Active damping of the resonant vibrations of a flexible cylindrical panel with sensors and actuators

Abstract

The active damping of the resonant vibrations of a flexible cylindrical panel with rectangular planform and clamped edges is considered. The damping is done with distributed piezoelectric sensors and actuators. It is shown that the amplitude of the resonant vibrations can be substantially decreased by choosing the appropriate feedback factors. The combined effect of geometrical nonlinearity and dissipative properties of the material on the effectiveness of damping is analyzed Keywords: piezoelectric sensor, piezoelectric actuator, active damping, flexible cylindrical panel with hinged edgeIntroduction. Cylindrical panels made of passive (no piezoelectric effect) elastic and viscoelastic materials are widely used in various fields of modern engineering [5,9]. Harmonic loads with nearly resonance frequency induce intensive vibrations, which may cause failure of the panel due to fatigue or other factors. To prevent these consequences, such vibrations should be damped. Wide use is made of the passive method to damp stationary and nonstationary vibrations of a structure with elements with high hysteresis losses [6,7,10].Recent trends are toward using active methods to damp the vibrations of thin-walled structures with piezoactive inclusions [11][12][13][14][15][16][17][18][19]. There are two basic active-damping methods. One of them employs only one type of piezoelectric inclusions, so-called actuators to which a voltage is applied to balance the resonant component of the mechanical load. This voltage is calculated with classical methods (use of actuators to balance some most energy-intensive vibration modes) or optimal-control methods [12,13].The second method applies to the actuator a voltage proportional to the first derivative of the sensor voltage with respect to time. Then there is not only energy dissipation in the viscoelastic material (passive damping), but also additional damping determined by the feedback factor. Resonant vibrations, high levels of mechanical loading, and small thickness of the element may cause amplitudes comparable to the panel thickness, which requires taking geometrical nonlinearity into account.It should be noted that the modern literature on active damping pays little attention to the collective effect of geometrical nonlinearity and viscoelasticity on the effectiveness of active damping of panels. The latter is commonly described by using elementary differential models or by adding a term proportional to the derivative of the positional variable with respect to time to the equation of motion.The present paper addresses the forced harmonic vibrations of flexible cylindrical panels with rectangular planform and hinged edges. Geometrical nonlinearity is described using an elementary model that allows for squared angles of rotation. To describe the viscoelastic behavior of the material, use is made of an integral viscoelastic model [3]. To solve the problem, we will use the Bubnov-Galerkin method, which allows reducing the original nonlinear problem to a system of ordinary nonlinear inte...

Non-linear vibrations of shells: A literature review from 2003 to 2013

“…The Koltunov Rzhanitsyn singular kernel with three rheological parameters was used for the viscoe lastic model and it was observed that an increase in the concen trated mass leads to a sharp drop in the frequency and amplitude of the panel. The effect of damping on the non stationary vibra tions of a viscoelastic simply supported cylindrical panel with distributed piezoelectric sensors and actuators was investigated by Karnaukhov and Tkachenko [188]. An integral viscoelastic model was used to describe the viscoelastic behavior of the material, and the effect of viscosity and geometric non linearity on the resonant vibrations of the cylindrical panel was discussed.…”