كنترل فعال ارتعاشات ورق مستطيلي با استفاده از سري فوريه و تبديل لاپلاس

ACTIVE CONTROL OF VIBRATIONS OF A RECTANGULAR PLATE USING FOURIER SERIES AND LAPLACE TRANSFORM

In this research, active control of vibrations of a simply supported rectangular plate is investigated by a new method. At first, differential equation of motion of a plate with piezoelectric patches is developed by means of classical plate theory in order to apply in this method, and a local function is used for applying the mass and stiffness effects. Then, natural frequencies and modeshapes of the plate with patches are obtained using Fourier series. A PID controller is designed and closed loop poles are calculated. Forced response of the system and mode shapes will be calculated using Laplace transform. The effect of PID on active control of plate is investigated simply for the first time. Some examples are presented to illustrate the validity of this method.