References
- Y. Zhai, S. Li, and S. Liang, Free vibration analysis of five-layered composite sandwich plates with two-layered viscoelastic cores, Compos. Struct., vol. 200, pp. 346–357, 2018. DOI: https://doi.org/10.1016/j.compstruct.2018.05.082.
- A. Arani, G. Jafari, and R. Kolahchi, Nonlinear vibration analysis of viscoelastic micro nano-composite sandwich plates integrated with sensor and actuator, Microsyst. Technol., vol. 23, no. 5, pp. 1509–1535, 2017. DOI: https://doi.org/10.1007/s00542-016-3095-9.
- M. Sheng, Z. Guo, Q. Qin, and Y. He, Vibration characteristics of a sandwich plate with viscoelastic periodic cores, Compos. Struct., vol. 206, pp. 54–69, 2018. DOI: https://doi.org/10.1016/j.compstruct.2018.07.110.
- L. Irazu and M.J. Elejabarrieta, A novel hybrid sandwich structure: Viscoelastic and eddy current damping, Mater. Design., vol. 140, pp. 460–472, 2018. DOI: https://doi.org/10.1016/j.matdes.2017.11.070.
- Y.H. Li, Y.H. Dong, Y. Qin, and H.W. Lv, Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam, Int. J. Mech. Sci., vol. 138–139, no. 139, pp. 131–145, 2018. DOI: https://doi.org/10.1016/j.ijmecsci.2018.01.041.
- D. Younesian, A. Hosseinkhani, H. Askari, and E. Esmailzadeh, Elastic and viscoelastic foundations: A review on linear and nonlinear vibration modeling and applications, Nonlinear Dyn., vol. 97, no. 1, pp. 853–895, 2019. DOI: https://doi.org/10.1007/s11071-019-04977-9.
- B.D. Vogt, Mechanical and viscoelastic properties of confined amorphous polymers, J. Polym. Sci. Part B: Polym. Phys., vol. 56, no. 1, pp. 9–30, 2018. DOI: https://doi.org/10.1002/polb.24529.
- X.Q. Zhou, D.Y. Yu, X.Y. Shao, S.Q. Zhang, and S. Wang, Research and applications of viscoelastic vibration damping materials: A review, Compos. Struct., vol. 136, pp. 460–480, 2016. DOI: https://doi.org/10.1016/j.compstruct.2015.10.014.
- X.Y. Xu, R. Augello, and H. Yang, The generation and validation of a CUF-based FEA model with laser-based experiments, Mech. Adv. Mater. Struct., 2019.
- X.Y. Xu, H. Yang, R. Augello, and E. Carrera, Optimized free-form surface modeling of point clouds from laser-based measurement, Mech. Adv. Mater. Struct., 2019.
- H. Yang and X.Y. Xu, Multi-sensor technology for B-spline modelling and deformation analysis of composite structures, Compos. Struct., vol. 224, pp. 111000, 2019. DOI: https://doi.org/10.1016/j.compstruct.2019.111000.
- Y. Chen, P.P. Yang, Y.X. Zhou, Z.Y. Guo, L.T. Dong, and E.P. Busso, A micromechanics-based constitutive model for linear viscoelastic particle-reinforced composites, Mech. Mater., vol. 140, pp. 103228, 2020. DOI: https://doi.org/10.1016/j.mechmat.2019.103228.
- Y. Chen, Z. Guo, X.L. Gao, L. Dong, and Z. Zhong, Constitutive modeling of viscoelastic fiber-reinforced composites at finite deformations, Mech. Mater., vol. 131, pp. 102–112, 2019. DOI: https://doi.org/10.1016/j.mechmat.2019.02.001.
- H. Liu, G.A. Holzapfel, B.H. Skallerud, and V. Prot, Anisotropic finite strain viscoelasticity: Constitutive modeling and finite element implementation, J. Mech. Phys. Solids., vol. 124, pp. 172–188, 2019. DOI: https://doi.org/10.1016/j.jmps.2018.09.014.
