Tabaka İle Örtülü Yarı Düzlemdeki Yüzey Dalgalarına Tabaka Kalınlığı ve Ön Gerilmelerin Etkisinin Tam Temas Koşulları Altında İncelenmesi
Öz
Yapı malzemelerinde ve birçok ortamda çok değişik nedenlerden dolayı ön gerilmeler oluşabilmektedir. Oluşan bu ön gerilmelerin bu ortamlardaki dalga yayılma hızına olan etkilerinin incelenmesi bu ortamlardaki ön gerilmelerin belirlenmesi gerek teorik gerekse mühendislik uygulamaları açısından büyük önem taşımaktadır. Bu çalışmada lineer elastik malzemeden yapılmış bir tabaka ile kaplanmış olan yine lineer elastik malzemeden yapılmış olan bir yarı düzlem ele alınmıştır. Bunun için öncelikle tabaka ve yarı düzlem üzerine herhangi bir öngerilmenin etki etmediği (ön gerilmesiz) durumda yarı düzlemdeki yüzey dalgalarının dispersiyonu üzerinde çalışılmıştır. Daha sonra yine öngerilmesiz durumda tabaka kalınlığı değiştirilmek suretiyle tabaka kalınlığının yarı düzlemdeki yüzey dalgalarının dispersiyonuna olan etkisi incelenmiştir. Son durumda ise tabaka üzerine çekme ve basınç ön gerilmeleri uygulanmış ve bu ön gerilmelerin yarı düzlemdeki yüzey dalgarına olan etkisi incelenmiştir. Yapılan çalışmaların tamamı parçalı homojen cisim modeli çerçevesinde klasik lineer elastisite teorisi uygulanarak tabaka ve yarı düzlem arasında tam temas koşullarının gerçekleştiği varsayılarak yapılmıştır. Sayısal sonuçlar elde edilerek grafikler oluşturulmuş, bilinen sonuç ve fiziksel görüşlerle örtüştüğü gösterilmiştir.
Anahtar Kelimeler
Half space Surface wave Prestress Wave propagation Dispersion
Kaynakça
- Abd-Alla, A. M., Aftab K., Abo-Dahab, S. M. (2017). Rotational effect on thermoelastic Stoneley, Love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order. Computers, Materials & Continua, vol. 53, no. 1, pp. 52-72.
- Achenbach, J.D. ve Epstein, H.I. (1967). “Dynamic Interaction f A Layer and a Half-Space” I. Eng. Mech. Div. Proc. Amer. Soc. Civ. Eng 93, EM5, 24-42.
- Akbarov, (2007). “Recent investigations on the dynamical problems of the elastic body with initial (residual) stresses, (review),” Int. Appl. Mech., 43, No. 12, 3-27.
- Akbarov, S. D. ve Ozisik, M. (2003). “The Influence of the Third Order Elastic Constants to the Generalized Rayleigh Wave Dispersion in a Pre-Stressed Stratified Half-Plane”, Int. Journal of Engineering Science, vol. 41, pp. 2047-2061.
- Chattopadhyay, A.ve Kar, B. K. (1981). “Love Waves Due to a Point Source in an Isotropic Elastic Medium Under Initial Stress”, Int. J. Non-Linear Mech., 16, 247-258.
- Demiray, H. ve Suhubi, E.S. (1970), “Small Torsional Oscillations in Initially Twisted Circular Subber Cylinder”, Int. J. Eng. Sci., 8 (1).
- Eringen, A.C. ve E., S. Suhubi (1975). Elastodynamics, Volume II, Linear Theory,–Academic Press New York, 343-1001.
- Green, A.E. (1961). “Torsional Vibrations of an Initially Stressed Circular Cylinder in “Problems of Contunium Mechanics (Muskheloshvili anniv. vol)’ ” , Society for Industrial and Appl. Math. , Philadelphia, Pennsylvania, 148-154.
- Guz, A.N. (1995a). “Elastic waves in Laminated Periodic Bodies with Initial (Residual) Stresses”, Book of Absracts of ICIAM 95 Hamburg 3-7 Temmuz, 173
- Guz, A.N. (1995b). “Surface Waves Along Planar and Curcilinear Surfaces in Bodies with Initial Stresses”, Book of Absracts of ICIAM 95 Hamburg 3-7 Temmuz, 296.
- Love, A.E.H.(1944). Mathematical Theory of Elasticity, 4th Ed., Cambridge University Press. (reprinted by Dover Publications, New York)
- Makhort, F.G. (1975). “To the Surface Wave Propagation in the Elastic Body with Initial Deformation.”, Prikl Mech., V 7( 2) , 34-40.
- Guz, A.N. ve Makhort, F.G. (2000). “Physical Principles of Ultrasonic Non-Destructive Method of Determination of Stresses in Rigid Solids”, Int. Appl. Mech. 36 (9), 3-34.
- Hayes, K. ve Rivlin, R.S. (1961). “Surface Waves in Deformed Materials”, Arch. Rat. Mech. And Anal. 8 (5), 358 – 380.
- Negin, M.; Akbarov, S. D.; Erguven, M. E. (2014). Generalized Rayleigh wave dispersion analysis in a pre-stressed elastic stratified half-space with imperfectly bonded interfaces. Computers, Materials & Continua, vol. 42, no. 1, pp. 25-61.
- Suhubi, E.S. (1965). “Small Longitudinal Vibration of a n Initially Stressed Circular Cylinder”, Int. J. Eng. Sci. , 2(5), 509-515.
