Fig. 8. Linear-linear and logarithmic-linear comparisons for Coulombic free vibration decay between ANSYS and for the analytical model 5. CONCLUSION Naturally debonded composites can accurately be analysed, and the behaviour predicted, using finite element methods, however these methods are computationally expensive, especially for transient analyses, and require large DOF models to include every layer and their nonlinear interfaces. In this work, an analytical validity model has been developed in the context of a debonded multilayer composite in the form of a cantilever beam bending behavioural model. The validity is emphasised for a model reduction technique that can be used for numerical analyses and/or as a straightforward analytical approach. Comparisons between the analytical models and numerical models have been made and indicate acceptable accuracy. The numerical model is in good agreement with both the stiffness model and the damping model. Current experiments are being conducted to validate the analytical and numerical models in addition to the inclusion of presliding behaviour is being investigated to extend the accuracy of the models and to help determine localized damping effects. REFERENCES [1] Beards, C. F., Structural Vibration Analysis and Damping, Wiley, New York, 1996 [2] Karnopp, D., Computer Simulations of Stick-slip Friction in Mechanical Dynamic Systems, ASME J. of Dynamic Systems, Measurement and Control, 107(1),100-103,1985. [3] Prime, M. B., Shevitz, D. W., Linear and Nonlinear Methods for Detecting Cracks in Beams, 14th International Modal Analysis Conference, 1437-1443, 1996. [4] Lord, C. E., Rongong, J. A., Hodzic, A., Linearized Material Properties of Nonlinear Interfacial Contact for Layered Composites, International Conference on Interfaces & Interphases in Multicomponent Materials, 2010. [5] Timoshenko, S. P., Goodier, J.N., Theory of Elasticity, McGraw-Hill, New York, 1970. [6] Rivin, E. I., Handbook on Stiffness & Damping, ASME, New York, 2010. [7] Liang, J., Feeny, B. F., Balancing Energy to Estimate Damping Parameters in Forced Oscillators, 2005. [8] Chawla, N., Jester, B., Vonk, D. T., Bauschinger effect in porous sintered steels, Material Science and Engineering, A346, 266-272, 2002. [9] Dupont, P., Armstrong, B., Hayward, V., Elasto-Plastic Friction Model: Contact Compliance and Stiction, AACC, 2000. 298
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