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Parametric Study on Thick Plate Vibration Using FSDT

Kalita K., Haldar S.

Mechanics and Mechanical Engineering

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2015

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Vol. 19, nr 2

81--90

EN

The prime objective of the research is to investigate the influence of various structural parameters like aspect ratio, boundary condition, size of cut-out etc. on the free vibration frequencies of a thick rectangular plate. Plates being one the most common structural elements has always enticed the interest of many researchers towards this problem. In here a general first order shear deformation theory (FSDT) is used to analyse the free vibration behaviour of rectangular isotropic plates. A finite element program has been developed using 9 node isoparametric element. A number of numerical examples are presented here. Two different sets of mass lumping scheme are considered to carry the analysis using and without using rotary inertia. The definite advantage of this work over other similar works done by using FEM pakages is its exceptional accuracy. At most the error calculated for convergence study with published literature is 1%.

2

Vibration of thick/thin skewed taper cylindrical shell panel

Haldar S., Majumder A.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 3

649-660

EN

In this paper, a nine node isoparametric plate bending element is used for free vibration analysis of isotropic skewed taper cylindrical shell panels. The thickness of panels varies linearly in one direction only. In the present analysis first order shear deformation theory is incorporated. Two types of mass lumping schemes are recommended. In one of the mass lumping schemes the effect of rotary inertia is incorporated. Free vibration of skewed taper cylindrical shell panels having different shell thickness to radius (h/R) ratios, length to radius ratios (L/R), skew angles and different boundary conditions are analyzed following the shallow shell theory.

3

A sub-parametric shear deformable element for free vibration analysis of thick/thin rectangular plates with tapered thickness

Manna M. C.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 4

901-913

EN

A sub-parametric shear deformable element is proposed for free vibration analysis of isotropic plates with linearly varying thickness in one direction. The element has sixteen nodes and thirty-six degrees of freedom. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The geometry of the element is defined by a polynomial of lower order than the polynomials used for field variables. The entire formulation is made based on first-order shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios (varying from 0.01 to 0.2), tapered ratios, aspect ratios and boundary conditions are analyzed. The results obtained by the present element show an excellent agreement with the available published results. Some numerical results have been given as new results.

4

Free vibration of isotropic thick/thin plates using a sub-parametric shear deformable element

Manna M. C., Haldar S., Sheikh A. H.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 3

441-448

EN

A free vibration analysis of isotropic plates is investigated in this paper. A sixteen node sub-parametric element having thirty-six degrees of freedom is developed for this purpose. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The entire formulation is made based on the first-order shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios, aspect ratios and boundary conditions are analyzed. The results show an excellent agreement with the available published analytical results.