Many of mechanical systems are exposed to undesired vibrations, so designing an active vibration control (AVC) system is important in engineering decisions to reduce this vibration. Smart structure technology is used for vibration reduction. Therefore, the cantilever beam is embedded by a piezoelectric (PZT) as an actuator. The optimal LQR controller is designed that reduce the vibration of the smart beam by using a PZT element.  

In this study the main part is to change the length of the aluminum cantilever beam, so keep the control gains, the excitation, the actuation voltage, and mechanical properties of the aluminum beam for each length of the smart cantilever beam and observe the behavior and effec

The deployment of UAVs is one of the key challenges in UAV-based communications while using UAVs for IoT applications. In this article, a new scheme for energy efficient data collection with a deadline time for the Internet of things (IoT) using the Unmanned Aerial Vehicles (UAV) is presented. We provided a new data collection method, which was set to collect IoT node data by providing an efficient deployment and mobility of multiple UAV, used to collect data from ground internet of things devices in a given deadline time. In the proposed method, data collection was done with minimum energy consumption of IoTs as well as UAVs. In order to find an optimal solution to this problem, we will first provide a mixed integer linear programming m

    This paper  concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.  

     This paper deals with the numerical solution of the discrete classical optimal control problem (DCOCP) governing by linear hyperbolic boundary value problem (LHBVP). The method which is used here consists of: the GFEIM " the Galerkin finite element method in space variable with the implicit finite difference method in time variable" to find the solution of the discrete state equation (DSE) and the solution of its corresponding discrete adjoint equation, where a discrete classical control (DCC) is given.  The gradient projection method with either the Armijo method (GPARM) or with the optimal method (GPOSM) is used to solve the minimization problem which is obtained from the necessary conditi

"This paper presents a study of inclined magnetic field on the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative between two inclined infinite circular cylinders through a porous medium. The analytic solutions for velocity field and shear stress are derived by using the Laplace transform and finite Hankel transform in terms of the generalized G functions. The effect of the physical parameters of the problem on the velocity field is discussed and illustrated graphically.

     The time fractional order differential equations are fundamental tools that are used for modeling neuronal dynamics. These equations are obtained by substituting the time derivative of order  where , in the standard equation with the Caputo fractional formula. In this paper, two implicit difference schemes: the linearly Euler implicit and the Crank-Nicolson (CN) finite difference schemes, are employed in solving a one-dimensional time-fractional semilinear equation with Dirichlet boundary conditions. Moreover, the consistency, stability and convergence of the proposed schemes are investigated. We prove that the IEM is unconditionally stable, while CNM is conditionally stable. Furthermore, a comparative study between these two s

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions.