A study on vibration of tapered rectangular plate under non-uniform temperature field

Abstract

Nomenclature W(x, y) -deflection function; x, y -coordinates in the plane of plate; v -Poisson's ratio; ρ -density of the plate material, kg/m 3 ; g -plate thickness, m; T(t) -time function; D % -visco-elastic operator; E -Young modulus, N/m 2 ; a -length of the rectangular plate, m; b -breadth of the rectangular plate, m; η -visco-elastic constant, Ns/m 2 ; G -shear modulus, N/m 2 .

Natural vibration of tapered rectangular plate with exponential variation in non homogeneity

“…Table 4 provides the information that frequency modes in present paper are less when compared with [11,12]. The frequency modes of present paper, [11,12] are coincides at = = = 0. a) b) Fig. 5.…”

“…A comparison of present analysis with [11,12] are presented in tabular (Table 4 and Table 5) as well as in graphical form (Fig. 5 and Fig.…”

“…Table 4 shows the comparison of frequency modes of present paper with [11,12] corresponding to tapering parameter for fixed value of thermal gradient and non homogeneity constant i.e., = = 0. Table 4 provides the information that frequency modes in present paper are less when compared with [11,12]. The frequency modes of present paper, [11,12] are coincides at = = = 0. a) b) Fig.…”

“…Therefore, deflection function (i.e, maximum displacement) which satisfy boundary condition given in Eq. 17is taken as [11]:…”

“…Sharma et al [10] also studied the vibration of tapered rectangular plate with linear variation in density and evaluated first two modes of vibration on clamped edges. Khanna and Kaur [11,12] analyzed the free vibration of non uniform (linear and exponential variation in thickness) and non homogeneous (exponential variation in Poisson's ratio) of rectangular plate with temperature (linear and exponential) variation by using Rayleigh Ritz method on clamped boundary condition. Hwu [13] presented closed-form solution for the free vibration problems, to study the effects of rotary inertia and shear deformation on frequency and provided numerical examples which shows the importance of considering the effects of rotary inertia and shear deformation.…”