Gradient Chain Structure Model for Characterizing Frequency Dependence of Viscoelastic Materials
Publication: Journal of Engineering Mechanics
Volume 146, Issue 9
Abstract
The frequency dependence modeling of viscoelastic (VE) materials faces the challenge of high modeling accuracy over a wide frequency range and double-objective optimization in model parameter identification. To address these two issues, a gradient chain structure model and a model parameter identification method are proposed. Inspired by chain structure models, two gradient functions are introduced to update the roles of a chain network and free chains in the mechanical behavior of VE materials. A two-step parameter identification method is proposed to obtain the model parameters and gradient functions. Then a dynamic property test of VE dampers is conducted to study the frequency effect on the equivalent stiffness and loss factor. Also, the test results are used to verify the proposed gradient model. Further, a comparison of the gradient model, a 5-parameter rheological model, the fractional derivative Zener model, and 10 sets of experimental data are conducted to illustrate the feasibility and superiority of the proposed gradient model for VE materials with different kinds of properties. The numerical data from the gradient chain structure model fit well with the experimental data over a wide frequency range, and the proposed model performs much better than the other two typical models in terms of both modeling accuracy and stability.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
Financial support for this research was provided by the National Science Fund for Distinguished Young Scholars (Grant No. 51625803), Changjiang Scholars Program of the Ministry of Education of China, Superior Academic Discipline Construction Project of Jiangsu Higher Education Institutions (Grant No. CE02-1-50), Postgraduate Research & Practice Innovation Program of Jiangsu Province (3205008712, KYCX17_0122), and the China Scholarship Council. These organizations’ support is gratefully acknowledged.
References
Abe, M., J. Yoshida, and Y. Fujino. 2004. “Multiaxial behaviors of laminated rubber bearings and their modeling. I: Experimental study.” J. Struct. Eng. 130 (8): 1119–1132. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:8(1119).
Aprile, A., J. A. Inaudi, and J. M. Kelly. 1997. “Evolutionary model of viscoelastic dampers for structural applications.” J. Eng. Mech. 123 (6): 551–560. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:6(551).
Chang, K. C., T. T. Soong, S. T. Oh, and M. L. Lai. 1991. Seismic response of a 2/5 scale steel structure with added viscoelastic dampers. Buffalo, NY: State Univ. of New York at Buffalo.
Chen, S., F. Liu, X. Jiang, I. Turner, and K. Burrage. 2016. “Fast finite difference approximation for identifying parameters in a two-dimensional space-fractional nonlocal model with variable diffusivity coefficients.” SIAM J. Numer. Anal. 54 (2): 606–624. https://doi.org/10.1137/15M1019301.
Dai, J., Z. D. Xu, and P. P. Gai. 2019. “Dynamic analysis of viscoelastic tuned mass damper system under harmonic excitation.” J. Vib. Control 25 (11): 1768–1779. https://doi.org/10.1177/1077546319833887.
Deng, W. 2007. “Short memory principle and a predictor–corrector approach for fractional differential equations.” J. Comput. Appl. Math. 206 (1): 174–188. https://doi.org/10.1016/j.cam.2006.06.008.
Ghaemmaghami, A. R., and O. S. Kwon. 2018. “Nonlinear modeling of MDOF structures equipped with viscoelastic dampers with strain, temperature and frequency-dependent properties.” Eng. Struct. 168 (Aug): 903–914. https://doi.org/10.1016/j.engstruct.2018.04.037.
Gong, S., and Y. Zhou. 2017. “Experimental study and numerical simulation on a new type of viscoelastic damper with strong nonlinear characteristics.” Struct. Control Health 24 (4): e1897. https://doi.org/10.1002/stc.1897.
Gong, S., Y. Zhou, and P. Ge. 2017. “Seismic analysis for tall and irregular temple buildings: A case study of strong nonlinear viscoelastic dampers.” Struct. Des. Tall Special Build. 26 (7): e1352. https://doi.org/10.1002/tal.1352.
Greco, R., and G. C. Marano. 2015. “Identification of parameters of Maxwell and Kelvin–Voigt generalized models for fluid viscous dampers.” J. Vib. Control 21 (2): 260–274. https://doi.org/10.1177/1077546313487937.
Housner, G. W., L. A. Bergman, T. K. Caughey, A. G. Chassiakos, R. O. Claus, S. F. Masri, R. E. Skelton, T. T. Soong, B. F. Spencer, and J. T. Yao. 1997. “Structural control: Past, present, and future.” J. Eng. Mech. 123 (9): 897–971. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:9(897).
Jiang, J., P. Zhang, D. Patil, H. N. Li, and G. Song. 2017. “Experimental studies on the effectiveness and robustness of a pounding tuned mass damper for vibration suppression of a submerged cylindrical pipe.” Struct. Control Health 24 (12): e2027. https://doi.org/10.1002/stc.2027.
Lewandowski, R., and M. Baum. 2015. “Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model.” Arch. Appl. Mech. 85 (12): 1793–1814. https://doi.org/10.1007/s00419-015-1019-2.
Lewandowski, R., and B. Chorążyczewski. 2010. “Identification of the parameters of the Kelvin–Voigt and the maxwell fractional models, used to modeling of viscoelastic dampers.” Comput. Struct. 88 (1–2): 1–17. https://doi.org/10.1016/j.compstruc.2009.09.001.
Lewandowski, R., and M. Łasecka-Plura. 2016. “Design sensitivity analysis of structures with viscoelastic dampers.” Comput. Struct. 164 (Feb): 95–107. https://doi.org/10.1016/j.compstruc.2015.11.011.
