Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Żur, Krzysztof Kamil; Jankowski, Piotr

doi:10.3390/sym11030429

Cited by 14 publications

(8 citation statements)

References 43 publications

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“…The mesh displacement is maximum for the sonic excitation frequency of 75 Hz corresponding to the natural frequency of the speaker diaphragm. The maximum vertical displacement of the vibrating mesh screen can also be predicted from the porous circular plate approach in which the droplet weight opposes the sound pressure force acting normal to the mesh surface 29 ; hence resulting in the expression: , here: is sound pressure level, is the effective stiffness of mesh screen, is the droplet weight, is wire diameter, is Poison ratio, is the radius of the top speaker opening and is the elastic modulus of steel. The vertical displacement amplitude is predicted using the expression for the various mesh/plate structures considered in the present study.…”

Section: Resultsmentioning

confidence: 99%

Droplet motion on sonically excited hydrophobic meshes

Abubakar

Yilbaş

Al‐Qahtani

et al. 2022

Sci Rep

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The sonic excitation of the liquid droplet on a hydrophobic mesh surface gives rise to a different oscillation behavior than that of the flat hydrophobic surface having the same contact angle. To assess the droplet oscillatory behavior over the hydrophobic mesh, the droplet motion is examined under the external sonic excitations for various mesh screen aperture ratios. An experiment is carried out and the droplet motion is recorded by a high-speed facility. The findings revealed that increasing sonic excitation frequencies enhance the droplet maximum displacement in vertical and horizontal planes; however, the vertical displacements remain larger than those of the horizontal displacements. The resonance frequency measured agrees well with the predictions and the excitation frequency at 105 Hz results in a droplet oscillation mode (n) of 4. The maximum displacement of the droplet surface remains larger for the flat hydrophobic surface than that of the mesh surface with the same contact angle. In addition, the damping factor is considerably influenced by the sonic excitation frequencies; hence, increasing sonic frequency enhances the damping factor, which becomes more apparent for the large mesh screen aperture ratios. The small-amplitude surface tension waves create ripples on the droplet surface.

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Section: Resultsmentioning

confidence: 99%

Droplet motion on sonically excited hydrophobic meshes

Abubakar

Yilbaş

Al‐Qahtani

et al. 2022

Sci Rep

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“…Solving the simultaneous equation [Eqs. (20) and (21)] to find the unknowns and substitute back to Eq. (17).…”

Section: Application Of Galerkin Methods Of Weighted Residual To the Governing Equationmentioning

confidence: 99%

“…Meanwhile, the HPM also suffers the setback of finding the embedded parameter and initial approximation of the governing equation that satisfies the given conditions. Nonetheless, several researches on a free vibration of circular plates using different methods have been presented in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, the reliability and flexibility of the Galerkin method of weighted residual [26] have made it more effective than any other semi-numerical method.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Dynamic Behaviour of Non-Uniform Thickness Circular Plates Resting on Winkler and Pasternak Foundations

2020

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The study of the dynamic behaviour of non-uniform thickness circular plate resting on elastic foundations is very imperative in designing structural systems. This present research investigates the free vibration analysis of varying density and non-uniform thickness isotropic circular plates resting on Winkler and Pasternak foundations. The governing differential equation is analysed using the Galerkin method of weighted residuals. Linear and nonlinear case is considered, the surface radial and circumferential stresses are also determined. Thereafter, the accuracy and consistency of the analytical solutions obtained are ascertained by comparing the existing results available in pieces of literature and confirmed to be in a good harmony. Also, it is observed that very accurate results can be obtained with few computations. Issues relating to the singularity of circular plate governing equations are handled with ease. The analytical solutions obtained are used to determine the influence of elastic foundations, homogeneity and thickness variation on the dynamic behaviour of the circular plate, the effect of vibration on a free surface of the foundation as well as the influence of radial and circumferential stress on mode shapes of the circular plate considered. From the results, it is observed that a maximum of 8.1% percentage difference is obtained with the solutions obtained from other analytical methods. Furthermore, increasing the elastic foundation parameter increases the natural frequency. Extrema modal displacement occurs due to radial and circumferential stress. Natural frequency increases as the thickness of the circular plate increases, Conversely, a decrease in natural frequency is observed as the density varies. It is envisioned that; the present study will contribute to the existing knowledge of the classical theory of vibration.

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“…The statistics of papers called for this Special Issue related to published or rejected items were [7][8][9][10][11][12][13][14][15][16][17][18][19][20]: total submissions (21), published (13; 62%), and rejected (8; 38%). The authors' geographical distribution by countries of authors in published papers is shown in Table 1, and it can be seen that 35 authors are from 11 different countries.…”

Section: Statistics Of the Special Issuementioning

confidence: 99%

Symmetry in Applied Continuous Mechanics

2019

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Engineering practice requires the use of structures containing identical components or parts, which are useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analysis of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Such applications can be used in most engineering fields including machine building, automotive, aerospace, and civil engineering.

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Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Cited by 14 publications

References 43 publications

Droplet motion on sonically excited hydrophobic meshes

Droplet motion on sonically excited hydrophobic meshes

Investigation of the Dynamic Behaviour of Non-Uniform Thickness Circular Plates Resting on Winkler and Pasternak Foundations

Symmetry in Applied Continuous Mechanics

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