Thermo-elastic damping is a significant dissipation mechanism in high quality factor Microstructures. In this paper, thermo-elastic damping of the in-plane vibration of fully clamped Rectangular Micro-plates has been studied. The governing equation of the Micro-plate motion and heat conduction equation were derived. Then, The Galerkin method has been used to solve the coupled heat-displacement equations. Eventually, considering the Micro-plate of various materials, the effects of geometrical parameters including the length and width of Micro-plate and also ambient temperature on the thermo-elastic damping quality factor have been investigated.

In the present study, a vibration analysis of functionally graded Rectangular nano-/Microplates was considered based on modified nonlinear coupled stress exponential and trigonometric shear deformation plate theories. Modified coupled stress theory is a non-classical continuum mechanics theory. In this theory, a material-length scale parameter is applied to account for the effect of nanostructure size that earlier classical plate theories are not able to explain. The material properties of the plate were assumed to vary according to a powerlaw form in the thickness direction. The governing equation of the motion of functionally graded, Rectangular nano-/Microplates with different boundary conditions were obtained based on the Rayleigh-Ritz method using complete algebraic polynomial displacement and rotation functions. The advantage of the present Rayleigh-Ritz method is that it can easily handle the different conditions at the boundaries of moderately thick Rectangular plates (e. g., clamped, simply supported, and free). A comparison of the results with those available in the literature has been made. Finally, the effect of various parameters, such as the powerlaw index, thickness-to-length scale parameter ratio h/l, and aspect ratio a/b, on the natural frequency of nano/Micro-plates are presented and discussed in detail.

This study presents critical buckling of functionally graded soft ferromagnetic porous (FGFP) Rectangular plates, under magnetic field with simply supported boundary condition. Equilibrium and stability equations of a porous Rectangular plate in transverse magnetic field are derived. The geometrical nonlinearities are considered in the Love- Kirchhoff hypothesis sense. The formulations are compared to those of homogeneous isotropic plates were given in the literature. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are studied.

In the present paper, the behavior of steel plate shear walls (SPSWs) with stiffened full height Rectangular openings is studied. A series of single and multi-story SPSWs of various aspect ratios, with different opening features (i.e. length and horizontal location) and without openings is analyzed using the finite element method to investigate the changes in system behavior due to the introduction of openings in terms of strength, stiffness and ductility. Results show that the opening features can have an important impact on the behavior of SPSWs with the openings. The introduction of stiffened openings always reduces the infill plate strength and also the initial stiffness and ductility, while it somewhat increases the frame strength. It is found that the relative reduction in the infill plate strength as well as the relative reduction in the initial stiffness and ductility due to the introduction of the openings can be reasonably assessed based on the relative reduction in the infill plate area.

In this paper, a Rectangular sandwich plate with a constrained layer and an electrorheological (ER) fluid core is investigated. The Rectangular plate is covered an ER fluid core and a constraining layer to improve the stability of the system. The two outer layers of the sandwich structure are elastic. The viscoelastic materials express the middle layer behavior under electric field and small strain. Rheological property of an ER material, such as viscosity, plasticity, and elasticity, may be changed when applying an electric field. The ER core is found to have a significant effect on the stability of the sandwich plate. In this paper, based on the displacement field of each layer, the kinetic energy and strain energy are separately obtained for each layer. Transverse displacement of the second layer changes linearly between the transverse displacement of the first and third layers. The loss energy of the second layer consisting of the ER fluid is also calculated and, with the replacement of total kinetic energy, total strain energy, and energy dissipation in the Lagrange's equation, the structural motion equation is obtained. Natural frequencies and loss factor for the electric fields as well as the ratio of different thicknesses calculated are by Navier analytical method. As the applied electric field increases, the natural frequency of the sandwich plate increases and the modal loss factor decreases. With increasing the thickness of the ER layer, the natural frequencies of the sandwich plate are decreased. Thickness of the constrained layer also affects the stability of the sandwich plate.