nonlinear behavior are amplitude-limited, causing discrepancies with experimental results.
- Nonlinearities in piezoelectric materials can significantly affect device performance.
Purpose of the Study:
- To develop a generalized analytical method for understanding nonlinear behavior in piezoelectric resonators.
- To extend the analysis of nonlinearities to any nonlinear function without substantial mathematical complexity.
Main Methods:
- A simplified resonator model is employed, treating weak nonlinearities as perturbations.
- An asymptotic method is utilized to derive first and second-order perturbation terms of the system's response.
- The response is decomposed into Fourier series, and nonlinearity is modeled by specific functions added to constitutive equations.
Main Results:
- The method allows for the analysis of nonlinear behavior across a wide range of amplitudes.
- Symmetrical and antisymmetrical parts of the nonlinearity functions have distinct impacts on perturbation terms.
- The approach successfully models second harmonic generation for a specific nonlinearity.
Conclusions:
- The proposed simplified model and asymptotic method provide a robust framework for analyzing nonlinear piezoelectric resonator dynamics.
- This approach enhances the accuracy of theoretical predictions, bridging the gap between theory and experiment.
- The method is versatile and applicable to various nonlinear functions in piezoelectric systems.
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