Ảnh hưởng của hướng sợi đến hiện tượng phản xạ và suy giảm trong môi trường viscoelastic gia cường bằng sợi

Archive of Applied Mechanics - Tập 93 - Trang 2993-3005 - 2023
Suman Nain1, Sayantan Guha2
1Department of Mathematics, Kurukshetra University, Thanesar, India
2Centre for Data Science, Institute of Technical Education and Research (ITER), Siksha ’O’ Anusandhan (Deemed to be University), Bhubaneswar, India

Tóm tắt

Các nghiên cứu hiện có về hiện tượng phản xạ trong môi trường gia cường bằng sợi khẳng định sự nghiêng của các sợi dọc theo trục tọa độ và sự tác động của sóng đồng nhất. Tuy nhiên, do môi trường là dị hướng, các sóng lan truyền trong môi trường gia cường bằng sợi có bản chất không đồng nhất. Những góc nghiêng tùy ý và bình thường của các sợi với các trục tọa độ dẫn đến các đối xứng hình học monoclinic và isotropy ngang trong môi trường. Điều này tạo ra các hình dạng khác nhau trong các vật liệu composite. Vì vậy, nghiên cứu hiện tại bàn luận về hiện tượng phản xạ của các sóng suy giảm ba chiều tại biên giới phẳng của môi trường viscoelastic gia cường bằng sợi (FRVM). Sự lan truyền sóng suy giảm được điều khiển bởi một vectơ chậm phức tạp, các thành phần của nó dọc theo và vuông góc với hướng lan truyền xác định các vectơ lan truyền và suy giảm. Vectơ suy giảm được phân tích để có được sự suy giảm đồng nhất/không đồng nhất. Độ lệch góc giữa các vectơ suy giảm và lan truyền đại diện cho các sóng không đồng nhất. Sự tác động của sóng không đồng nhất tại bề mặt không bị căng sinh ra ba sóng phản xạ. Định luật Snell tổng quát được sử dụng để tìm các vectơ chậm của các sóng phản xạ. Phân rã vectơ chậm mang lại những đặc tính khác nhau của các sóng phản xạ. Ma trận năng lượng được tính toán để phân chia năng lượng giữa các sóng phản xạ tại biên giới. Một ví dụ số được xem xét để nghiên cứu ảnh hưởng của các tham số hiện hành đến đặc tính của các sóng phản xạ.

Từ khóa

#phản xạ #suy giảm #môi trường viscoelastic #gia cường bằng sợi #sóng không đồng nhất