- G. He, Y.C. Liu, Y. Hammi, D.J. Bammann, and M.F. Horstemeyer, A combined viscoelasticity-viscoplasticity-anisotropic damage model with evolving internal state variables applied to fiber reinforced polymer composites, Mech. Adv. Mater. Struct., 2020.
- M.M. Svanadze, Potential method in the theory of thermoviscoelastic mixtures, J. Therm. Stress., vol. 41, no. 8, pp. 1022–1041, 2018. DOI: https://doi.org/10.1080/01495739.2018.1446203.
- H.L. Dai, Z.Q. Zheng, W.L. Xu, H.B. Liu, and A.H. Luo, Thermoviscoelastic dynamic response for a rectangular steel plate under laser processing, Int. J. Heat. Mass. Transf., vol. 105, pp. 24–33, 2017. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.063.
- H. Zeng, J.S. Leng, J.P. Gu, and H.Y. Sun, A thermovisoelastic model incorporated with uncoupled structural and stress relaxation mechanisms for amorphous shape memory polymers, Mech. Mater., vol. 124, pp. 18–25, 2018. DOI: https://doi.org/10.1016/j.mechmat.2018.05.010.
- V. Peshkov, Second sound in helium II, J. Phys., vol. 8, pp. 381–382, 1944.
- V. Narayana and R.C. Dynes, Observation of second sound in bismuth, Phys. Rev. Lett., vol. 28, no. 22, pp. 1461–1465, 1972. DOI: https://doi.org/10.1103/PhysRevLett.28.1461.
- S.L. Sobolev, On hyperbolic heat-mass transfer equation, Int. J. Heat. Transf., vol. 122, pp. 629–630, 2018. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.022.
- C. Cattaneo, A form of heat equation which eliminates the paradox of instantaneous propagation, CR. Acad. Sci., vol. 247, pp. 431–433, 1958.
- P. Vernotte, Paradoxes in the continuous theory of the heat conduction, CR. Acad. Sci., vol. 246, pp. 3154–3155, 1958.
- D.D. Joseph, and L. Preziosi, Heat waves, Rev. Mod. Phys., vol. 61, no. 1, pp. 41–73, 1989. DOI: https://doi.org/10.1103/RevModPhys.61.41.
- M.A. Ezzat, and A.S. Ei-Karamany, The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with two relaxation times, Int. J. Eng. Sci., vol. 40, no. 11, pp. 1275–1284, 2002. DOI: https://doi.org/10.1016/S0020-7225(01)00099-4.
- A.S. El-Karamany, and M.A. Ezzat, On the boundary integral formulation of thermo-viscoelasticity theory, Int. J. Eng. Sci., vol. 40, no. 17, pp. 1943–1956, 2002. DOI: https://doi.org/10.1016/S0020-7225(02)00043-5.
- A.S. Ei-Karamany, Boundary integral equation formulation in generalized thermo-viscoelasticity with rheological volume, J. Appl. Mech., vol. 70, pp. 661–667, 2003.
- M. Mirzaei, Lord-Shulman nonlinear generalized thermoviscoelasticity of a strip, Int. J. Str. Stab. Dyn., vol. 20, no. 2, pp. 2050017, 2020. DOI: https://doi.org/10.1142/S0219455420500170.
- M.A. Ezzat, M.I. Othman, and A.M.S. Ei-Karamany, State space approach of two-dimensional generalized thermo-viscoelasticity with two relaxation times, Int. J. Eng. Sci., vol. 40, no. 11, pp. 1251–1274, 2002. DOI: https://doi.org/10.1016/S0020-7225(02)00012-5.
- A.S. El-Karamany and M.A. Ezzat, Thermal shock problem in generalized thermo-viscoelasticity under four theories, Int. J. Eng. Sci., vol. 42, no. 7, pp. 649–671, 2004. DOI: https://doi.org/10.1016/j.ijengsci.2003.07.009.
