Nonlinear vibration of symmetrically laminated composite skew plates by finite element method

Singha, M.K.; Daripa, Rupesh

doi:10.1016/j.ijnonlinmec.2007.08.001

Cited by 82 publications

(37 citation statements)

References 42 publications

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“…Step 2Vibration analysis: Assuming a harmonic solution of the form { d }={ d max }sin w t to the differential eqn 5(b) and following the solution procedure as outlined by Singha and Daripa 14 , the following matrix amplitude equation is obtained: …”

Section: Solution Proceduresmentioning

confidence: 99%

“…A complete cubic polynomial shape function was used to interpolate in-plane displacements for better accuracy in capturing the nonuniform stresses near localised load. The nonlinear matrixamplitude equation 14 has been solved by direct iteration technique to obtain linear and nonlinear vibration frequencies of simply supported square composite plates subjected to tensile or compressive partial in-plane load. …”

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confidence: 99%

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Flexural Vibration Characteristics of Initially Stressed Composite Plates

Daripa

Singha

2010

DSJ

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employed finite element method to study the linear vibration frequencies of stiffened isotropic, composite, and sandwich plates subjected to in-plane partial edge loads. Recently, Cheung 9 , et al. used finite strip method. Chen 10 , et al. and Chen and Fung 11 used Runge-Kutta method. and Chen and Doong 12 used Galerkins method, to study nonlinear vibration characteristics of isotropic and laminated composite plates subjected to initial in-plane stress.In the present work, a four-noded shear flexible quadrilateral high precision plate bending element developed for the stability analysis 13 has been extended to study the vibration characteristics of isotropic and composite plates under concentrated or partial in-plane load. A complete cubic polynomial shape function was used to interpolate in-plane displacements for better accuracy in capturing the nonuniform stresses near localised load. The nonlinear matrixamplitude equation 14 has been solved by direct iteration technique to obtain linear and nonlinear vibration frequencies of simply supported square composite plates subjected to tensile or compressive partial in-plane load. Flexural Vibration Characteristics of Initially Stressed Composite PlatesRupesh Daripa and M.K. Singha * Indian Institute of Technology Delhi, New Delhi110 016 * E-mail: maloy@am.iitd.ac.in ABSTRACTThe influence of localised in-plane load on the flexural vibration characteristics of isotropic and composite plates have been studied using a four-noded shear flexible high precision plate bending finite element. First, the critical buckling loads of such plates subjected to partial or concentrated compressive loads were calculated, then the linear and nonlinear flexural vibration frequencies were obtained. Limited parametric study was carried out to study the influences of location and distribution of tensile or compressive in-plane load on the vibration frequencies of such plates.

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Section: Solution Proceduresmentioning

confidence: 99%

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confidence: 99%

Flexural Vibration Characteristics of Initially Stressed Composite Plates

Daripa

Singha

2010

DSJ

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“…In general, one can distinguish two main approaches to investigating nonlinear vibrations of multi-layer plates and shells. Namely, one can employ: (i) a hypothesis of a straight, nondeformed normal (to all layers), and reduce the problem to computing a quasi-homogeneous plate/shell with reduced elastic parameters [15][16][17][18][19][20][21][22]; (ii) non-classical 2D theories based on integral hypotheses for the entire packet of layers, taking into account deformations and stresses of the transverse shear in all layers [5,6,[23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

et al. 2018

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Mathematical models of multi-layer orthotropic shells were reconsidered based on the Timoshenko hypothesis. A new mathematical model with ε-regularisation was proposed, and the theorem regarding the existence of a generalised solution to the model was formulated and proved. The algorithms of numerical investigation of models studied with the aid of the variational-difference method were developed. The associated stability problem was also addressed. A comparison of the results yielded by the considered models was carried out and discussed for numerous factors and parameters.

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“…Singh and Darip [8] analyzed nonlinear vibration of composite skew plate using a four-noded shear flexible quadrilateral high precision plate bending element. Nonlinear free vibration analysis of laminated composite skew thin plates was reported by Malekzadeh [9] using DQM.…”

Section: Introductionmentioning

confidence: 99%

Elastic analysis of polymeric cylinders reinforced with carbon nanotubes

Hosseini

Kolahchi

Heydari

2016

J. Appl. Math. Comput. Mech.

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Abstract. In this work, stress analysis of a polymeric cylinder's cylindrical shell reinforced with carbon nanotubes (CNTs) is investigated. The cylinder is subjected to mechanical and thermal loadings. All the equivalent mechanical and thermal properties of nano-composite cylinder are obtained using Mori-Tanaka model. Based on equilibrium, the governing equation is derived. Using an exact solution, the stresses and radial displacement distributions in the structure are calculated. The effects of CNTs volume percent on the stresses and radial displacement for internal and external pressure cylinder are the main discussion of this study. Numerical results indicate that with increasing CNTs volume percent, the stresses decrease. However, this shows the important effect of nanotechnology in stress reduction of cylinder which may be useful in sensors and actuators.

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Nonlinear vibration of symmetrically laminated composite skew plates by finite element method

Cited by 82 publications

References 42 publications

Flexural Vibration Characteristics of Initially Stressed Composite Plates

Flexural Vibration Characteristics of Initially Stressed Composite Plates

On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

Elastic analysis of polymeric cylinders reinforced with carbon nanotubes

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