Abstract
A control optimization problem for functionally graded (FG) plates is presented using a first-order shear deformation plate theory including through-the-thickness normal strain effect. The aim of the optimization is to minimize the vibrational response of FG plate with constraints on the control energy used in the damping process. An active control optimization is presented to determine the optimal level of a closed loop control function. Plate thickness and a homogeneity parameter of FG plates are used as design variables. Numerical results for the optimal control force and the total energy for a simply supported FG plate are given. The influence of through-the-thickness normal strain effect on the accuracy of the obtained results is illustrated. The effectiveness of the present control and design procedure is examined.
Highlights
The rapid development in various industrial fields requires new materials that can serve useful functions under certain conditions
Functionally graded materials (FGMs) have gained considerable attention in many engineering applications, and they are considered as a potential structural material for future high-speed spacecraft and power generation industries
Most studies related to the topic of design and control optimization of composite plates and shells were carried out based on classical theories which neglect the shear deformation and normal strain effects
Summary
The rapid development in various industrial fields requires new materials that can serve useful functions under certain conditions. In another work of Fares et al [17], nonlinear optimization schemes are presented to solve multiobjective design and control problems for composite laminated plates Other studies on this topic may be found in [18, 19]. Most studies related to the topic of design and control optimization of composite plates and shells were carried out based on classical theories which neglect the shear deformation and normal strain effects. The present formulation is based on a first-order theory including a normal strain and shear deformation effects derived using a mixed variational approach. This theory preserves the transverse shear stresses which vanish on the top and the bottom of the plate surfaces; the condition of introducing shear correction factors is not required.
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