كنترل فعال ارتعاشات ورق چندلايه به‌كمك حس‌گرها و عملگرهاي پيزوالكتريك

Active Vibration Control of Laminated Plate using Piezoelectric Sensors and Actuators

در اين مقاله كنترل ارتعاشات ورق چندلايه به‌كمك حس‌گرها و عملگرهاي پيزوالكتريك به بحث گذاشته شده است. معادلات حركت ورق كامپوزيت به‌همراه لايه‌هاي پيزوالكتريك با استفاده از نظريه‌ي برشي مرتبه اول، اصل هميلتون و حساب تغييرات به دست آمده است. براي حل معادلات ورق از روش عددي بدون المان گلركين استفاده شده است. در اين روش از كم‌ترين مربعات متحرك براي ساخت توابع شكل براساس توزيع نقاط در ميدان مسيله‌ استفاده مي‌شود. پس از گسسته‌سازي ميدان كرنش و ميدان الكتريكي و قرار دادن آنها در رابطه‌ي هميلتون، معادلات ديناميكي حركت ورق به دست مي‌آيد. براي تحليل پاسخ گذراي ورق از روش نيومارك استفاده شده است. پس از صحه‌گذاري مدل ساخته شده براي كنترل فعال ارتعاشات، از روش بازخورد سرعت استفاده شده و تاثير اين روش بر ميرايي و كاهش ارتعاشات ورق نشان داده شده است.

Based on the desirable properties of smart materials, many studies on the application of these materials in the field of vibration control, damage detection, shape control and buckling control have been undertaken. For the design and analysis of smart beams, plates or shells, several considerations, such as the type and number of sensors and actuators and their locations, the method of modelling, and different analyses and the types of control system, are considered. In this paper, vibration control of a laminated composite plate, with piezoelectric actuators and sensors, is investigated. Governing equations of the laminated composite plate were derived using piezoelectric constitutive equations and Hamiltonʹs principle. For modelling of the laminated plate, one of the numerical mesh-less methods; Element Free Galerkin (EFG), is used. In such methods, for discretization of a continuous field, a scattered set of particles instead of elements are distributed in the field, and the method of moving least squares (MLS) is used to construct the shape functions. In order to model the displacement and strain field of the laminated plate, the first-order shear deformation theory (FSDT) is used to consider its shear deformation effects. To verify the results, the natural frequency of isotropic and orthotropic plates with different boundary conditions was calculated and compared with other studies. The accuracy of the piezoelectric modelling is verified by calculating the displacement in different points of a bimorph piezoelectric beam in response to applying the electrical potential. After verification of the proposed method, the Newmark method is used to solve the dynamic equations of the laminated composite plate. For active vibration control of the laminated plate, a feedback control algorithm is used. The model is applied for the solution of two illustrative cases and the results are presented and discussed.