Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T23:56:58.514Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic Dynamic Response of a Simplified Nonlinear Fluid Model for Viscoelastic Materials

Published online by Cambridge University Press:  08 May 2012

T.-P. Chang
T.-P. Chang*
Affiliation:
Department of Construction Engineering, National Kaohsiung First University of Science & Technology, Kaohsiung, Taiwan 81164, R.O.C.
*
*Corresponding author (tpchang@ccms.nkfust.edu.tw)
Get access

Abstract

In the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

Keywords

Simplified nonlinear fluid modelViscoelastic materialsClosed-form solutionStochastic dynamic response
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 2 , June 2012 , pp. 365 - 372
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Drozdov, A. D., Mechanics of Viscoelastic Solids, New York, John Wiley Sons (1998).Google Scholar
2. Lakes, R. S., Viscoelastic Solids, Boca Raton, FL, CRC Press (1999).Google Scholar
3. Geil, M. D., “An Iterative Method for Viscoelastic Modeling of Prosthetic Feet,” Journal of Biomechanics, 35, pp. 1405–1410 (2002).CrossRefGoogle ScholarPubMed
4. Weiss, J. A., Gardiner, J. C. and Bonifasi-Lista, C., “Ligament Material Behavior is Nonlinear, Viscoelastic and Rate-Independent Under Shear Loading,” Journal of Biomechanics, 35, pp. 943–950 (2002).Google Scholar
5. Koop, B. E. and Lewis, J. L., “A Model of Fracture Testing of Soft Viscoelastic Tissues,” Journal of Biomechanics, 36, pp. 605–608 (2003).Google Scholar
6. Allen, K. D. and Athanasiou, K. A., “Viscoelastic Characterization of the Porcine Temporomandibular Joint Disc Under Unconfined Compression,” Journal of Biomechanics, 39, pp. 312–322 (2006).CrossRefGoogle ScholarPubMed
7. Ciarletta, P., Micera, S., Accoto, D. and Dario, P., “A Novel Microstructural Approach in Tendon Viscoelastic Modelling at the Fibrillar Level,” Journal of Biomechanics, 39, pp. 2034–2042 (2006).Google Scholar
8. Guedes, R. M., Simões, J. A. and Morais, J. L., “Viscoelastic Behaviour and Failure of Bovine Cancellous Bone Under Constant Strain Rate,” Journal of Biomechanics, 39, pp. 49–60 (2006).Google Scholar
9. Li, J. and Weng, G. J., “Growth and Stress-Strain Relations of a Class of Viscoelastic Porous Materials,” Mechanics of Materials, 22, pp. 179–188 (1996).Google Scholar
10. Ju, B. F. and Liu, K. K., “Characterizing Viscoelastic Properties of Thin Elastomeric Membrane,” Mechanics of Materials, 34, pp. 485–491 (2002).Google Scholar
11. Wang, B. and Xiao, Z., “A Constitutive Equation for Viscoelastic Porous Gels During Syneresis and Drying,” Mechanics of Materials, 34, pp. 299–311 (2002).CrossRefGoogle Scholar
12. Kumar, R. S. and Talreja, R., “A Continuum Damage Model for Linear Viscoelastic Composite Materials,” Mechanics of Materials, 35, pp. 463–480 (2003).CrossRefGoogle Scholar
13. Liu, Q. and Subhash, G., “Characterization of Viscoelastic Properties of Polymer Bar Using Iterative Deconvolution in the Time Domain,” Mechanics of Materials, 38, pp. 1105–1117 (2006).Google Scholar
14. Herzog, W. and Leonard, T. R., “Depression of Cat Soleus Forces Following Isokinetic Shortening,” Journal of Biomechanics, 30, pp. 865–872 (1997).Google Scholar
15. Forcinito, M., Epstein, M. and Herzog, W., “Can a Rheological Muscle Model Predict Force Depression/Enhancement?” Journal of Biomechanics, 31, pp. 1093–1099 (1998).Google Scholar
16. Chang, T.-P. and Liu, M.-F., “Nonlinear Vibration Analysis of an Elastic Plate Subjected to Heavy Fluid Loading in Magnetic Field,” International Journal of Solids and Structures, 46, pp. 1705–1715 (2009).Google Scholar