FREE-VIBRATION ANALYSIS OF RIGHT TRIANGULAR PLATES WITH VARIABLE THICKNESS

FREE VIBRATION ANALYSIS OF RECTANGULAR PLATES WITH VARIABLE THICKNESS

Vibration of arbitrarily-shaped triangular plates with elastically restrained edges

FREE VIBRATION OF ORTHOTROPIC SQUARE PLATES WITH A SQUARE HOLE

Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method

Thermal analysis has been performed in this work on a different designs of fin in order to investigate the temperature distribution, heat flux, and thermal stresses using ANSYS workbench. For this work total nine designs of fin have been created such as rectangular plate fin, rectangular plate fin with hole, rectangular perforated fin, rectangular plate fin with slot, rectangular plate with pin inserted fin, rectangular plate inserted pin with hole fin, triangular plate fin, triangular plate with perforated fin & triangular plate fin with slot. Aluminum 1060 is used as a material for all designs of fin, The 13 W of heat supply at the bottom of the fin have been applied which is equal to the power supply at ambient temperature of 22 oC. Results show that the 48.76 oC is the lowest temperature for the rectangular plate inserted pin with hole fin which is 8.9% lower than the plane rectangular plate fin and the 51.67 oC is the lowest temperature for the rectangular plate fin with hole which is 5.5% lower than the plane rectangular plate fin while the 0.0378 W/mm2 is the lowest temperature for the triangular plate fin with slot which is 3.5 times greater than the plane rectangular plate fin. The 7.3 degree is the highest temperature difference for the rectangular perforated fin which is 4.2 times higher than the plane rectangular plate fin and the 0.0276 MPa is the lowest thermal stress for the rectangular plate fin with hole & triangular plate with perforated fin which is 5.74 times lower than the plane rectangular plate fin. Hence the rectangular plate inserted pin with hole fin is suggested for better heat transfer.

An approximate method is extended for analyzing the free vibration problem of simply supported orthotropic square plate with a square hole. In this paper, a square plate with a square hole is transformed into an equivalent square plate with non-uniform thickness byconsidering the hole as an extremelythin part of the equivalent plate. Therefore, the dynamic characteristics of a plate with a hole can be obtained by analyzing the equivalent plate. The Green function, which is the discrete solution for the deflection of the equivalent plate, is used to obtain the characteristic equation of the free vibration. The effects of the side to thickness ratio, hole side to plate side ratio and the variation of the thickness on the frequencies are considered. Some numerical analyses are carried out for the simplysupported orthotropic square plate with a square hole. The efficiency and accuracyof the numerical solutions bythe present method are investigated.

CHAPTER 5 - Vibrations of Plates and Shells

Natural frequencies of thin rectangular plates using homotopy-perturbation method

Chapter 4 - Vibration of Plates

Large amplitude free flexural vibrations of thin plates of arbitrary shape

Study on flexural vibration of triangular composite plates influenced by fibre orientation

Analysis of stress concentration in isotropic and orthotropic plates with hole under uniformly distributed loading conditions

This investigation is concerned with the notion of concentrated loads in classical elastostatics and related issues. Following a limit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and stress singularities, as well as the stress resultants of the latter, are determined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theorem. In addition, the present work supplies a reciprocal theorem and an integral representation-theorem applicable to singular problems of the type under consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended.

Forced vibrations of a rectangular plate with non-uniform thickness

Artificial boundary conditions, which can be identified as Robin boundary conditions positioned at a complex space coordinate, are introduced in order to obtain pertinent approximations for the Green's functions in grounded layered media. These artificial boundary conditions include perfectly matched layers backed by perfectly electric or magnetic conductors. As a first result, we obtain analytical expressions for the differences of Green's functions subject to different boundary conditions. Since weighted sums of Green's functions are again Green's functions, the need arises to solve an optimization problem, in the sense of obtainingthe optimal weig hted mixture of Green's functions, as compared to the exact Green's function. Comprehensive eigenexpansions for the Green's functions are given in the general case, and a few examples illustrate the goodness of fit between the approximate Green's functions and the exact Green's function.