Determination of Physical Properties of Laminated Composite Beam via the Inverse Vibration Problem Method
DOI:
https://doi.org/10.15282/jmes.5.2013.7.0058Keywords:
Inverse problem; finite element method; laminated composite beam; genetic algorithm; free vibration.Abstract
In this study, some physical properties of a laminated composite beam were estimated by using the inverse vibration problem method. Laminated composite plate was modeled and simulated to obtain vibration responses for different length-to-thickness ratios in ANSYS. A numerical model of the laminated composite beam with unknown parameters was also developed using a two-dimensional finite element model by utilizing the Euler-Bernoulli beam theory. Then, these two models were embedded into the optimization program to form the objective function to be minimized using genetic algorithms. After minimizing the squared difference of the natural frequencies from these two models, the unknown parameters of the laminated composite beam were found. It is observed in this study that the Euler-Bernoulli beam theory suppositions approximated the real results with a rate of %0.026 error as the thickness of the beam got thinner. The estimated values were finally compared with the expected values and a very good correspondence was observed.
References
Adebisi, A. A., Maleque, M. A., & Rahman, M. M. (2011). Metal matrix composite brake rotor: Historical development and product life cycle analysis. International Journal of Automotive and Mechanical Engineering, 4, 471-480.
Aster, R. C., Borchers, B., & Thurber, C. H. (2013). Parameter estimation and inverse problems. USA: Academic Press.
Balci, M. (2011). Estimation of physical properties of laminated composites via the method of inverse vibration problem. (Ph.D), Ataturk University, Erzurum.
Chandra, R., Singh, S. P., & Gupta, K. (1999). Damping studies in fiber-reinforced composites–a review. Composite structures, 46(1), 41-51.
Chirn, J. L., & McFarlane, D. C. (2000, 2000). A holonic component-based approach to reconfigurable manufacturing control architecture. Paper presented at the Database and Expert Systems Applications, 2000. Proceedings. 11th International Workshop on.
Chiwiacowsky, L. D., de Campos Velho, H. F., & Gasbarri, P. (2004). A variational approach for solving an inverse vibration problem. Paper presented at the Inverse Problems, Design and Optimization Symposium, Rio de Janeiro, Brazil.
De Abreu, G., Ribeiro, J., & Steffen Jr, V. (2004). Finite element modeling of a plate with localized piezoelectric sensors and actuators. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 26(2), 117-128.
Della, C. N., & Shu, D. (2005). Free vibration analysis of composite beams with overlapping delaminations. European Journal of Mechanics-A/Solids, 24(3), 491-503.
Ghayesh, M. H., Yourdkhani, M., Balar, S., & Reid, T. (2010). Vibrations and stability of axially traveling laminated beams. Applied Mathematics and Computation, 217(2), 545-556.
Giunta, G., Biscani, F., Belouettar, S., Ferreira, A., & Carrera, E. (2013). Free vibration analysis of composite beams via refined theories. Composites Part B: Engineering, 44(1), 540-552.
Gladwell. (1997). Inverse vibration problems for finite-element models. Inverse Problems, 13(2), 311.
Gladwell. (1999). Inverse finite element vibration problems. Journal of Sound and Vibration, 221(2), 309-324.
Gladwell. (2006). Minimal mass solutions to inverse eigenvalue problems. Inverse Problems, 22(2), 539.
Hariprasad, T., Dharmalingam, G., & Praveen Raj, P. (2013). A study of mechanical properties of banana-coir hybrid composite using experimental and fem techniques. Journal of Mechanical Engineering and Sciences, 4, 518- 531.
Huang, C.-H. (2005). A nonlinear inverse problem in estimating simultaneously the external forces for a vibration system with displacement-dependent parameters. Journal of the Franklin Institute, 342(7), 793-813.
Huang, C.-H., Shih, C.-C., & Kim, S. (2009). An inverse vibration problem in estimating the spatial and temporal-dependent external forces for cutting tools. Applied Mathematical Modelling, 33(6), 2683-2698.
Huzni, S., Ilfan, M., Sulaiman, T., Fonna, S., Ridha, M., & Arifin, A. K. (2013). Finite element modeling of delamination process on composite laminate using cohesive element. International Journal of Automotive and Mechanical Engineering, 7, 1023-1030.
Jeffrey, K. J. T., arlochan, F., & Rahman, M. M. (2011). Residual strength of chop strand mats glass fiber/epoxy composite structures: Effect of temperature and water absorption. International Journal of Automotive and Mechanical Engineering, 4, 504-519.
Kollár, L. P., & Springer, G. S. (2003). Mechanics of composite structures: Cambridge university press.
Li, J., Wu, Z., Kong, X., Li, X., & Wu, W. (2014). Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups. Composite structures, 108, 767-778.
Marinov, T. T., & Vatsala, A. S. (2008). Inverse problem for coefficient identification in the euler–bernoulli equation. Computers & Mathematics with Applications, 56(2), 400-410.
Petyt, M. (1990). Introduction to finite element vibration analysis: Cambridge university press.
Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: Theory and analysis: CRC press.
Umar, A. H., Zainudin, E. S., & Sapuan, S. M. (2012). Effect of accelerated weathering on tensile properties of kenaf reinforced high-density polyethylene composites. Journal of Mechanical Engineering and Sciences, 2, 198-205.
Wang, C. M., Reddy, J. N., & Lee, K. H. (2000). Shear deformable beams and plates: Relationships with classical solutions. Oxford: Elsevier.
Wang, G. (2013). Coupled free vibration of composite beams with asymmetric cross-sections. Composite structures, 100(0), 373-384.
