0
Research Papers

Buckling and Vibration of Orthotropic Nonhomogeneous Rectangular Plates With Bilinear Thickness Variation

[+] Author and Article Information
Yajuvindra Kumar

 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, Indiayaju_saini@yahoo.com

R. Lal

 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India

J. Appl. Mech 78(6), 061012 (Aug 25, 2011) (11 pages) doi:10.1115/1.4003913 History: Received August 08, 2010; Revised March 08, 2011; Posted April 04, 2011; Published August 25, 2011; Online August 25, 2011

An analysis and numerical results are presented for buckling and transverse vibration of orthotropic nonhomogeneous rectangular plates of variable thickness using two dimensional boundary characteristic orthogonal polynomials in the Rayleigh–Ritz method on the basis of classical plate theory when uniformly distributed in-plane loading is acting at two opposite edges clamped/simply supported. The Gram–Schmidt process has been used to generate orthogonal polynomials. The nonhomogeneity of the plate is assumed to arise due to linear variations in elastic properties and density of the plate material with the in-plane coordinates. The two dimensional thickness variation is taken as the Cartesian product of linear variations along the two concurrent edges of the plate. Effect of various plate parameters such as nonhomogeneity parameters, aspect ratio together with thickness variation, and in-plane load on the natural frequencies has been illustrated for the first three modes of vibration for four different combinations of clamped, simply supported, and free edges correct to four decimal places. Three dimensional mode shapes for a specified plate for all the four boundary conditions have been plotted. By allowing the frequency to approach zero, the critical buckling loads in compression for various values of plate parameters have been computed correct to six significant digits. A comparison of results with those available in the literature has been presented.

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

(a) Geometry of the plate, (b) plate under compression on two opposite edges, and (c) boundary conditions

Grahic Jump Location
Figure 2

Frequency parameter Ω for (a) CCCC, (b) SCSC, (c) FCFC and (d) FSFS square plate: for γ1=γ2=δ2=ψ1=ψ2=0.5.—, first mode; - - -, second mode; □, β=-0.5, δ1=-0.5; ○, β=-0.5, δ1=0.5; Δ, β=0.5, δ1=-0.5; ×, β=0.5, δ1=0.5, and N¯=20

Grahic Jump Location
Figure 3

Frequency parameter Ω for (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS square plate: for α=β=δ2=ψ1=ψ2=0.5. —, first mode; - - -, second mode; □, γ2=-0.5, δ1=-0.5; ○, γ2=-0.5, δ1=0.5; Δ, γ2=0.5, δ1=-0.5; ×, γ2=0.5, δ1=0.5, and N¯=20

Grahic Jump Location
Figure 4

Frequency parameter Ω for (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS square plate: for α=β=γ1=γ2=ψ2=0.5. —, first mode; - - -, second mode; □, δ2=-0.5, ψ1=-0.5; ○, δ2=-0.5, ψ1=0.5; Δ, δ2=0.5, ψ1=-0.5; ×, δ2=0.5, ψ1=0.5, and N¯=20

Grahic Jump Location
Figure 5

Frequency parameter Ω for (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS square plate: for α=γ1=γ2=δ1=δ2=0.5. —, first mode; - - -, second mode; □, ψ2=-0.5, β=-0.5; ○, ψ2=-0.5, β=0.5; Δ, ψ2=0.5, β=-0.5; ×, ψ2=0.5, β=0.5, and N¯=20

Grahic Jump Location
Figure 6

Frequency parameter Ω for (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS square plate: for β=γ1=γ2=δ2=ψ1=ψ2=0.5. —, first mode; - - -, second mode; □, α=-0.5, δ1=-0.5; ○, α=-0.5, δ1=0.5; Δ, α=0.5, δ1=-0.5; ×, α=0.5, δ1=0.5

Grahic Jump Location
Figure 7

Frequency parameter Ω for (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS plate: for β=γ1=γ2=δ2=ψ1=ψ2=0.5. —, first mode; - - -, second mode; □, α=-0.5, δ1=-0.5; ○, α=-0.5, δ1=0.5; Δ, α=0.5, δ1=-0.5; ×, α=0.5, δ1=0.5,and N¯=20

Grahic Jump Location
Figure 8

Frequency parameter Ω versus in-plane force parameter N¯ for (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS square plates for first mode α=-0.5,β=γ1=γ2=δ1=δ2=0.5. —; ψ1=ψ2=-0.5; - · -; ψ1=-0.5,ψ2=0.5, - ··-; ψ1=0.5,ψ2=-0.5

Grahic Jump Location
Figure 9

First three mode shapes of orthotropic (a) CCCC, (b) SCSC, (c) FCFC, and (d) FSFS square plates for α=β=γ1=γ2=δ1=δ2=ψ1=ψ2=0.5 and N¯=50

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In