Nonlinear vibro-acoustic behaviour in a circular membrane oscillator

Abstract

Oscillating systems that produce noise at a frequency of excitation may have as an abatement solution the increase of the frequency of excitation to above the audible frequency limit, viz. 20kHz. This approach may not be possible for systems subject to non-linear behavior as subharmonics can be generated within the audible range. This paper describes the analysis of a small metal annulus over which a thin membrane is stretched. The membrane is indirectly excited via a piezoelectric transducer attached to the annulus and has an application as an appliance in the electronics sector. The generation of noise is unwanted but found to occur occasionally. The analysis confirms the non-linear behaviour of the system with sub-harmonics resulting from a non-linear interaction with a low natural frequency. An experimental technique using a 2-D Scanning Laser Vibrometer (Polytec PSV-400) allows the vibrational modes of the annulus and membrane to be measured as a function of frequency and presented graphically and demonstrates the membrane to be radiating the noise. The paper discusses with the aid of both an analytical and numerical solution to the Duffing Equation how an increase in damping will suppress the sub-harmonics. A practical damping solution is found for the design which successfully eliminates the noise without negatively effecting its performance.