Frequency Response Analysis of Diaphragm for Small Earphone Supported by Nonlinear Springs with Hysteresis Using Finite Element Method

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For small earphones, this paper describes vibration analysis using three-dimensional finite element method for elastic diaphragm supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the springs have cubic nonlinearity. Finite element for the nonlinear springs with hysteresis are expressed and are connected to the elastic diaphragm modeled by linear solid finite elements in consideration of complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. Harmonic balance method is applied to the equations to obtain nonlinear resonance responses. This transformation yields computation efficiency. The calculated resonance responses by the proposed method are verified by experimental responses. In the experiment, the earphone's diaphragm displacement and the envelope response are measured using a laser displacement meter.