Free Vibration Analysis of Thick Rectangular and Elliptical Plates with Concentric Cut-Out

This research paper deals with a numerical method which is modified and applied, by the authors to derive an eigenvalue of a thick plate having cut-out in which geometries of plate and cut-outs are different, through a deflection matching condition by including shear deformation and rotary inertia effects, with less computational efforts and high accuracy. The modified Independent Coordinate Coupling Method (ICCM) is validated with FEM package (ANSYS) and applied to know the change in eigenvalues for a plate with cut-out by varying various parameters like aspect ratios, cut-out size, and thickness ratios. Trigonometric functions considered at the boundary level conditions of a simply supported plate should be satisfied. Free vibrational exploration on a thick isotropic plate with various aspect ratios and an elliptical plate with various sizes is carried out through the modified ICCM. Independent coordinates are applied for a plate domain and for a hole domain individually followed by equating the deflection condition of hole and plate, a reduced mass to express with cut-out from which eigenvalues can be obtained. The deflection matching condition facilitates the analysis even though the geometries of plate and cut-outs are different.

Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

In the present work, effect of hygrothermal environment on vibration and buckling behavior of embedded functionally graded elliptical plate under uniform in plane compression is studied. The properties of elliptical plate vary in transverse direction following power law. The functionally graded elliptical plate is considered to be resting on the Winkler–Pasternak elastic foundation. The governing equations are derived using the principle of virtual work and solved by employing the Rayleigh–Ritz method. The algebraic polynomials are employed to satisfy the different boundary constraints. The advantage of the presented mathematical model over the previously reported methods is that it eliminates the constraints regarding edge conditions, and it is simple and computationally fast. The inclusive results depicting the effect of various parameters namely, material property exponents, foundation parameters, aspect ratio on mechanical and thermomechanical buckling, and natural frequency of embedded functionally graded elliptical plate in a hygrothermal environment are reported after the test of convergence and extensive comparisons. The study shows that increase in foundation moduli lead to an increase in natural frequency and buckling parameter. Furthermore, it is noticed that the temperature and moisture concentration remarkably affect the buckling and vibration behavior of functionally graded elliptical plate.

Positioning Effect on Free Convection with an Elliptical Plate Placed in a Circular Enclosure

In this analysis we have examined the process of the steady state laminar natural convection around heated elliptical plate with Rayleigh number 10^6 positioned inside a circular enclosure. The purpose of the numerical analysis is to analyze the behavior of isotherms, streamlines and heat transfer rate in enclosure plate system due to the variation in the position of elliptical plate (r/D =0.00, 0.05, and 0.2) and aspect ratio, where the given diameter of the enclosure is D and r is the distance between the centre of elliptical plate and centre of circle. Elliptical plate is inclined at different angles and results are summed up in relative manner. There are two cases, in first case aspect ratio a/D and b/D is varied and D is kept constant, whereas in second case aspect ratio a/D and b/D is kept constant and D is varied. Temperature difference between the enclosure and the inner body (i.e., temperature of inner body is kept high as compared to the enclosure) is maintained. Two dimensional study is followed by considering air as a fluid in enclosure. The effects of the Heat Transfer and Flow of Fluid are analyzed by the streamlines and isotherms plotted for the body placed inside enclosure. Value of local Nusselt number (Nu) is also plotted along the wall of elliptical plate and along the surface of the circular enclosure. For every aspect ratio isotherms and streamlines had been plotted. This work has been validated with various other numerical studies and was in good conciliation.