- H.H. Sherief, F.A. Hamza, and A.M. Abd El-Latief, Abd EI-Latief, 2D problem for a half-space in the generalized theory of thermo-viscoelasticity, Mech. Time-Depend. Mater., vol. 19, no. 4, pp. 557–568, 2015. DOI: https://doi.org/10.1007/s11043-015-9278-4.
- Y. Xu, Z.D. Xu, Y.Q. Guo, Y. Dong, and X. Huang, A generalized magneto-thermoviscoelastic problem of a single-layer plate for vibration control considering memory-dependent heat transfer and nonlocal effect, J. Heat Transf., vol. 141, pp. 082002, 2019.
- J.N. Sharma and M.I.A. Othman, Effect of rotation on generalized thermo-viscoelastic Rayleigh-Lamb waves, Int. J. Solids. Struct., vol. 44, no. 13, pp. 4243–4255, 2007. DOI: https://doi.org/10.1016/j.ijsolstr.2006.11.016.
- G. Liu, X. Liu, and R. Ye, The relaxation effects of a saturated porous media using the generalized thermoviscoelasticity theory, Int. J. Eng. Sci., vol. 48, no. 9, pp. 795–808, 2010. DOI: https://doi.org/10.1016/j.ijengsci.2010.04.006.
- O. Narayan and S. Ramaswamy, Anomalous heat conduction in one-dimensional momentum-conserving systems, Phys. Rev. Lett., vol. 89, no. 20, pp. 200601, 2002. DOI: https://doi.org/10.1103/PhysRevLett.89.200601.
- I. Calvo, R. Sanchez, B.A. Carreras, and B.P. van Milligen, Fractional generalization of Fick’s law: A microscopic approach, Phys. Rev. Lett., vol. 99, no. 23, pp. 230603, 2007. DOI: https://doi.org/10.1103/PhysRevLett.99.230603.
- Y. Sagi, M. Brook, I. Almog, and N. Davidson, Observation of anomalous diffusion and fractional selfsimilarity in one dimension, Phys. Rev. Lett., vol. 108, no. 9, pp. 093002, 2012. DOI: https://doi.org/10.1103/PhysRevLett.108.093002.
- S. Deswal and K.K. Kalkal, Fractional order heat conduction law in micropolar thermo-viscoelasticity with two temperatures, Int. J. Heat. Mass. Transf., vol. 66, pp. 451–460, 2013. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2013.07.047.
- M.A. Ezzat, A.S. Ei-Karamany, and A.A. Ei-Bary, Generalized thermo-viscoelasticity with memory-dependent derivative, Int. J. Mech. Sci., vol. 89, pp. 470–475, 2014. DOI: https://doi.org/10.1016/j.ijmecsci.2014.10.006.
- C.L. Li, H.L. Guo, and X.G. Tian, Shock-induced thermal wave propagation and response analysis of a viscoelastic thin plate under transient heating loads, Wave. Random. Complex., vol. 28, no. 2, pp. 270–286, 2018. DOI: https://doi.org/10.1080/17455030.2017.1341670.
- MDi Paola, A. Pirrotta, and A. Valenza, Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results, Mech. Mater., vol. 43, no. 12, pp. 799–806, 2011. DOI: https://doi.org/10.1016/j.mechmat.2011.08.016.
- X.X. Guo, G.Q. Yan, L. Benyahia, and S. Sahraoui, Fitting stress relaxation experiments with fractional Zener model to predict high frequency moduli of polymeric acoustic foams, Mech. Time-Depend. Mater., vol. 20, no. 4, pp. 523–533, 2016. DOI: https://doi.org/10.1007/s11043-016-9310-3.
