Shear deformable dynamic stiffness elements for a free vibration analysis of composite plate assemblies – Part I: Theory

Nefovska-Danilović, Marija; Kolarević, Nevenka; Marjanović, Miroslav; Petronijević, Mira

doi:10.1016/j.compstruct.2016.09.022

Cited by 26 publications

(15 citation statements)

References 33 publications

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“…where L is the matrix of the differential operators [20][21][22][23][24] defined in terms of the plate stiffness coefficients, the mass moments of inertia and the angular frequency ω.…”

Section: Transformation Of the Governing Equations Of Motion To Frequ...mentioning

confidence: 99%

“…Displacement or rotation amplitudes of a rectangular plate element ˆ( , ) u x y can be presented as a superposition of four symmetry contributions: both symmetric (SS), symmetric -anti-symmetric (SA), anti-symmetric -symmetric (AS) and both anti-symmetric (AA), [20][21][22][23][24]. By the superposition of 4 symmetry contributions, it is possible to analyze only one quarter of a rectangular plate, which significantly reduces the size of the corresponding dynamic stiffness matrices.…”

Section: Superposition Of Symmetry Contributionsmentioning

confidence: 99%

“…The issue can be overcome with the aid of the projection method [18]. Therefore, instead of using the vectors ˆij q and ˆij Q , new projection vectors ij q and ij Q are introduced, which components are the Fourier coefficients in the series expansion (see [20][21][22][23][24][25][26] for details).…”

Section: Superposition Of Symmetry Contributionsmentioning

confidence: 99%

“…In a series of further studies, authors formulated dynamic stiffness matrices for a completely free rectangular isotropic plate element based on the first order (FSDT) [20] and higher order shear deformation theory (HSDT) [21], as well as for the plate element ongoing in-plane vibration [22]. Recently, the above formulations have been extended to the free vibration analysis of sandwich [23], symmetric cross-ply laminated composite plates [24,25], and composite stiffened plate assemblies [26]. Moreover, starting from the developed dynamic stiffness elements, object-oriented software in Python environment -FREEVIB [27] has been developed, enabling free vibration analysis of a wide range of possible structural problems.…”

Section: Introductionmentioning

confidence: 99%

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2019

SJCE

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Scientific Journal of Civil Engineering (SJCE) is an international, peer-reviewed journal published bi-annually since December 2012. It is an open access Journal available at the web site of the Faculty of Civil Engineering in Skopje (www.gf.ukim.edu.mk). This Journal is committed to publish and disseminate high quality and novel scientific research work in the broad field of engineering sciences. SJCE is designed to advance technical knowledge and to foster innovative engineering solutions in the field of civil engineering, geotechnics, survey and geo-spatial engineering, environmental protection, construction management etc. The year 2019 was an important milestone in the history of the South Eastern European School for Master and PhD FORMation in Engineering. It is a year in which we proudly honor and celebrate 15 years since SEEFORM was established as part of a wider DYNET network, 15 years of support given to many enthusiastic doctoral candidates through a well-structured doctoral program.It was therefore a decision of the editorial board to honour this milestone with a special issue of the Journal. We decided to contact all SEEFORM participants and ask them for a contribution. We were delighted that many of them expressed the interest in publishing their research work in our Journal.As an editor-in-chief of the Scientific Journal of Civil Engineering, it is my great pleasure to present the Second Issue of Volume 8, a special issue of the Journal dedicated to the celebration of 15 th anniversary of SEEFORM.

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“…where L is the matrix of the differential operators [20][21][22][23][24] defined in terms of the plate stiffness coefficients, the mass moments of inertia and the angular frequency ω.…”

Section: Transformation Of the Governing Equations Of Motion To Frequ...mentioning

confidence: 99%

Section: Superposition Of Symmetry Contributionsmentioning

confidence: 99%

Section: Superposition Of Symmetry Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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2019

SJCE

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“…The reason for this can be attributed to the fact that the exact solution is readily available from the theory of elasticity for a simply-supported plate which makes it possible to develop the DSM in an exact sense to compute the natural frequencies and mode shapes of plates and plate assemblies in all frequency ranges. The absence of an exact solution for other types of plate boundary conditions substantially narrowed the range of applicability of the DSM in the past, but this restriction has recently been removed by some outstanding publications in recent years [11][12][13][14][15][16][17]. It should be recognized that seeking an exact solution for free vibration of plates with boundary conditions other than the simply-supported one is really very difficult task but, nevertheless, it is necessary because it is a fundamental step to make the DSM development sufficiently general when modelling complex structures.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stiffness formulation and free vibration analysis of specially orthotropic Mindlin plates with arbitrary boundary conditions

Papkov

Banerjee

2019

Journal of Sound and Vibration

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A novel dynamic stiffness formulation which includes the effects of shear deformation and rotatory inertia is proposed to carry out the free vibration analysis of thick rectangular orthotropic plates i.e. the formulation is based on an extension of the Mindlin theory to orthotropic plates in a dynamic stiffness context. The modified trigonometric basis is used to construct the general solution for the free vibration problem of the plate in series form, permitting the derivation of an infinite system of linear algebraic equations which connect the Fourier coefficients of the kinematic boundary conditions of its four edges.The boundary conditions are essentially the deflections and angles of rotations constituting the displacement vector and shear forces and bending moments constituting the force vector. The forcedisplacement relationship is then obtained by relating the two vectors via the dynamic stiffness matrix.Essentially the ensuing infinite system forms the fundamental basis of the paper, which defines the dynamic stiffness matrix for an orthotropic Mindlin plate in an exact sense. Numerical results are obtained by using the Wittrick-Williams algorithm as solution technique. The theory is first validated using published results and then further illustrated by a series of numerical examples. The paper concludes with significant conclusions.

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