Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness

Lal, Roshan; Rani, Rashmi

doi:10.1007/s00707-013-1018-8

Cited by 10 publications

(6 citation statements)

References 35 publications

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“…(26)(27)(28) Tables 1 and 2, respectively, for which the various constants are [21], R c = 2.3090, R f r ¼ 155:7000; R f h ¼ 491:1462; R q ¼ 13:8462;m c ¼ 0:32 and m f r ¼ 0:0247; m f h ¼ 0:078 and k s = 1 from Ref. [15].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…together with relations (9,(12)(13)(14)(15), the equations of motion (11) can be written as follows:…”

Section: Equations Of Motionmentioning

confidence: 99%

“…These theories predict the inter-laminar behavior at the cost of high computational efforts since the involvement of field variables is large. Along with the development of various plate theories, there has been significant development towards the solution methodologies and reported by the authors in their recent paper [15].…”

Section: Introductionmentioning

confidence: 99%

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On the radially symmetric vibrations of circular sandwich plates with polar orthotropic facings and isotropic core of quadratically varying thickness by harmonic differential quadrature method

Lal

Rani

2015

Meccanica

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In the present paper, analysis and numerical results are presented for free axisymmetric vibrations of circular sandwich plate with isotropic core and polar orthotropic face sheets employing harmonic differential quadrature (HDQ) method. The thickness of the core is assumed to vary quadratically in the radial direction and the face sheets are treated as membranes of constant thickness. The effect of shear deformation and rotatory inertia in the core has been taken into account and the mathematical analysis is based upon Mindlin's theory/first-order shear deformation theory. The governing differential equations of motion of the model have been obtained by using Hamilton's energy principle. In the resulting equation HDQ method is employed to obtain the frequency equations for the three edges, namely; clamped, simply supported and free. The lowest three roots of these equations have been reported as the frequencies for the first three modes of vibration for all the three plates. The effect of various plate parameters such as taper parameter, core thickness at the centre and facing thickness on the natural frequencies has been studied. Three-dimensional mode shapes for the specified plates have been illustrated. To check the validity of the present considerations and the technique, frequency parameter has been compared in particular cases.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

“…together with relations (9,(12)(13)(14)(15), the equations of motion (11) can be written as follows:…”

Section: Equations Of Motionmentioning

confidence: 99%

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On the radially symmetric vibrations of circular sandwich plates with polar orthotropic facings and isotropic core of quadratically varying thickness by harmonic differential quadrature method

Lal

Rani

2015

Meccanica

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“…Optimum placement of holes/cut-outs in laminated composite panels has also been investigated [13]. With regards to modal testing of sandwich composite panels, there exist experimental and numerical studies in which the influence of material properties of the core and the face-sheet (including its layup and orientation) were investigated [14][15][16][17][18][19][20] and found to be significant.…”

Section: Introductionmentioning

confidence: 99%

Dynamic performance of sandwich composite plates with circular hole/cut-out: A mixed experimental–numerical study

Mondal

Patra

Chakraborty

et al. 2015

Composite Structures

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“…A lot of researchers have been concerned with the dynamic behavior of sandwich structures (Magnucki et al, 2014;Lal and Rani, 2013;Zhang, 2013;Duan, 2005;Kączkowski, 2000). The boundary value problem of transverse vibrations for the multilayered and homogeneous fixed plates is one of the most frequently considered issues in engineering practice (Starovoitov et al, 2009;Ebrahimi and Rastgo, 2008).…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions To Boundary Value Problem Of Free Vibration Of Sandwich Thin Circular Plates With Discrete Elements

Żur¹,

Jaroszewicz²,

Dragun³

2015

International Journal of Applied Mechanics and Engineering

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In the paper the influence function and the method of partial discretization in free axisymmetric vibration analysis of multilayered circular plates of constant and linearly variable thickness were presented. The effects of shear deformation and rotary inertia for the core as well as the facings were neglected. An analytical investigation based on the classical plate theory was made for the multilayered plate which satisfies Sokołowski's condition. Discretization of mass and replacing stiffness of a fixed circular plate were presented. Formulas of influence matrix and Bernstein-Kieropian's estimators for different steps of discretization were defined. The influence of variable distribution of parameters on the value of double estimators of natural basic and higher frequency of a sandwich circular plate was investigated.

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Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness

Cited by 10 publications

References 35 publications

On the radially symmetric vibrations of circular sandwich plates with polar orthotropic facings and isotropic core of quadratically varying thickness by harmonic differential quadrature method

On the radially symmetric vibrations of circular sandwich plates with polar orthotropic facings and isotropic core of quadratically varying thickness by harmonic differential quadrature method

Dynamic performance of sandwich composite plates with circular hole/cut-out: A mixed experimental–numerical study

Analytical Solutions To Boundary Value Problem Of Free Vibration Of Sandwich Thin Circular Plates With Discrete Elements

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