Consider a single piezoelectric layer (plate), polarized in its thickness direction and a top and bottom electrodes with nonzero external voltages exerted on them. Do this external voltages affect the natural frequencies of the plate? If yes how? If no why?
Do they play external load role, don't affect natural frequencies?
Normally we compute the natural frequencies (mode shapes) of these types of problems in two cases (open circuited and closed circuited) but which of them are used in forced vibration analysis?
The deformation of a structure is due to the applied force and its inertia, this is why usually there is a phase shift between deformation and the exernal load. The stress generated in the piezoelectric layer depends on the deformation, this is why it cannot be seen just as an additional external load and this is why the resonance can be shifted.
But I dont know how is it possible in linear piezoelectricity. please explain more how?
Actually, sorry i think my previous explanation was wrong. In fact it seems that indeed the rigidity of the piezoelectric layer depends on electrical conditions. You can see this in a simple piezoelectri element used in compression.
Dear Mehdi,
Natural frequencies of a finite body depends on the geometric properties and elastic constants and physical constraints of the body.It is independent of externally applied voltage. The change in the applied voltage only changes the amplitude of the resonance peak not the frequency. Natural frequencies for Open and closed circuit cases of the plate differs because of the change in the elastic constant(Young's modulus) in both the conditions. There are several other factors can change the resonance frequency like thickness of the electrode, thickness of the soldering and type of lead wires and temperature. Plate does behave linearly in up to certain range of electric field and temperature.it usually depends on type of piezoelectric material used.
The externally applied load ( I mean physical load) does change the resonance behaviour of the plate beacuse of the coupled nature of piezoelectric constitute equation, geometric and elastic constants changes.
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