Stochastic micro-vibration response of a spherically symmetric piezoelectric shell structure as sensor

The micro-vibration monitoring and control of vibration-sensitive precision facilities are important and the accurate measurement of micro-vibrations is necessary. The piezoelectric sensors such as piezoelectric shell structure have better electrical-mechanical coupling properties and less effect of bulk and weight. This paper studies the response characteristics of an interceptive spherical piezoelectric shell under stochastic boundary micro-vibration excitations. The equation for electric potential is integrated, and the displacement is transformed and expanded to yield the ordinary differential equations for the shell. The frequency-response function, power spectral density and correlation function matrices of the shell system response are derived. Then the root-mean-square displacement, stress and electric potential of the piezoelectric shell can be calculated. The numerical results are given to illustrate the stochastic electrical-mechanical coupling properties and the relation between boundary electric potential responses and micro-vibration excitations.