Vibration of non-homogeneous circular Mindlin plates with variable thickness

Gupta, Utkarsh; Lal, Roshan; Sharma, Seema

doi:10.1016/j.jsv.2006.07.005

Cited by 38 publications

(23 citation statements)

References 46 publications

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“…Namely, not only the results obtained should be close to the exact solutions but also no natural frequency is missed in the computation. Table 5 give a comparative study of the first three non-zero frequency parameters¯ = 1 − μ 2 of the present solutions with those, respectively, from the classical plate theory and the Mindlin plate theory [30] for axisymmetric vibration of completely free circular plates with symmetrically linearly varying thickness (i.e., the mid-plane of the plate exists). Two boundary conditions are considered: clamped and completely free.…”

Section: Comparison Studiesmentioning

confidence: 99%

“…Gupta and Lal [29] and Gupta et al [30] used the Chebyshev collocation technique to study the axisymmetric vibration of polar orthotropic Mindlin annular plates and non-homogeneous Mindlin circular plates with variable thickness, respectively. Xiang and Zhang [31] used the exact analytical method to study the free vibrations of stepped Mindlin circular plates.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional vibrations of annular thick plates with linearly varying thickness

Zhou

2011

Arch Appl Mech

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The free vibration of annular thick plates with linearly varying thickness along the radial direction is studied, based on the linear, small strain, three-dimensional (3-D) elasticity theory. Various boundary conditions, symmetrically and asymmetrically linear variations of upper and lower surfaces are considered in the analysis. The well-known Ritz method is used to derive the eigen-value equation. The trigonometric functions in the circumferential direction, the Chebyshev polynomials in the thickness direction, and the Chebyshev polynomials multiplied by the boundary functions in the radial direction are chosen as the trial functions. The present analysis includes full vibration modes, e.g., flexural, thickness-shear, extensive, and torsional. The first eight frequency parameters accurate to at least four significant figures for five vibration categories are obtained. Comparisons of present results for plates having symmetrically linearly varying thickness are made with others based on 2-D classical thin plate theory, 2-D moderate thickness plate theory, and 3-D elasticity theory. The first 35 natural frequencies for plates with asymmetrically linearly varying thickness are compared to the finite element solutions; excellent agreement has been achieved. The asymmetry effect of upper and lower surface variations on the frequency parameters of annular plates is discussed in detail. The first four modes of axisymmetric vibration for completely free circular plates with symmetrically and asymmetrically linearly varying thickness are plotted. The present results for 3-D vibration of annular plates with linearly varying thickness can be taken as benchmark data for validating results from various plate theories and numerical methods.

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Section: Comparison Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Zhou

2011

Arch Appl Mech

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“…But Equation (12) involves the unknown A 1 and A 2 arising due to the substitution of W(ξ, η) from Equation (9). These two constants are to be determined from Equation (12), as follows:…”

Section: Solution and Frequency Equationmentioning

confidence: 99%

“…Yang [8] has considered the vibration of a circular plate with varying thickness. Gupta, Ansari and Sharma [9] discussed the vibration of non-homogeneous circular Mindlin plates with variable thickness. Bambill, Rossit, Laura and Rossi [10] have analyzed transverse vibration of an orthotropic rectangular plate of linearly varying thickness with a free edge.…”

Section: Introductionmentioning

confidence: 99%

Vibration of Visco-Elastic Parallelogram Plate with Parabolic Thickness Variation

Gupta¹,

Kumar²,

Gupta³

2010

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The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and that the thickness varies parabolically in one direction i.e. along length of the plate. Rayleigh-Ritz technique has been used to determine the frequency equation. A two terms deflection function has been used as a solution. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection and linear visco-elastic properties of "Kelvin" type are taken. We have calculated time period and deflection at various points for different values of skew angles, aspect ratio and taper constant, for the first two modes of vibration. Results are supported by tables. Alloy "Duralumin" is considered for all the material constants used in numerical calculations.

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“…The vibrational characteristics of such plates are used of practical interest in some fields of engineering. Several studies have been carried out for the vibration of complete circular plates [1][2][3][4][5][6][7]. However, relatively little research have been done on sectorial plates.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function

Jomehzadeh

Saidi

2009

Thin-Walled Structures

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Vibration of non-homogeneous circular Mindlin plates with variable thickness

Cited by 38 publications

References 46 publications

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Vibration of Visco-Elastic Parallelogram Plate with Parabolic Thickness Variation

Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function

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