Lewandowski, R., M. Slowik, and M. Przychodzki. 2017. “Parameters identification of fractional models of viscoelastic dampers and fluids.” Struct. Eng. Mech. 63 (2): 181–193. https://doi.org/10.12989/sem.2017.63.2.181.
Li, L., and Y. Hu. 2016. “State-space method for viscoelastic systems involving general damping model.” AIAA J. 56 (10): 3290–3295. https://doi.org/10.2514/1.J054180.
Li, Y., S. Tang, B. C. Abberton, M. Kröger, C. Burkhart, B. Jiang, G. J. Papakonstantopoulos, M. Poldneff, and W. K. Liu. 2012. “A predictive multiscale computational framework for viscoelastic properties of linear polymers.” Polymer 53 (25): 5935–5952. https://doi.org/10.1016/j.polymer.2012.09.055.
Makris, N., G. F. Dargush, and M. C. Constantinou. 1995. “Dynamic analysis of viscoelastic-fluid dampers.” J. Eng. Mech. 121 (10): 1114–1121. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:10(1114).
Marckmann, G., and E. Verron. 2006. “Comparison of hyperelastic models for rubber-like materials.” Rubber Chem. Technol. 79 (5): 835–858. https://doi.org/10.5254/1.3547969.
Miehe, C., S. Göktepe, and F. Lulei. 2004. “A micro-macro approach to rubber-like materials—Part I: The non-affine micro-sphere model of rubber elasticity.” J. Mech. Phys. Solids 52 (11): 2617–2660. https://doi.org/10.1016/j.jmps.2004.03.011.
Podlubny, I. 1999. Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. San Diego: Academic Press.
Richard, M. C. 2003. Theory of viscoelasticity. 2nd ed. New York: Dover Publications.
Shen, K. L., and T. T. Soong. 1995. “Modeling of viscoelastic dampers for structural applications.” J. Eng. Mech. 121 (6): 694–701. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:6(694).
Soong, T. T., and B. F. Spencer, Jr. 2002. “Supplemental energy dissipation: State-of-the-art and state-of-the-practice.” Eng. Struct. 24 (3): 243–259. https://doi.org/10.1016/S0141-0296(01)00092-X.
Szajek, K., and W. Sumelka. 2019. “Discrete mass-spring structure identification in nonlocal continuum space-fractional model.” Eur. Phys. J. Plus 134 (9): 448. https://doi.org/10.1140/epjp/i2019-12890-8.
Tang, S., M. S. Greene, and W. K. Liu. 2012. “Two-scale mechanism-based theory of nonlinear viscoelasticity.” J. Mech. Phys. Solids 60 (2): 199–226. https://doi.org/10.1016/j.jmps.2011.11.003.
Tomita, Y., W. Lu, M. Naito, and Y. Furutani. 2006. “Numerical evaluation of micro-to macroscopic mechanical behavior of carbon-black-filled rubber.” Int. J. Mech. Sci. 48 (2): 108–116. https://doi.org/10.1016/j.ijmecsci.2005.08.009.
Xiao, R., H. Sun, and W. Chen. 2016. “An equivalence between generalized Maxwell model and fractional Zener model.” Mech. Mater. 100 (Sep): 148–153. https://doi.org/10.1016/j.mechmat.2016.06.016.
Xu, C., Z. D. Xu, T. Ge, and Y. X. Liao. 2016a. “Modeling and experimentation of a viscoelastic microvibration damper based on a chain network model.” J. Mech. Mater. Struct. 11 (4): 413–432. https://doi.org/10.2140/jomms.2016.11.413.
Xu, Y., and Z. He. 2011. “The short memory principle for solving Abel differential equation of fractional order.” Comput. Math. Appl. 62 (12): 4796–4805. https://doi.org/10.1016/j.camwa.2011.10.071.
Xu, Z. D., T. Ge, and J. Liu. 2020. “Experimental and theoretical study of high energy dissipation viscoelastic dampers based on acrylate rubber matrix.” J. Eng. Mech. 146 (6): 04020057. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001802.
Xu, Z. D., Y. X. Liao, T. Ge, and C. Xu. 2016b. “Experimental and theoretical study of viscoelastic dampers with different matrix rubbers.” J. Eng. Mech. 142 (8): 04016051. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001101.
Xu, Z. D., C. Xu, and J. Hu. 2015. “Equivalent fractional Kelvin model and experimental study on viscoelastic damper.” J. Vib. Control 21 (13): 2536–2552. https://doi.org/10.1177/1077546313513604.
Yuan, Z. B., Y. F. Nie, F. Liu, I. Turner, G. Y. Zhang, and Y. Gu. 2016. “An advanced numerical modeling for Riesz space fractional advection–dispersion equations by a meshfree approach.” Appl. Math. Model 40 (17–18): 7816–7829. https://doi.org/10.1016/j.apm.2016.03.036.
Zheng, H., C. Cai, and X. M. Tan. 2004. “Optimization of partial constrained layer damping treatment for vibrational energy minimization of vibrating beams.” Comput. Struct. 82 (29–30): 2493–2507. https://doi.org/10.1016/j.compstruc.2004.07.002.
Zhou, J., L. Jiang, and R. E. Khayat. 2018. “A micro–macro constitutive model for finite-deformation viscoelasticity of elastomers with nonlinear viscosity.” J. Mech. Phys. Solids 110 (Jan): 137–154. https://doi.org/10.1016/j.jmps.2017.09.016.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 9 • September 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Aug 15, 2019
Accepted: Apr 22, 2020
Published online: Jun 26, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 26, 2020
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