Tài liệu tham khảo

Spencer, A.J.M.: Continuum theory of the mechanics of fibre-reinforced composites, vol. 282. Springer, Berlin (2014) Wineman, A., Rajagopal, K.: A constitutive theory for multi-functional fiber reinforced composites. Acta Mech. 226(8), 2671–2679 (2015) Singh, B., Singh, S.J.: Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space. Sadhana 29(3), 249–257 (2004) Nain, S.: Reflection of an inhomogeneous wave at the plane boundary of initially stressed fiber-reinforced viscoelastic medium. Mech Adv Mater Struct. 1–13 (2021) Carcione, J.M.: Constitutive model and wave equations for linear, viscoelastic, anisotropic media. Geophys. 60(2), 537–548 (1995) Sharma, M.D.: Snell’s law at the boundaries of real elastic media. Math Stud. 84(3–4), 75–94 (2015) Červenỳ, V.: Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media. Stud. Geophys. Geod. 51(3), 391–410 (2007) Sharma, M.D., Nain, S.: Complete phenomenon of reflection at the plane boundary of a dissipative anisotropic elastic medium. Geophys. J. Int. 224(2), 1015–1027 (2021) Guha, S., Singh, A.K.: Plane wave reflection/transmission in imperfectly bonded initially stressed rotating piezothermoelastic fiber-reinforced composite half-spaces. Eur. J. Mech. A. Solids 88, 104242 (2021) Guha, S., Singh, A.: Influence of varying fiber volume fractions on plane waves reflecting from the stress-free/rigid surface of a piezoelectric fiber-reinforced composite half-space. Mech. Adv. Mater. Struct., 1–15 (2021) Singh, A., Mahto, S., Guha, S.: Analysis of plane wave reflection phenomenon from the surface of a micro-mechanically modeled piezomagnetic fiber-reinforced composite half-space. Waves Random Complex Media 1–22 (2021) Singh, S., Singh, A., Guha, S.: Reflection of plane waves at the stress-free/rigid surface of a micro-mechanically modeled piezo-electro-magnetic fiber-reinforced half-space. Waves Random Complex Media. 1–30 (2022) Guha, S., Singh, A.K.: Effects of initial stresses on reflection phenomenon of plane waves at the free surface of a rotating piezothermoelastic fiber-reinforced composite half-space. Int. J. Mech. Sci. 181, 105766 (2020) Singh, A., Mahto, S., Guha, S.: Analysis of plane wave reflection and transmission phenomenon at the interface of two distinct micro-mechanically modeled rotating initially stressed piezomagnetic fiber-reinforced half-spaces. Mech. Adv. Mate. Struct. 29(28), 7623–7639 (2022) Singh, P., Singh, A.K., Chattopadhyay, A., et al.: Mathematical study on the reflection and refraction phenomena of three-dimensional plane waves in a structure with floating frozen layer. Appl. Math. Comput. 386, 125488 (2020) Perati, M.R., Ala, S., Gurijala, R.: Study of reflection and transmission of axially symmetric body waves incident on a base of semi-infinite poroelastic solid cylinder. Arch. Appl. Mech. 89, 2507–2517 (2019) Zenkour, A.M., Sobhy, M.: Axial magnetic field effect on wave propagation in bi-layer fg graphene platelet-reinforced nanobeams. Eng. Comput. 38(Suppl 2), 1313–1329 (2022) Abd-alla, A.N., Hamdan, A.M., Giorgio, I., et al.: The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials. Arch. Appl. Mech. 84, 1229–1248 (2014) Lotfy, K., El-Bary, A., Sarkar, N.: Memory-dependent derivatives (mdd) of magneto-thermal-elastic waves excited by laser pulses for two-temperature theory. Waves Random Complex Media. 1–20 (2020) Zenkour, A., Mashat, D., Abouelregal, A.: The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties. Acta Mech. Solida Sin. 26(6), 659–670 (2013) Sobhy, M., Zenkour, A.M.: Wave propagation in magneto-porosity fg bi-layer nanoplates based on a novel quasi-3d refined plate theory. Waves Random Complex Media. 31(5), 921–941 (2021) Abd-Alla, A.E.N.N., Alsheikh, F.A.: Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses. Arch. Appl. Mech. 79, 843–857 (2009) Tung, D.X.: The reflection and transmission of a quasi-longitudinal displacement wave at an imperfect interface between two nonlocal orthotropic micropolar half-spaces. Arch. Appl. Mech. 91(10), 4313–4328 (2021) Zenkour, A.M.: Thermoelastic diffusion problem for a half-space due to a refined dual-phase-lag green-naghdi model. J. Ocean Eng. Sci. 5(3), 214–222 (2020) Guha, S., Singh, A.K.: Transference of sh waves in a piezoelectric fiber-reinforced composite layered structure employing perfectly matched layer and infinite element techniques coupled with finite elements. Finite Elem. Anal. Des. 209, 103814 (2022) Mahdy, A.M, Lotfy, K., El-Bary, A., et al.: Influence of variable thermal conductivity on wave propagation for a ramp-type heating semiconductor magneto-rotator hydrostatic stresses medium during photo-excited microtemperature processes. Waves Random Complex Media. 