Forced Vibrations and Vibration Heating of Viscoelastic Beams with Piezoelectric Sensors and Actuators

Abstract

We study the problem of forced resonant vibrations and vibration heating of flexible viscoelastic beams with piezoelectric actuators and sensors. The viscoelastic behaviors of passive (without piezoelectric effect) and piezoactive materials are described in terms of the instantaneous and complex moduli. To solve the nonlinear coupled problem of electroviscoelasticity and heat conduction, we use the method of quasilinearization together with the numerical methods of discrete orthogonalization and finite differences. We also study the influence of boundary conditions and geometric nonlinearities on the dynamic characteristics and electric parameters of a sensor and on the temperature of vibration heating of the flexible beam. For the active damping of the beams, we propose a procedure of finding the actuator parameter according to the sensor parameter for the unknown external load.