- Stroh, A.N. (1962). “Steady State Problems in Anisotropic Elasticity”, J. Math. Phys., 41, 77 -103.
- Tolstoy, I., and Usdin, E. (1953). “Dispersive Properties of Stratified Elastic and Liquid Media. A Ray Theory.”, Geophysics, 18, 844-870.
Investigation of the Effect of Layer Thickness and Prestress on Surface Waves in the Half-Plane Covered by the Layer Under The Full Contact Conditions
Öz
Pre-stresses can occur in building materials and in many environments for many different reasons. Investigating the effects of these pre-stresses on the wave propagation velocity in these environments is of great importance in terms of both theoretical and engineering applications. In this paper, a half plane made of linear elastic material covered with a layer made of linear elastic material is considered. For this, first of all, the dispersion of the surface waves in the half plane in the case where no prestress affects the layer and the half plane (without pre-stresses) has been studied. Afterwards, the effect of layer thickness on the dispersion of surface waves in the half-plane was investigated by changing the layer thickness in the unstressed state. In the last case, tensile and compressive stresses were applied on the layer and the effect of these pre-stresses on the half-plane surface wave was investigated. All of the studies have been carried out by applying the classical linear elasticity theory within the framework of the piecewise homogeneous body model, assuming that the full contact conditions between the layer and the half-plane are complete. Graphs were created by obtaining numerical results, and it was shown that they coincide with the known result and physical views.
Anahtar Kelimeler
Half space Surface wave Prestress Wave propagation Dispersion.
Kaynakça
- Abd-Alla, A. M., Aftab K., Abo-Dahab, S. M. (2017). Rotational effect on thermoelastic Stoneley, Love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order. Computers, Materials & Continua, vol. 53, no. 1, pp. 52-72.
- Achenbach, J.D. ve Epstein, H.I. (1967). “Dynamic Interaction f A Layer and a Half-Space” I. Eng. Mech. Div. Proc. Amer. Soc. Civ. Eng 93, EM5, 24-42.
- Akbarov, (2007). “Recent investigations on the dynamical problems of the elastic body with initial (residual) stresses, (review),” Int. Appl. Mech., 43, No. 12, 3-27.
- Akbarov, S. D. ve Ozisik, M. (2003). “The Influence of the Third Order Elastic Constants to the Generalized Rayleigh Wave Dispersion in a Pre-Stressed Stratified Half-Plane”, Int. Journal of Engineering Science, vol. 41, pp. 2047-2061.
- Chattopadhyay, A.ve Kar, B. K. (1981). “Love Waves Due to a Point Source in an Isotropic Elastic Medium Under Initial Stress”, Int. J. Non-Linear Mech., 16, 247-258.
- Demiray, H. ve Suhubi, E.S. (1970), “Small Torsional Oscillations in Initially Twisted Circular Subber Cylinder”, Int. J. Eng. Sci., 8 (1).
- Eringen, A.C. ve E., S. Suhubi (1975). Elastodynamics, Volume II, Linear Theory,–Academic Press New York, 343-1001.
- Green, A.E. (1961). “Torsional Vibrations of an Initially Stressed Circular Cylinder in “Problems of Contunium Mechanics (Muskheloshvili anniv. vol)’ ” , Society for Industrial and Appl. Math. , Philadelphia, Pennsylvania, 148-154.
- Guz, A.N. (1995a). “Elastic waves in Laminated Periodic Bodies with Initial (Residual) Stresses”, Book of Absracts of ICIAM 95 Hamburg 3-7 Temmuz, 173
- Guz, A.N. (1995b). “Surface Waves Along Planar and Curcilinear Surfaces in Bodies with Initial Stresses”, Book of Absracts of ICIAM 95 Hamburg 3-7 Temmuz, 296.
- Love, A.E.H.(1944). Mathematical Theory of Elasticity, 4th Ed., Cambridge University Press. (reprinted by Dover Publications, New York)
- Makhort, F.G. (1975). “To the Surface Wave Propagation in the Elastic Body with Initial Deformation.”, Prikl Mech., V 7( 2) , 34-40.
- Guz, A.N. ve Makhort, F.G. (2000). “Physical Principles of Ultrasonic Non-Destructive Method of Determination of Stresses in Rigid Solids”, Int. Appl. Mech. 36 (9), 3-34.
- Hayes, K. ve Rivlin, R.S. (1961). “Surface Waves in Deformed Materials”, Arch. Rat. Mech. And Anal. 8 (5), 358 – 380.
- Negin, M.; Akbarov, S. D.; Erguven, M. E. (2014). Generalized Rayleigh wave dispersion analysis in a pre-stressed elastic stratified half-space with imperfectly bonded interfaces. Computers, Materials & Continua, vol. 42, no. 1, pp. 25-61.
- Suhubi, E.S. (1965). “Small Longitudinal Vibration of a n Initially Stressed Circular Cylinder”, Int. J. Eng. Sci. , 2(5), 509-515.
- Stroh, A.N. (1962). “Steady State Problems in Anisotropic Elasticity”, J. Math. Phys., 41, 77 -103.
- Tolstoy, I., and Usdin, E. (1953). “Dispersive Properties of Stratified Elastic and Liquid Media. A Ray Theory.”, Geophysics, 18, 844-870.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Ağustos 2021 |
| Yayımlandığı Sayı | Yıl 2021 Sayı: 25 |