1–23 (2021) Abouelregal, A.E.: The reflection of magneto-thermoelastic p and sv waves at a solid half space using dual-phase-lag model. Adv. Appl. Math. Mech. 3(6), 745–758 (2011) Ezzat, M., El-Bary, A.: Magneto-thermoelectric viscoelastic materials with memory-dependent derivative involving two-temperature. Int. J. Appl. Electromagn. Mech. 50(4), 549–567 (2016) Ezzat, M.A.: Modeling of gn type iii with mdd for a thermoelectric solid subjected to a moving heat source. Geomech. Eng. 23(4), 393–403 (2020) Kumar, R., Gupta, V.: Reflection and transmission of plane waves at the interface of an elastic half-space and a fractional order thermoelastic half-space. Arch. Appl. Mech. 83, 1109–1128 (2013) Othman, M.I., Said, S.M.: 2d problem of magneto-thermoelasticity fiber-reinforced medium under temperature dependent properties with three-phase-lag model. Meccanica 49(5), 1225–1241 (2014) Said, S.M., Othman, M.I.: Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model. Struct. Eng. Mech. 57(2), 201–220 (2016) Othman, M.I., Said, S.M.: The effect of rotation on two-dimensional problem of a fiber-reinforced thermoelastic with one relaxation time. Int. J. Thermophys. 33(1), 160–171 (2012) Shaw, S., Othman, M.I.: On the concept of a conformable fractional differential equation. J. Eng. Therm. Sci. 1(1), 17–29 (2021) Khamis, A.K., Lotfy, K., El-Bary, A., et al.: Thermal-piezoelectric problem of a semiconductor medium during photo-thermal excitation. Waves Random Complex Media. 31(6), 2499–2513 (2021) Ezzat, M., El-Bary, A.: Effects of variable thermal conductivity on stokes’ flow of a thermoelectric fluid with fractional order of heat transfer. Int. J. Therm. Sci. 100, 305–315 (2016) Mahdy, A., Lotfy, K., Ismail, E., et al.: Analytical solutions of time-fractional heat order for a magneto-photothermal semiconductor medium with thomson effects and initial stress. Results Phys. 18, 103174 (2020) Mahdy, A., Lotfy, K., Hassan, W., et al.: Analytical solution of magneto-photothermal theory during variable thermal conductivity of a semiconductor material due to pulse heat flux and volumetric heat source. Waves Random Complex Media. 31(6), 2040–2057 (2021) Guha, S., Singh, A.K.: Frequency shifts and thermoelastic damping in distinct micro-/nano-scale piezothermoelastic fiber-reinforced composite beams under three heat conduction models. J. Ocean Eng. Sci. (2022) Guha, S., Singh, A.K.: Frequency shifts and thermoelastic damping in different types of nano-/micro-scale beams with sandiness and voids under three thermoelasticity theories. J. Sound Vib. 510, 116301 (2021) Singh, A.K., Rajput, P., Guha, S., et al.: Propagation characteristics of love-type wave at the electro-mechanical imperfect interface of a piezoelectric fiber-reinforced composite layer overlying a piezoelectric half-space. Eur. J. Mech. A. Solids 93, 104527 (2022) Singh, S., Singh, A., Guha, S.: Shear waves in a piezo-fiber-reinforced-poroelastic composite structure with sandwiched functionally graded buffer layer: Power series approach. Eur. J. Mech. A. Solids 92, 104470 (2022) Singh, A.K., Guha, S.: Mathematical study of reflection and transmission phenomenon of plane waves at the interface of two dissimilar initially stressed rotating micro-mechanically modeled piezoelectric fiber-reinforced composite half-spaces. In: Wave dynamics. World Scientific. pp. 131–162 (2022) Singh, S., Singh, A., Guha, S.: Impact of interfacial imperfections on the reflection and transmission phenomenon of plane waves in a porous-piezoelectric model. Appl. Math. Model. 100, 656–675 (2021) Singh, A., Singh, S.: Application of polynomial functions in analyzing anti-plane wave profiles in a functionally graded piezoelectric–viscoelastic–poroelastic structure with buffer layer. In: Polynomial paradigms: Trends and applications in science and engineering. IOP Publishing, p. 1–24 (2022) Singh, S., Singh, A.: Anti-plane surface and interfacial waves influenced by layer reinforcement in piezo-electro-magnetic structures with surface energy. Eur. Phys. J. Plus. 136(3), 1–20 (2021) Singh, A., Singh, S., Kumari, R., et al.: Impact of point source and mass loading sensitivity on the propagation of an sh wave in an imperfectly bonded fgppm layered structure. Acta Mech. 231(6), 2603–2627 (2020) Nain, S.: Reflection of inhomogeneous waves at the plane boundary of anisotropic thermoelastic medium. J. Therm. Stresses 46(3), 182–197 (2023) Nain, S.: Reflection of an inhomogeneous wave at free surface of fiber-reinforced thermoelastic medium. Waves Random Complex Media. (2022) Sharma, M.D.: Propagation of inhomogeneous plane waves in anisotropic viscoelastic media. Acta Mech. 200(3), 145–154 (2008) Krebes, E.: The viscoelastic reflection/transmission problem: two special cases. Bull. Seismol. Soc. Am. 73(6A), 1673–1683 (1983) Červenỳ, V., Pšenčík, I.: Plane waves in viscoelastic anisotropic media-i theory. Geophys. J. Int. 161(1), 197–212 (2005)