A Moving-Load Problem for Elastic Half-plane

Year 2023, , 408 - 413, 30.11.2023

İpek Akkaya , Elçin Yusufoğlu

https://doi.org/10.35193/bseufbd.1252580

Abstract

In this study, a dynamic problem that takes into account the effect of a normal force moving at a constant speed along the boundary of an elastic half-plane has been discussed. The Lame equation of motion and the boundary conditions have been reduced to the related boundary value problem in terms of longitudinal and transverse wave functions. Then, by switching from the moving coordinate system to the stationary coordinate system, this boundary value problem was reduced to boundary value problems for differential equations with the help of the Fourier transform. The corresponding integral transformation of the longitudinal and transverse wave functions in the Fourier plane was determined and the displacement components were finally determined using the inverse Fourier technique. Cases in which the moving speed of a normal load is smaller and larger than the Rayleigh wave speed have been studied.

Keywords

Potansiyel Fonksiyonları, Fourier Dönüşümü, Rayleigh Dalga Hızı

Elastik Yarı Düzlem İçin Bir Hareketli Yük Problemi

Abstract

Bu çalışmada elastik bir yarı düzlemin sınırı boyu sabit hızla hareket eden bir normal kuvvetin etkisini dikkate alan bir dinamik problem konu edilmiştir. Lame hareket denklemi ve sınır koşulları boyuna ve enine dalga fonksiyonları cinsinden ilgili sınır değer problemine indirgenmiştir. Daha sonra hareketli koordinat sisteminden durağan koordinat sistemine geçilerek bu sınır değer problemi Fourier dönüşümü yardımıyla diferansiyel denklemler için sınır değer problemlerine indirgenmiştir. Fourier düzleminde boyuna ve enine dalga fonksiyonlarının ilgili integral dönüşümü belirlenmiş olup ters Fourier tekniği kullanılarak, nihayet yer değiştirme bileşenleri belirlenmiştir. Normal yükün hareket hızının Rayleigh dalga hızından küçük ve büyük olduğu durumlar incelenmiştir.

Keywords

Potansiyel Fonksiyonları, Fourier Dönüşümü, Rayleigh Dalga Hızı

References

• Poruchikov, V.B. (1993). Methods of the Classical Theory of Elastodynamics. Springer-Verlag Berlin Heidelberg .
• Gakenheimer, D.C. (1971). Response of elastic half-space to expanding surface loads. J. Applied Mechanics (38), 99-110.
• Achenbach, J. D. (1973). Wave Propagation in Elastic Solids. North-HollandElsevier, Amsterdam.
• Payton, R. G. (1983). Elastic Wave Propogation in Transversely Isotropic Media, Matrtinus Nijhoff Publishers, The Hague.
• Aleksandrov VM, Kovalenko YeV. (1986). Problems of Continuum Mechanics with Mixed Boundary Conditions. Moscow, Nauka.
• Gupta S and Ahmed M. (2017). On Rayleigh Waves in Self-reinforced Layer Embedded over an Incompressible Half-space with Varying Rigidity and Density. Procedia Eng (173), 1021–1028.
• Pal PC, Kumar S and Bose S. (2015). Propagation of Rayleigh waves in anisotropic layer overlying a semi-infinite sandy medium. Ain Shams Eng J , (6), 621–627.
• Mohseni H and Ng C-T. (2018). Rayleigh Wave propagation and scattering characteristics at debondings in fibre-reinforced polymer-retrofitted concrete structures. Struct Health Monit, (18), 303–317.
• Ebrahiminejad A, Mardanshahi A and Kazemirad S. (2022). Nondestructive evaluation of coated structures using lamb wave propagation. Appl Acoust (185), 108378.
• Abo-Dahab SM, Kilany AA, Allam MNM, Mohamed RA, Rida SZ. (2022). Influence of several fields on Rayleigh waves propagation in a fiber-reinforced orthotropic half-space material under four thermoelastic models. Waves in Random and Complex Media, 32(5), 2197–2220.
• Xu L, Ma M. (2022). Dynamic response of the multilayered half-space medium due to the spatially periodic harmonic moving load. Soil Dyn Earthquake Engn .157, 107246.