On the flexural vibrations of sandwich plates

A simplified approach to sandwich plate free vibrations, based on the superposition method, can provide approximations to the lowest modes for various boundary conditions, showing a characteristic influence of the bending-shear stiffness ratio.

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Sommario Un'analisi semplificata delle vibrazioni naturali di pannelli sandwich in diverse condizioni di vincolo, con il metodo di sovrapposizione degli effetti, consente l'individuazione approssimata dei modi più bassi, mostrando un comportamento vibratorio caratteristico al variare del rapporto tra le rigidezze di flessione e taglio.

     

Nonlinear damped vibrations of simply-supported rectangular sandwich plates

The nonlinear, forced, damped vibrations of simply-supported rectangular sandwich plates with a viscoelastic core are studied. The general, nonlinear dynamic equations of asymmetrical sandwich plates are derived using the virtual work principle. Damping is taken into account by modelling the viscoelastic core as a Voigt-Kelvin solid. The harmonic balance method is employed for solving the equations of motion. The influence of the thickness of the layers and material properties on the nonlinear response of the plates is studied.     

Nonlinear damped vibrations of simply-supported sandwich plates in a rapidly changing temperature field

The paper studies the effects of a rapidly changed temperature on the free vibrations of simply supported sandwich plates. It has been taken into account that the properties of the facings and of the core of the sandwich plate change with the temperature. The effects of geometrical nonlinearities on the behaviour of the plate have also been included. The damping is considered by modelling the viscoelastic core as a Voigt-Kelvin solid. A Runge-Kutta method is employed to solve the governing equations and obtain the numerical results. It was found that the rapid change of temperature strongly affects the amplitude and frequency of the vibrations.     

Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements

Meccanica - A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes...     

Non-linear vibrations of sandwich viscoelastic shells

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.     

Nonlinear analysis of skewed sandwich plates

Nonlinear static and dynamic behaviours of freely supported Rhombic sandwich plates have been studied following Banerjee's hypothesis. Numerical results for 0° skew angle are compared with other known results. Results for other skew angles are believed to be new.

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Sommario Si studia, seguendo l'ipotesi di Banerjee, il comportamento nonlineare statico e dinamico di piastre rombiche semplicemente appoggiate. Si presentano risultati numerici relativi a piastre rombiche e rettangolari: questi ultimi vengono paragonati a risultati già noti, mentre i primi si ritengono nuovi.

     

Low-velocity impact of sandwich composite plates

In this paper we investigate impact and compression after impact properties of plain weave carbon fiber sandwich composites. Impact tests were conducted on different sample types to obtain information about absorbed energy and maximum impact force. The different samples consisted of foam-filled and hollow honeycomb cores with four-layer carbon fiber facesheets on one or both sides. The impact and compression after impact data provided valuable information to allow for comparisons between the different sample types. Also, the compression after impact tests were conducted in order to determine the reduction in compressive strength when comparing impacted to non-impacted samples. In conclusion, a two-degrees-of-freedom spring/mass model was compared to experimental results. The comparison helped illustrate the limitations of current impact theory. This paper was presented, in part, at a symposium honoring Dr Christian P. Burger, Novel Applications of Experimental Methods in Mechanics, held at the 2003 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 2–4, 2003, Charlotte, North Carolina.     

Large deflection of rectangular sandwich plates

The governing differential equations and the boundary conditions for the large deflection of rectangular sandwich plates are derived using the principle of the complementary energy. The governing differential equations are transformed into systems of nonlinear algebraic equations using the finite difference method, and solved by successive iteration. For the purpose of illustration, deflection behavior of simply supported rectangular plates under uniform load is presented. The deflection behavior of plates with various values of shear rigidities and intensity of applied loads is studied. The change in the stress patterns of the face layers of the plate is also discussed.     

Nonlinear bending of circular sandwich plates

In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to siip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.Notation r, ,z system of cylindrical coordinates - a radius of plate boundary - t thickness of the face - h thickness of the core - h ₀ distance from middle of thickness of lower face to middle of thickness of upper face - E Young's modulus of the face - Poisson's ratio of the face - G ₂ shear modulus of the core - D _f flexural rigidity of the face - D flexural rigidity of the plate - C shear rigidity of the plate - q uniform lateral load - u _i ,v _i ,w _{i(i=1, 2, 3)} radial, tangential and normal displacement of upper face, core and lower face, respectively - u radial displacement of the middle plane of the plate - w deflection of the middle plane of the plate - rotation of connecting line of corresponding points in middle planes of two faces - _1i , _i , _zi , _ri , _zi , _{rzi (i=1,2,3)} strains at a point of upper face, core and lower face - _ri , _i , _zi , _ri , _zi , _rzi(i=1,2,3) stresses at a point of upper face, core and lower face - _r , ₀ radial and tangential stress of the middle plane of the plate, respectively - U _i(i =1, 2, 3) strain energy of upper face, core and lower face, respectively - V work done by the external force - U total potential energy of the plate - M _r radial moment of the plate - Q _r shearing force of the plate - m radial moment of the face - stress function - dimensionless radial coordinate - k dimensionless characteristic parameter - W dimensionless deflection - W ₀ dimensionless center deflection - S _r ,S ₀ dimensionless radial and tangential stress, respectively - S _r (0),S ₀ (0) dimensionless radial and tangential stress at center, respectively - S ₀(1) dimensionless tangential stress at edge - P dimensionless uniform lateral load - A ₂,A ₃,B ₂,B ₃,a ₁,.....,a ₂, ₁, ₂,l _1,1,...l _{1 1,3},m ₁,...,m ₃₃,n ₀,₂,...n ₂₂,₆,R ₁,,...R ₃₃ auxiliary quantity - L differential operator     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

