Forced resonance vibrations and dissipative heating of a flexible viscoelastic beam with piezoelectric actuators

We consider the problem of the forced resonance vibrations and dissipative heating of a viscoelastic beam with piezoelectric actuators with regard for geometric nonlinearity in the quadratic approximation. The viscoelastic behavior of passive (without the piezoelectric effect) and piezoactive materials is described in terms of instantaneous and complex moduli. To solve the nonlinear problem of electroviscoelasticity and heat conduction, we use the method of quasilinearization together with the numerical methods of discrete orthogonalization and finite differences. We have studied the influence of geometric nonlinearity on the dynamic characteristics, temperature of vibration heating, and active damping of a beam with using a piezoelectric actuator.