Abstract
In this study, the effect of nonlocal scale value and two phase lags on the free vibration of generalized thermoelastic multilayered LEMV (Linear Elastic Material with Voids)/CFRP (Carbon Fiber Reinforced Polymer) composite cylinder is studied using nonlocal form of linear theory of elasticity. The governing equation of motion is established in longitudinal axis and variable separation model is used to transform the governing equations into a system of differential equations. To investigate vibration analysis from frequency equations, the stress free boundary conditions are adopted at the inner, outer and interface boundaries. The graphical representation of the numerically calculated results for frequency shift, natural frequency, and thermoelastic damping is presented. A special care has been taken to inspect the effect of nonlocal parameter on the aforementioned quantities. The results suggest that the nonlocal scale and the phase lag parameters alter the vibration characteristics of composite cylinders significantly.
REFERENCES
A. C. Eringen, “Memory-dependent nonlocal electromagnetic elastic solids and super conductivity,” J. Math. Phys. 32, 787–796 (1991).
A. C. Eringen, Non-Local Polar Field Models (Academic, New York, 1996).
A. C. Eringen, Nonlocal Continuum Field Theories (Springer, New York, 2002).
A. C. Eringen, “Nonlocal polar elastic continua,” Int. J. Eng. Sci. 10, 1–16 (1972).
A. C. Eringen, “Theory of nonlocal thermoelasticity,” Int. J. Eng. Sci. 12 (12), 1063–1077 (1974).
A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys. 54, 4703–4710 (1983).
M. Davoodi, K. Zografos, P. J. Oliveira, and R. J. Poole, “On the similarities between the simplified Phan–Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell [Peterlin closure] model in simple and complex flows,” Phys. Fluids 34 (3), 033110 (2002).
R. Hassani, R. Ansari, and H. Rouhi, “An efficient numerical method to solve the problems of 2D incompressible nonlinear elasticity,” Contin. Mech. Thermodyn. 34, 1–21 (2002).
R. M. Chen, S. Walsh, and M. H. Wheeler, “Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics,” Nonlinearity 35 (4), 1927 (2022).
J. Chen, H. Yang, K. I. Elkhodary, S. Tang, and X. Guo, “G-MAP123: A mechanistic-based data driven approach for 3D nonlinear elastic modeling via both uniaxial and equibiaxial tension experimental data,” Extreme Mech. Lett. 50, 101545 (2022).
L. Zubov and M. Karyakin, “Nonlinear deformations of a cylindrical pipe with pre-stressed thin coatings,” Math. Mech. Solids 27 (9), 1703–1720 (2022).
W. Wagner and F. Gruttmann, “On a nonlinear elastic composite shell model with a refined 3D stress analysis,” in Current Trends and Open Problems in Computational Mechanics (Springer, Berlin, 2022), pp. 553–567.
C. D. Coman and A. P. Bassom, “Axially compressed thin cylindrical shells: Asymptotic limits for a nonlinear basic state,” Int. J. Non-Linear Mech. 138, 103848 (2022).
H. Babaei, “Thermomechanical analysis of snap-buckling phenomenon in long FG-CNTRC cylindrical panels resting on nonlinear elastic foundation,” Composite Struct. 286, 115199 (2022)
S. Mondal and M. Kanoria, “Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity,” Mech. Based Des. Struct. 48 (3), 277–298 (2020).
S. Mondal, “Memory response in a magneto-thermoelastic rod with moving heat source based on Eringen’s nonlocal theory under dual-phase lag heat conduction,” Int. J. Comput. Methods 17 (9), 1950072 (2020).
A. Alibeigloo, “Three-dimensional thermoelasticity analysis of graphene platelets reinforced cylindrical panel,” Eur. J. Mech. A Solids 81, 103941 (2020).
M. Bachher and N. Sarkar, “Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer,” Waves Random Complex Media 29 (4), 595–613 (2020).
R. Kumar and R. Prasad, “Thermoelastic interactions on hyperbolic two-temperature generalized thermoelasticity in an infinite medium with a cylindrical cavity,” Eur. J. Mech. A Solids 82, 104007 (2020).
E. Salari and S. S. Vanini, “Investigation of thermal preloading and porosity effects on the nonlocal nonlinear instability of FG nanobeams with geometrical imperfection,” Eur. J. Mech. A Solids 86, 104183 (2021).
D. K. Sharma, H. Mittal, and S. R. Sharma, “Forced vibration analysis in axisymmetric functionally graded viscothermoelastic hollow cylinder under dynamic pressure,” Proc. Natl. Acad. Sci. India Sect. A: Phys. Sci. 90 (5), 809–818 (2020).
D. K. Sharma, M. K. Sharma, and N. Sarkar, “Effect of three-phase-lag model on the analysis of three-dimensional free vibrations of viscothermoelastic solid cylinder,” Appl. Math. Model. 90, 281–301 (2021).
D. K. Sharma, D. Thakur, and N. Sarkar, “Effect of dual-phase-lag model on the vibration analysis of nonlocal generalized thermoelastic diffusive hollow sphere,” Waves Random Complex Media 32 (4), 1626–1643 (2022).
D. K. Sharma, D. Thakur, V. Walia, and N. Sarkar, “Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion,” J. Therm. Stresses 43 (8), 981–997 (2020).
D. K. Sharma, D. Thakur, and N. Sarkar, “Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with voids,” Mech. Based Des. Struct. 50 (11), 3949–3965 (2022).
N. Sharma, “Analysis of free vibrations in transracially isotropic spherically symmetric thermoelastic spheres,” Multidiscip. Model. Mater. Struct. 16 (6), 1631–1650 (2020).
R. Selvamani and S. Mahesh, “Mathematical modeling and analysis of elastic waves in a thermo piezoelectric multilayered rotating composite rod with LEMV/CFRP interface,” Tech. Mech.-Eur. J. Eng. Mech. 39 (3), 241–251 (2019).
R. Selvamani and S. Mahesh, “Viscothermoelastic waves in a gravitated piezoelectric multilayered LEMV/CFRP cylinder coated with thin film,” Tech. Mech.-Eur. J. Eng. Mech. 41 (1), 14–23 (2021).
R. Selvamani, S. Mahesh, and F. Ebrahimi, “Frequency characteristics of a multiferroic Piezoelectric/LEMV/CFRP/Piezomagnetic composite hollow cylinder under the influence of rotation and hydrostatic stress,” Coupled Syst. Mech. 10 (2), 185–198 (2021).
S. Mahesh and R. Selvamani, “Bending analysis of generalized thermoelastic waves in a multilayered cylinder using theory of dual phase lagging,” J. Phys. Conf. Ser. 1597 (1), 012013 (2020).
A. M. Zenkour, “Thermal-shock problem for a hollow cylinder via a multi-dual phase-lag theory,” J. Therm. Stresses 43 (6), 687–706 (2020).
V. K. Nelson and S. Karthikeyan, “Axisymmetric vibration of pyrocomposite hollow cylinder,” World Acad. Sci. Eng. Technol. Int. J. Math. Comput. Phys. Electrical Comput. Eng. 2 (1), 9–15 (2008).
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Mahesh, S., Selvamani, R. & Ebrahimi, F. The Effect of Nonlocal Scale Value and Phase Lags on Thermoelastic Waves in a Multilayered LEMV/CFRP Composite Cylinder. Comput. Math. and Math. Phys. 63, 1717–1730 (2023). https://doi.org/10.1134/S0965542523090129
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DOI: https://doi.org/10.1134/S0965542523090129