On the elastostatics of thin periodic plates with large deflections

Paś²

2014

Meccanica

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Medium thickness plates resting on a periodic Winkler's foundation are investigated. New averaged non-asymptotic models for those plates are proposed. These models are based on the tolerance averaging technique. The main feature of these models is that they describe the effect of period lengths on the overall behaviour of the plate. It is also shown that from governing equations of these models, equations of simplified averaged models (called asymptotic models) can be obtained. An additional interesting feature of the proposed models is that the equations describe also the effect of normal stress in the thickness direction.

Section: àD=2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of medium thickness plates interacting with a periodic Winkler’s foundation: non-asymptotic tolerance modelling

Paś²

2014

Meccanica

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“…Static problems of periodic structures are also considered, e.g. periodic thin plates with moderately large deflections are analysed by Domagalski and Jędrysiak [33,34]. This modelling method is applied successfully to analysis some non-stationary and stationary problems of functionally graded structures, e.g.…”

Section: Introductionmentioning

confidence: 99%

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

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.

“…Various thermomechanical problems of periodic structures were investigated in a series of papers applying this method, e.g. dynamics of periodic plane structures by Wierzbicki and Woźniak (2000), vibrations of medium-thickness plates by Baron (2006), static problems of thin plates with moderately large deflections by Domagalski and Jędrysiak (2012), nonlinear vibrations of beams by Domagalski and Jędrysiak (2014), vibrations of thin plates resting on an elastic nonhomogeneous foundation by Jędrysiak (1999Jędrysiak ( , 2003, vibrations of medium-thickness plates resting on an elastic foundation by Paś (2005, 2014), vibrations with damping of plate strips with a periodic system of concentrated masses by Marczak and Jędrysiak (2014), vibrations of wavy-type plates by Michalak (2002), vibrations of thin plates with stiffeners by Nagórko and Woźniak (2002), vibrations of thin cylindrical shells by Tomczyk (2007Tomczyk ( , 2013. These papers show that the effect of the microstructure size plays a crucial role in nonstationary (and some stationary) problems of periodic structures.…”

Section: Introductionmentioning

confidence: 99%

On free vibrations of thin functionally graded plate bands resting on an elastic foundation

Kaźmierczak-Sobińska

2015

jtam

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In this note free vibrations of plate bands with functionally graded properties, resting on an elastic foundation, are investigated. On the micro-level, these plate bands have a tolerance-periodic structure. It can be shown that in dynamic problems of those objects, the effect of the microstructure size plays a role. This effect can be described in the framework of the tolerance model, which is presented here for these bands. Obtained results are evaluated introducing the asymptotic model. Both fundamental and higher free vibration frequencies of these plate bands are calculated using the Ritz method. The effects of differences of material plate properties in the cell on the microlevel and of the foundation are shown.