Abstract
In the present work, the effect of frequency-dependent viscoelastic property on the forced/parametric resonant amplitude of viscoelastic sandwich beam is investigated by deriving a reduced-order finite element model (ROM) in frequency domain. In this concern, the frequency-dependent viscoelasticity is modelled using fractional Zener model and the corresponding responses of sandwich beam are compared with that are derived using an equivalent Kelvin-Voigt model. The ROM in frequency domain is derived by implementing harmonic balance method prior to the finite element discretization and reduced-order transformation. The comparison of frequency responses evaluated using ROM and full-order model revealed that the ROM with reduction basis from modal strain energy method provides the response of frequency-dependent viscoelastic sandwich beam with reasonable accuracy. Further, the frequency-dependent viscoelastic property has shown a significant effect on the resonant amplitudes especially when compared with an equivalent Kelvin-Voigt model in wide-frequency range. Moreover, the results suggest that the nonlinear frequency response analysis of viscoelastic layered beams using Kelvin-Voigt model may be reasonably accurate when the different model parameters are considered around each modal natural frequency.
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References
Jacques, N., Daya, E.M., Potier-Ferry, M.: Nonlinear vibration of viscoelastic sandwich beams by the harmonic balance and finite element methods. J. Sound Vib. 329(20), 4251–4265 (2010)
Zhu, B., Dong, Y., Li, Y.: Nonlinear dynamics of a viscoelastic sandwich beam with parametric excitations and internal resonance. Nonlinear Dyn. 94(4), 2575–2612 (2018)
Reddy, R.S., Panda, S., Gupta, A.: Nonlinear dynamics and active control of smart beams using shear/extensional mode piezoelectric actuators. Int. J. Mech. Sci. 106495 (2021)
Dwivedy, S.K., Sahu, K.C., Babu, S.: Parametric instability regions of three-layered soft-cored sandwich beam using higher-order theory. J. Sound Vib. 304(1–2), 326–344 (2007)
Gupta, A., Panda, S., Reddy, R.S.: Passive control of parametric instability of layered beams using graphite particle-filled viscoelastic damping layers. Mech. Adv. Mater. Struct. 1–16 (2021)
Gupta, A., Panda, S., Reddy, R.S.: Improved damping in sandwich beams through the inclusion of dispersed graphite particles within the viscoelastic core. Compos. Struct. 247, 112424 (2020)
Madeira, J.F.A., Araújo, A.L., Soares, C.M.M., Soares, C.A.M.: Multiobjective optimization for vibration reduction in composite plate structures using constrained layer damping. Comput. Struct. 232, 105810 (2020)
Detroux, T., Renson, L., Masset, L., Kerschen, G.: The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Comput. Methods Appl. Mech. Eng. 296, 18–38 (2015)
Litewka, P., Lewandowski, R.: Steady-state non-linear vibrations of plates using Zener material model with fractional derivative. Comput. Mech. 60, 333–354 (2017)
Galucio, A.C., Deü, J.-F., Ohayon, R.: Finite element formulation of viscoelastic sandwich beams using fractional derivative operators. Comput. Mech. 33(4), 282–291 (2004)
Rutzmoser, J.: Model order reduction for nonlinear structural dynamics. Doctoral dissertation, Technische Universität München (2018)
Touzé, C., Vidrascu, M., Chapelle, D.: Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models. Comput. Mech. 54(2), 567–580 (2014)
Givois, A., Grolet, A., Thomas, O., Deü, J.-F.: On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models. Nonlinear Dyn. 97(2), 1747–1781 (2019)
Lv, H.-W., Li, L., Li, Y.-H.: Non-linearly parametric resonances of an axially moving viscoelastic sandwich beam with time-dependent velocity. Appl. Math. Model. 53, 83–105 (2018)
Ray, M.C., Baz, A.: Control of nonlinear vibration of beams using active constrained layer damping. J. Vib. Control. 7(4), 539–549 (2001)
Rouleau, L., Deü, J.-F., Legay, A.: A comparison of model reduction techniques based on modal projection for structures with frequency-dependent damping. Mech. Syst. Signal Process. 90, 110–125 (2017)
Rutzmoser, J.B., Rixen, D.J., Tiso, P., Jain, S.: Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics. Comput. Struct. 192, 196–209 (2017)
Shih, Y.-S., Yeh, Z.-F.: Dynamic stability of a viscoelastic beam with frequency-dependent modulus. Int. J. Solids Struct. 42(7), 2145–2159 (2005)
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Shashidhar Reddy, R., Gupta, A., Panda, S. (2022). Nonlinear Frequency Response of Sandwich Beam with Frequency-Dependent Viscoelastic Core Using Reduced-Order Finite Element Method. In: Popat, K.C., Kanagaraj, S., Sreekanth, P.S.R., Kumar, V.M.R. (eds) Advances in Mechanical Engineering and Material Science. ICAMEMS 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-0676-3_1
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DOI: https://doi.org/10.1007/978-981-19-0676-3_1
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