- G. Reiter, et al., Residual stresses in thin polymer films cause rupture and dominate early stages of dewetting, Nat. Mater., vol. 4, no. 10, pp. 754–758, 2005. DOI: https://doi.org/10.1038/nmat1484.
- R.L. Bagley and P.J. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, J. Rheol., vol. 27, no. 3, pp. 201–210, 1983. DOI: https://doi.org/10.1122/1.549724.
- F.C. Meral, T.J. Royston, and R. Magin, Fractional calculus in viscoelasticity: An experimental study, Commun. Nonlinear Sci. Numer. Simulat., vol. 15, no. 4, pp. 939–945, 2010. DOI: https://doi.org/10.1016/j.cnsns.2009.05.004.
- S. Mashayekhi, P. Miles, M.Y. Hussaini, and W.S. Oates, Fractional viscoelasticity in fractal and non-fractal media: Theory, experimental validation, and uncertainty analysis, J. Mech. Phys. Solids., vol. 111, pp. 134–156, 2018. DOI: https://doi.org/10.1016/j.jmps.2017.10.013.
- N. Heymans and J.C. Bauwens, Fractional rheological models and fractional differential-equations for viscoelastic behavior, Rheola. Acta., vol. 33, no. 3, pp. 210–219, 1994. DOI: https://doi.org/10.1007/BF00437306.
- J.D. Ferry, R.F. Landel, and M.L. Williams, Extensions of the Rouse theory of viscoelastic properties to undiluted linear polymers, J. Appl. Phys., vol. 26, no. 4, pp. 359–362, 1955. DOI: https://doi.org/10.1063/1.1721997.
- K. Adolfsson, M. Enelund, and P. Olsson, On the fractional order model of viscoelasticity, Mech. Time-Depend. Mater., vol. 9, no. 1, pp. 15–34, 2005. DOI: https://doi.org/10.1007/s11043-005-3442-1.
- A. Chirilă and M. Marin, The theory of generalized thermoelasticity with fractional order strain for dipolar materials with double porosity, J. Mater. Sci., vol. 53, no. 5, pp. 3470–3482, 2018. DOI: https://doi.org/10.1007/s10853-017-1785-z.
- C.L. Li, H.L. Guo, X.G. Tian, and T.H. He, Generalized thermoelastic diffusion problems with fractional order strain, Eur. J. Mech. A-Solid., vol. 78, pp. 103827, 2019. DOI: https://doi.org/10.1016/j.euromechsol.2019.103827.
- H.M. Youssef and E.A.N. Al-Lehaibi, State-space approach to three-dimensional generalized thermoelasticity with fractional order strain, Mech. Adv. Mater. Struct., vol. 26, no. 10, pp. 878–885, 2019. DOI: https://doi.org/10.1080/15376494.2018.1430270.
- C.L. Li, H.L. Guo, X.G. Tian, and T.H. He, Generalized thermoviscoelastic analysis with fractional order strain in a thick viscoelastic plate of infinite extent, J. Therm. Stress., vol. 42, no. 8, pp. 1051–1070, 2019. DOI: https://doi.org/10.1080/01495739.2019.1587331.
- S.A. Meftah, E.M. Daya, and A. Tounsi, Finite element modeling of sandwich boc column with viscoelastic layer for passive vibrations control under seismic loading, Thin-Wall Struct., vol. 51, pp. 174–185, 2012. DOI: https://doi.org/10.1016/j.tws.2011.10.015.
- J.S. Moita, A.L. Araujo, C.M.M. Soares, and C.A.M. Soares, Vibration analysis of functionally graded material sandwich structures with passive damping, Compos. Struct., vol. 183, pp. 407–415, 2018. DOI: https://doi.org/10.1016/j.compstruct.2017.04.045.
- L. Brancik, Programs for fast numerical inversion of Laplace Transforms in MATLAB Language Environment, Proc. Seventh Prague Conference MATLAB., vol. 99, pp. 27–39, 1999.