Free vibrations of thin functionally graded plates with microstructure

Jędrysiak, Jarosław

doi:10.1016/j.engstruct.2014.05.030

Cited by 11 publications

(3 citation statements)

References 25 publications

(33 reference statements)

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“…Furthermore, the exact frequency of many FGM plates with different boundary conditions was also presented. Jedrysiak [153] used asymptotic tolerance, asymptotic, and tolerance model to analyze the frequency of microstructure FGM plates. It was suggested that all presented models can be applied to analyze lower free vibration frequencies.…”

Section: Fgm Platesmentioning

confidence: 99%

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Zhang

Khan

Guo

et al. 2019

Advances in Materials Science and Engineering

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Functionally graded materials (FGMs) are novel materials whose properties change gradually with respect to their dimensions. It is the advanced development of formerly used composite materials and consists of two or more materials in order to achieve the desired properties according to the application where an FGM is used. FGMs have obtained a great attention of researchers in the past decade due to their graded properties at every single point in various dimensions. The properties of an FGM are not identical to the materials that constitute it. This paper aims to present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade. Moreover, the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper. At the end, future work is also suggested in this review paper.

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Section: Fgm Platesmentioning

confidence: 99%

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Zhang

Khan

Guo

et al. 2019

Advances in Materials Science and Engineering

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“…Geometrically nonlinear vibrations of slender mesoperiodic beams were investigated in the paper by Domagalski and Jędrysiak (2016). The method was widely applied in the analysis of microstructured plates: thin plates with an elastic periodic foundation, Jędrysiak (2003), honeycomb lattice-type plates, Cielecka and Jędrysiak (2006), geometrically nonlinear thin plates, Domagalski and Jędrysiak (2015) and thin functionally graded plates, Jędrysiak (2013Jędrysiak ( , 2014 and Kaźmierczak and Jędrysiak (2011). The TA technique was also applied in plates stability problems, cf.…”

Section: Prefacementioning

confidence: 99%

Free vibrations spectrum of periodically inhomogeneous Rayleigh beams using the tolerance averaging technique

Świątek

Domagalski

Jędrysiak

2019

Journal of Theoretical and Applied Mechanics

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In this paper, linear-elastic Rayleigh beams with a periodic structure are considered. Dynamics of such beams is described by partial differential equations with non-continuous highly oscillating coefficients. The analysis of dynamic problems using the aforementioned equations is very often problematic to perform. Thus, other simplified models of Rayleigh beams are proposed. Some of these models are based on the concept of the effective stiffness. Among them, one can distinguish the theory of asymptotic homogenization. However, in these models, the size of the mesostructure parameter (the size of a periodicity cell) is often neglected. Therefore, a non-asymptotic averaged model of the periodic beam is introduced, called the tolerance model, which is derived by applying the tolerance averaging technique (TA). The obtained tolerance model equations have constant coefficients, and in contrast to other averaged models, some of them depend on the size of the periodicity cell.

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“…Jędrysiak (2010), Woźniak et al (2010). Some applications to dynamic and stability problems for thin transversally graded plates with the microstructure size bigger than the plate thickness were shown by Jędrysiak and Michalak (2011), Kaźmierczak and Jędrysiak (2010, 2011, 2014; for thin functionally graded plates with the microstructure size of an order of the plate thickness by Jędrysiak (2013, 2014), Jędrysiak and Pazera (2014); for functionally graded skeletonal shells by Michalak (2012); for heat conduction in functionally graded hollow cylinders by Ostrowski and Michalak (2011); for thin longitudinally graded plates by Michalak and Wirowski (2012), Wirowski (2012). An extended list of papers can be found in the books by Woźniak et al (2008Woźniak et al ( , 2010.…”

Section: Introductionmentioning

confidence: 99%

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

Jędrysiak

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.

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Free vibrations of thin functionally graded plates with microstructure

Cited by 11 publications

References 25 publications

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

Free vibrations spectrum of periodically inhomogeneous Rayleigh beams using the tolerance averaging technique

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

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