Vibration control of a laminated composite plate subjected to blast loading

Anlık basınç yükü etkisi altındaki katmanlı kompozit bir plağın titreşimlerinin kontrolü

Abstract

Plates and shells are the most widely used elements in aeronautics industry and the use of layered composite materials in the manufacturing of these parts is increasing. Layered composite materials, commonly used in aerospace structures, are chosen as plate material. Still, applications of smart structures which involve the use of piezoelectric parts not only in the desired shape changes of command and control surfaces of aeronautics and space structures, but also in vibration suppression, is one of the most popular research subjects. For this reason, static and dynamical analyses of these types of structural parts are very important.In this numerical study, vibrations of a cantilever composite plate subjected to blast loading are controlled and suppressed by the use of piezoelectric actuators. The dynamic responses of structures under blast loading have been investigated in many applications. Blast loading depends on magnitude and orientation of the blast pressure, geometry and size of the surface that the shock wave encounters and on the distance from the detonation source. Commonly, Friedlander exponential decay function can be used for expressing uniform time dependent blast loading which affects object surface through normal direction. Various parameters of the equation can be obtained from some of the experimental studies.Piezoelectric materials also have been investigated in many applications. Piezoelectric elements are used for controlling and suppression as preferred widely in recent years. The development of piezoelectric composite materials offers great potential for use in advanced aerospace structural applications. For a material to exhibit an anisotropic property such as piezoelectricity, its crystal structure must have no centre of symmetry. The piezoelectric effects can be seen as transformations between electrical and mechanical energy. That is linear piezoelectric constitutive equations include electromechanical coupling.Semiloof shell finite element including piezoelectric effects is used for finite element modeling of the plate. Semiloof shell element is one of the most efficient elements for solution of shells having arbitrary geometry and it accounts for both membrane and bending actions. Three displacement degrees of freedom at the corner and mid-side nodes are sufficient for defining the membrane action. The rotations at loof nodes are necessary to impart C1 continuity and account for bending action.Stiffness, mass and damping matrices which express the structural model are obtained from the semiloof shell finite element. In order to reduce the degrees of freedom of the finite element model, mode summation method is used with weighted modal vector including dominant modes in the dynamic behavior. Calculated results of the static and dynamic analyses of the plate are compared with those modeled by using Ansys software. A good agreement is observed. After noticing the good agreement between dynamic and static analysis, state-space equations are obtained from the reduced finite element model. The system of equation must satisfy the controllability condition in order to be taken under control. If this system is also desired to be controlled by using a state observer, it must satisfy the observability condition. Optimal linear quadratic regulator (LQR) problem has been investigated to guarantee the stability of the system on the stability edge due to neglecting structural damping.In this work, both piezoelectric pairs were used as actuators. This change doubled the force used in vibration suppression. In this case the voltages applied to the piezoelectric actuators are determined by employing state observer feedback control system which estimates all states by using displacements of some specific points of the plate. Structural vibrations due to blast loading have been successfully controlled and suppressed by using a state observer feedback control system.This study will provide noteworthy supports for experimental works in this area in the future. Vibration control of plates under different loads such as random or harmonic can be investigated by using different control strategies in experimentally or numerically. The influence of different boundary conditions and addition of stiffeners to the plate on structural vibrations and vibration control can also be investigated. Furthermore, some issues like nonlinear effects on plate deformations and adding structural damping are needed to be explored.

Özet

Bu sayısal çalışmada, bir kenarından ankastre olarak mesnetlenmiş konsol bir plağın üzerine etkyen anlık basınç yükü nedeniyle oluşan titreşimler, plak üzerine yerleştirilmiş piezoelektrik uyrıcılarla kontrol edilerek sönümlenmiştir. Anlık basınç yükü modeli için zamana bağlı olarak üstel bir biçimde azalan Friedlander fonksiyonu kullanılmış ve bu fonksiyondaki parametreler için deneysel çalışmalardan elde edilen değerlerden yararlanılmıştır. Plağın sonlu eleman modelinin oluşturulması için bilinen semiloof kabuk eleman ile piezoelektrik etkilerin eklendiği semiloof kabuk sonlu eleman modeli kullanılmıştır. Sonlu eleman modelinin serbestlik derecesi yüksek olduğundan ve günümüzün modern kontrol yöntemlerinde yaygın olarak kullanılan durum denklemleriyle sistmin ifade edilmesi halinde serbestlik derecesinin ikiye katlanması nedeniyle sonlu eleman modelini indirgemek için mod toplama yöntemi ile indirgeme işlemleri yapılmıştır. Bu işlemler socunda elde edilen plak modelinin statik ve dinamik analizleri yapılmıştır. Plak aynı zamanda ANSYS yazılımı ile de modellenerek statik ve dinamik analizlerin sonuçları karşılaştırılmış ve bu sonuçların uyumluluğu gösterilmiştir. İndirgenmiş plak sonlu eleman modelinden sistemin durum denklemleri elde edilmiştir. Kararlılık sınırında bulunan sistemin kararlı olmasını garantilemek için optimum doğrusal regülatör problemi (optimal linear regulator problem, LQR) araştırılmıştır. Dyargalardan ölçülen deplasman değerlerini kullanarak sistemin durumlarını tahmin edecek göleyicili bir kontrol sistemi ile oluşan yapısal titreşimler başarılı bir şekilde kontrol edilmiş ve sönümlenmiştir.