ＰＯＳＴＢＵＣＫＬＩＮＧＢＥＨＡＶｉＯＲＯＦＲＥＣＴＡＮＧＵＬＡＲＭＯＤＥＲＡＴＥＬＹＴＨＩＣＫＰＬＡＴＥＳＡＮＤＳＡＮＤＷＩＣＨＰＬＡＴＥＳＣｈｅｎｇＺｈｅｎ－ｑｉａｎｇ（成振强）ＷａｎｇＸｉｕ－ｘｉ（王秀喜）ＨｕａｎｇＭａｏ－ｇｕａｎｇ（黄茂光）...     

Coupled piezoelectric vibrations of quartz plates

The contributions of coupling with the electric field and mass of electrode coatings are taken into account in solutions of equations governing coupled thickness-shear, flexure and face-shear vibrational modes in rotated-Y-cut quartz plates.     

Viscoelastic vibrations of a triangular plates

The problem of stationary vibrations of a viscoelastic equilateral triangular plate is treated. The vibrations are caused by the action of a uniformly distributed load which varies harmonically and by the motion of the simply supported boundary of the plate as a rigid body which vibrates at the same frequency. The level lines of the vibration amplitude are studied and the graphs of the amplitude distribution along the height of the triangle are given.     

Flexural vibrations of fissured poroelastic plates

Summary The governing equations of flexural vibrations of thin, fluid-saturated, poroelastic plates are derived in detail. The plate material obeys the Aifantis-Beskos theory of poroelasticity with two degrees of porosity, while the plate theory employed is the one due to Kirchhoff. The dynamic response of a rectangular, simply supported, poroelastic plate with two degrees of porosity to harmonic load is obtained analytically-numerically and the effects of porosities and permeabilities on the response are studied. A comparison between the single and double porosity material models is also made. The quasi-static problem is analysed as as special case of the dynamic one.

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Biegeschwingungen geklüfteter poroelastischer Platten

Übersicht Es werden die Gleichungen, die die Biegeschwingungen von dünnen, mit Flüssigkeit gefüllten, poroelastischen Platten beschreiben, im einzelnen hergeleitet. Das Materialverhalten der Platte wird durch die Poroelastizitätstheorie von Aifandis und Beskos für Materialien mit doppelter Porosität beschrieben, während für die Platten die Kirchhoffsche Plattentheorie angewandt wird. Man erhält auf analytisch-numerischem Weg das dynamische Verhalten einer rechteckigen, einfach gestützten, poroelastischen Platte mit doppelter Porosität bezüglich einer harmonischen Belastung. Der Einfluß der Porosität und Permeabilität auf das dynamische Verhalten wird untersucht. Weiterhin werden die Modelle für Materialien mit einfacher und doppelter Porosität miteinander verglichen. Das quasi-statische Problem wird als Spezialfall des dynamischen Problems analysiert.

     

Harmonic waves in elastic sandwich plates

Motions of a sandwich plate with symmetric facings are studied in the framework of the three-dimensional equations of elasticity. Both the core and facings are assumed to be isotropic and linearly elastic.Harmonic wave solutions, which satisfy traction-free face conditions and continuity conditions of tractions and displacements at the interfaces, are obtained for four cases: symmetric plane strain solutions for extensional motion, antisymmetric plane strain solutions for flexural motion, and solutions for the symmetric and antisymmetric SH-waves. The dispersion relation for each of these cases is obtained and computed. In order to exhibit the effect of the ratios of facing to core thicknesses, elastic stiffnesses and densities, on the dynamic behavior of sandwich plates, dispersion curves are computed and compared for plates with thick, light, and soft facings as well as for plates with thin, heavy, and stiff facings. Asymptotic expressions of dispersion relations for extensional, flexural, and symmetric SH-waves are obtained in explicit form, as the frequencies and wave numbers approach zero.The thickness vibrations in sandwich plates are studied in detail. The resonance frequencies and modal functions of the thickness-shear and thickness-stretch motions are obtained. Simple algebraic formulas for predicting the lowest thickness-shear and the lowest thickness-stretch frequencies are deduced. The orthogonality of the thickness modal functions is established.