An improved high-order theory is presented to investigate the dynamic behavior of thin and thick fiber-reinforced plastic (FRP) plates with a soft viscoelastic flexible core. Shear deformation theory is used for the face sheets while three-dimensional elasticity theory is used for the soft core. The analysis permits nonlinear distortions of the cross-sectional plane of the core as well as changes in its height. The analysis determines the damped natural frequencies, loss factors, and local and global mode shapes of plates. Some of the results are hitherto not reported in the literature based on a higher-order plate theory (HSAPT). Transverse shear and rotary inertia effects of face sheets are taken into consideration. For simply supported boundary condition, closed-form solutions are obtained by Navier’s technique. Numerical results are presented and compared with the experimental and theoretical results found in literature.

In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FO-PID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.

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A new equivalent three-degree-of-freedom (TDOF) spring–mass– damper (SMD) model has proposed to predict the low-velocity impact response of composite sandwich panels with transversely flexible core. Impacts are assumed to occur normally over the top face-sheet with the arbitrary different impactor masses and initial velocities. The interaction between the impactor and the panel is modeled with the help of a new proposed system having TDOF consisting of springs, damper, and masses. An analytical procedure that includes the transverse flexibility and structural damping of the core has not yet been dealt with. In the present model, the effects of transverse flexibility of the core and structural damping of the panel are considered analytically. The analysis yields analytic functions describing the history of contact force, displacements of the impactor and the panel in the transverse direction etc. The effects of some physical and geometrical parameters such as initial potential energy of the impactor, the aspect ratio of the panel, location of the impacted point on the panel and the material density of the core on dynamic response of composite sandwich panels have been discussed.