Low frequency antiplane shear vibrations of a three-layered elastic plate

Year 2018, Volume: 19 Issue: 4, 867 - 879, 31.12.2018

Barış Erbaş

https://doi.org/10.18038/aubtda.460365

Cited By: 1

Abstract

Antiplane shear vibrations of three-layered strongly vertically inhomogeneous laminates are considered. Polynomial long wave low frequency approximations of the exact dispersion relation are derived and further simplified for the two setups of material and geometric problem parameters corresponding, particularly, to laminated glass plates as well as photovoltaic panels. The associated 1D shortened equations of motion are also established using the conventional asymptotic procedure earlier developed for thin homogeneous structures.

Keywords

Asymptotic, cut-off, dispersion, wave

References

• [1] Vinson JR. The Behaviour of Sandwich Structure of Isotropic and Composite Material, CRC Press, 1999.
• [2] Altenbach H, Eremeyev VA, Naumenko K. On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer. ZAMM-J.Appl. Math. Mech./Zeitsch. Ange. Mathe. Mech. 2015, 95.10: 1004-1011.
• [3] Naumenko K, Eremeyev VA. A layer-wise theory for laminated glass and photovoltaic panels. Composite Structures 2014, 112: 283-291.
• [4] Martin TP, Layman CN, Moore KM and Orris GJ. Elastic shells with high-contrast material properties as acoustic metamaterial components. Physical Review B 2012, 85.16: 161103.
• [5] Lee P, Chang N. Harmonic waves in elastic sandwich plates. Journal of Elasticity 1979, 9.1: 51-69.
• [6] Wang CM, Reddy JN and Lee KH. Shear deformable beams and plates: Relationships with classical solutions, Elsevier, 2000.
• [7] Milton GW. The theory of composites, Cambridge University Press, 2002.
• [8] Hohe J, Librescu L. Advances in the structural modelling of elastic sandwich panels. Mechanics of Advanced Materials and Structures 2004, 11.4-5: 395-424.
• [9] Berdichevsky VL. An asymptotic theory of sandwich plates. International Journal of Engineering Science 2010, 48.3: 383-404.
• [10] Kaplunov J, Prikazchikov DA and Sergushova O. Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods. Journal of Sound and Vibration 2016, 366: 264-276.
• [11] Kaplunov J, Prikazchikov DA and Prikazchikov LA. Dispersion of elastic waves in a strongly inhomogenous three-layered plate. International Journal of Solids and Structures 2017, 113:169-179.
• [12] Kaplunov J, Prikazchikov DA and Prikazchikov LA. Dispersion of elastic waves in laminated glass. Procedia Engineering 2017, 199:1489-1494.
• [13] Prikazchikov LA, Aydın YE, Erbaş B and Kaplunov J. Asymptotic analysis of anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate. Mathematics and Mechanics of Solids 2018, doi: 10.1177/1081286518790804.[14] Ewing WM, Jardetzky WS. Elastic waves in layerede media. 1st Ed. McGraw-Hill, 1957.
• [15] Achenbach J. Wave propagation in elastic solids. Elsevier, 2012.
• [14] Ewing WM, Jardetzky WS. Elastic waves in layered media, McGraw-Hill, 1957