Elastic buckling of a sandwich beam with variable mechanical properties of the core

Grygorowicz, Magdalena; Magnucki, Krzysztof; Malinowski, Marek T.

doi:10.1016/j.tws.2014.11.014

Cited by 70 publications

(25 citation statements)

References 37 publications

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“…Magnucka-Blandzi [31] proposed the mathematical modelling of a simply supported rectangular sandwich porous plate with Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/tws differential equations formulated by using the principle of stationarity of the total potential energy. Grygorowicz et al [32] presented analytical and numerical studies of elastic buckling of a sandwich beam with FG porous core under a broken line hypothesis and a nonlinear hypothesis to define the displacement fields. Mojahedin et al [33] used the higher order shear deformation plate theory and nonlinear strain-displacement relations to derive the closed form solution for the critical buckling load of a radically loaded circular plate made of FG porous materials saturated with fluid, and compared the results with the outcome of classical and first order plate theories.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Chen

Kitipornchai

Yang

2016

Thin-Walled Structures

311

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a b s t r a c tThe nonlinear free vibration behavior of shear deformable sandwich porous beam is investigated in this paper within the context of Timoshenko beam theory. The proposed beam is composed of two face layers and a functionally graded porous core which contains internal pores following different porosity distributions. Two non-uniform functionally graded distributions are considered in this paper based on the equivalent beam mass, associated with a uniform distribution for purpose of comparison. The elastic moduli and mass density are assumed to vary along the thickness direction in terms of the coefficients of porosity and mass density, whose relationship is determined by employing the typical mechanical characteristic of an open-cell metal foam. The Ritz method and von Kármán type nonlinear strain-displacement relationships are applied to derive the equation system, which governs the nonlinear vibration behavior of sandwich porous beams under hinged or clamped end supports. A direct iterative algorithm is then used to solve the governing equation system to predict the linear and nonlinear frequencies which are presented by a detailed numerical study to discuss the effects of porosity coefficient, slenderness ratio, thickness ratio and to compare the varying porosity distributions and boundary conditions, providing a feasible way to improve the vibration behavior of sandwich porous beams.

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Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Chen

Kitipornchai

Yang

2016

Thin-Walled Structures

311

View full text Add to dashboard Cite

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“…Magnucka-Blandzi [12] investigated the problem of axi-symmetrical deflection and buckling of circular porous-cellular plate with the geometric model of nonlinear hypothesis. Grygorowicz et al [13] studied the elastic buckling of three-layered beam consisting of metal foam core with varying mechanical properties, and applied a broken line hypothesis and a nonlinear hypothesis to the displacement field, respectively. Jabbari et al [14] presented the buckling analysis of a solid circular plate under radial loading made of FG porous materials based on the geometrical nonlinearities in the Love-Kirchhoff hypothesis and Sanders nonlinear strain-displacement relationship.…”

Section: Introductionmentioning

confidence: 99%

Free and forced vibrations of shear deformable functionally graded porous beams

Chen

Yang

Kitipornchai

2016

International Journal of Mechanical Sciences

361

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This paper investigates the free and forced vibration characteristics of functionally graded (FG) porous beams with non-uniform porosity distribution whose elastic moduli and mass density are nonlinearly graded along the thickness direction. Both symmetric and asymmetric porosity distributions are considered. The relationship between coefficients of porosity and mass density is determined based on the typical mechanical property of an open-cell metal foam. Within the framework of Timoshenko beam theory to include the effect of transverse shear strain and by employing Lagrange equation method together with Ritz trial functions, the equation of motion is derived then solved by using Newmark-β method in the time domain. Natural frequencies and transient dynamic deflections are obtained for porous beams under different loading conditions, including a harmonic point load, an impulsive point load and a moving load with constant velocity. A detailed numerical study is conducted to examine the effects of varying porosity distribution, porosity coefficient, slenderness ratio and boundary condition, shedding important insights into the design of functionally graded porous beams to achieve improved dynamic behaviour.

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“…Some buckling problems using analytical and numerical methods for sandwich beams with variable properties of the core are also considered, cf. Grygorowicz et al [13].…”

Section: Introductionmentioning

confidence: 99%

The effect of uncertain material properties on free vibrations of thin periodic plates

Jędrysiak

Ostrowski

2017

Meccanica

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Thin periodic plates with uncertain properties in a periodicity cell are investigated. To describe dynamics of these plates the non-asymptotic tolerance modelling method, cf. Woźniak and Wierzbicki (Averaging techniques in thermomechanics of composite solids. Wydawnictwo Politechniki Często-chowskiej, Częstochowa, 15), Woźniak et al. (eds.) (Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach. Wydawnictwo Politechniki Łódzkiej, Łódź, 16), for those plates is applied. The governing equations of tolerance models based on this method take into account the effect of period lengths on the overall behaviour of the plate. Hence, the additional effects of the periodicity can be analysed, as higher order vibrations. Moreover, properties of the plate in the periodicity cell are determined uncertainly. To analyse an influence of random variables of the properties with a fixed probability distribution on vibrations of the plate the Monte Carlo analysis is applied.

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Elastic buckling of a sandwich beam with variable mechanical properties of the core

Cited by 70 publications

References 37 publications

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Free and forced vibrations of shear deformable functionally graded porous beams

The effect of uncertain material properties on free vibrations of thin periodic plates

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