Tolerance modelling of free vibration frequencies of thin functionally graded plates with one-directional microstructure

Jędrysiak, Jarosław

doi:10.1016/j.compstruct.2016.11.061

Cited by 19 publications

(13 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, we obtain the differential equations for ( = 10, 11, 12, 13, 14) 10 ] + (48), we obtain the differential equations used for ( = 15, 16, 17, 18, 19, 20) 15 ] + 1 10 + where 9 , 9 , 5 and 14 are shown in the solutions obtained above.…”

Section: Biparametric Perturbation Solution On Andmentioning

confidence: 99%

“…(1 − ) 15 ] + 1 10 + which may be solved under the boundary conditions (84) ( = 15, 16, 17, 18, 19, 20). Thus, we obtain…”

Section: Biparametric Perturbation Solution On Andmentioning

confidence: 99%

“…In the dynamic analyses of FGM plates, an interesting method, named tolerance modelling, is applied to the known differential equation of Kirchhoff‐type plates with transversally graded macrostructure (see Refs. []). This method leads from the governing differential equation with non‐continuous, tolerance‐periodic coefficients to the system of differential equations with smooth, slowly varying coefficients.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression

Yang

et al. 2019

Z Angew Math Mech

View full text Add to dashboard Cite

In this study, a biparametric perturbation method is used for the solution of the large‐deflection bending problem of a functionally graded thin plate with different moduli in tension and compression. First, the Föppl‐von Kármán equations for the bimodular functionally graded thin plate are established in rectangular coordinates system, thus obtaining the axisymmetric simplified form in polar coordinates system. By adopting two groups of perturbation parameters, one group is gradient index and central deflection, another is gradient index and load, the biparametric perturbation solution for the established governing equations are obtained, respectively, under different boundary constrains. The result indicates that the two groups of parameter selections are valid, and the biparametric perturbation solution is also consistent to single‐parameter perturbation solution. The bimodular effects on stiffness and deformation of thin plates are also discussed via biparametric perturbation solutions obtained. The study indicates that the dominant factor influencing the stiffness is the relative magnitudes relation among the tensile modulus, the neutral layer modulus and the compressive modulus.

show abstract

Section: Biparametric Perturbation Solution On Andmentioning

confidence: 99%

“…(1 − ) 15 ] + 1 10 + which may be solved under the boundary conditions (84) ( = 15, 16, 17, 18, 19, 20). Thus, we obtain…”

Section: Biparametric Perturbation Solution On Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression

Yang

et al. 2019

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

“…Different thermomechanical problems of functionally graded media with microstructures were also considered using the tolerance modelling approach; e.g., Michalak and Wirowski [ 58 ], Perliński et al [ 59 ] and Wirowski et al [ 60 ] analyzed dynamics and stability of plates with longitudinally graded structures with or without an elastic foundations; free vibrations of transversally graded thin plates on an elastic foundation were presented by Jędrysiak and Kaźmierczak-Sobińska [ 61 ]; the dynamics of a thin-walled structure with a dense system of ribs was considered by Michalak [ 62 ]; Ostrowski and Michalak [ 63 ] showed an application for heat conduction in cylindrical composite conductors with non-uniform microstructure; the effect of microstructure in thermoelastic problems of transversally graded laminates was investigated by Pazera and Jędrysiak [ 64 ]; vibrations of thin plates with the microstructure size of an order of the plate thickness were analyzed by Jędrysiak [ 65 ]; Tomczyk and Szczerba [ 66 ] proposed a new asymptotic-tolerance model of dynamics for thin microstructured transversally graded shells; Jędrysiak [ 67 ] considered free vibrations of medium thickness functionally graded plates with a microstructure.…”

Section: Introductionmentioning

confidence: 99%

Tolerance Modelling of Vibrations and Stability for Periodic Slender Visco-Elastic Beams on a Foundation with Damping. Revisiting

Jędrysiak

2020

Materials

Self Cite

View full text Add to dashboard Cite

The mathematical modelling of certain problems of vibrations and stability for periodic slender visco-elastic beams is presented in this note. To consider these problems and take into account the effect of the microstructure, the tolerance modelling approach is proposed. Using this technique, the equation with non-continuous, periodic, highly oscillating coefficients is replaced by a system of differential equations with constant coefficients. Moreover, these governing equations describe the effect of the microstructure on the overall behavior of the beams under consideration. The tolerance modelling can lead to equations of two different tolerance models—the standard and the general, under weakened assumptions. This averaging tolerance method was assessed by comparison with the asymptotic homogenization, the governing equations of which omit this effect. My considerations were limited to proposing and presenting only mathematical models describing investigated beams. In a simple analytical example, the application of the presented average models is shown.

show abstract

“…This technique is expanded and applied in many publications to analyze various issues concerning periodic as well as functionally graded structures. Among them are thermoelasticity problems [10][11][12], thermal issues [13][14][15], dynamic [16][17][18][19][20] and stability problems [21].…”

Section: Introductionmentioning

confidence: 99%

On Thermoelasticity in FGL – Tolerance Averaging Technique

Pazera

Ostrowski

Jędrysiak

2018

Mechanics and Mechanical Engineering

Self Cite

View full text Add to dashboard Cite

In this paper the problem of linear thermoelasticity in a laminate with functional gradation of properties is considered. In micro level this laminate is made of two different materials, microlaminas, distributed non-periodically but also not randomly along one of directions, what in macro level results in aforementioned functionally gradation of laminate properties. In order to describe behavior of such structure, equations of two models are here presented – the tolerance and the tolerance-asymptotic model. Both are obtained by the tolerance averaging technique. The basic aim of this work is to analyse the influence of some terms from these averaged equations on the distribution and the values of the displacements and the temperature functions. To solve the equations of two proposed models the finite difference method is used.

show abstract

Tolerance modelling of free vibration frequencies of thin functionally graded plates with one-directional microstructure

Cited by 19 publications

References 55 publications

Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression

Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression

Tolerance Modelling of Vibrations and Stability for Periodic Slender Visco-Elastic Beams on a Foundation with Damping. Revisiting

On Thermoelasticity in FGL – Tolerance Averaging Technique

Contact Info

Product

Resources

About