Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions

Khedmati

Lat. Am. j. solids struct.

2014

In this study, vibration behavior of orthotropic cylindrical shells with variable thickness is investigated. Based on linear shell theory and applying energy method and using spline functions, free vibration relations are derived for shell with variable thickness and curvature. Frequency parameter and mode shapes are found after solving the frequency Eigenvalue equation. Effects of variable thickness along axial and circumferential directions of the shell on its frequency parameter are studied and compared against each other. Shell thickness is assumed to be varied in a parabolic profile along both directions. Also, frequency parameters for both circular and parabolic curvatures along circumferential direction are investigated and results are compared together. In addition, effect of variable thickness on the mode shapes is studied.

Section: Verification Of Present Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of orthtropic thin cylindrical shells with variable thickness by using spline functions

Khedmati

Lat. Am. j. solids struct.

2014

“…The differential equation governing the free transverse vibration of monoclin ic rectangular plate is given by (1) where w(x,y,t) is the transverse deflection, t the time, ρ the mass density, c 11 , c 12 , c 21 , c 22 and c 66 are the material constants.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Notable contribution made thereafter dealing with rectangular plates with uniform / non-uniform thickness with various boundary conditions are given in the refs. [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Generalised Differential Quadrature Method in the Study of Free Vibration Analysis of Monoclinic Rectangular Plates

Singhal¹,

Bindal²

2012

AJCAM

Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Lévy approach i.e. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations C-C, C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been carried out for four decimal exactitude. Mode shapes for all the three plates have been presented. The efficiency of generalized differential quadrature method for the natural frequencies of vibrat ion of monoclin ic rectangular p lates has been examined.

“…Notable contributions, made thereafter are listed in references [6][7][8][9][10][11][12][13][14][15]. In this context, authors have come across a limited number of papers in which the thickness of the plate varies in both the directions and reported in references [16][17][18][19][20][21][22][23], to mention a few. Out of these, Sakiyama and Huang [19] considered sinusoidal variation, Cheung and Zhou [20] assumed the power functions of both the coordinates and the rest deal with bilinear variation in thickness.…”

Section: Introductionmentioning

confidence: 99%

Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation

Lal

Kumar

2012

Shock and Vibration

Abstract. The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.