Simplified Method Using Homogenization Approach for Nonlinear Dynamic Analysis of Dissipative Energy in Multilayered Beams
| Autor: | A. Sekhri, S. Benissaad, T. Benmansour |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Arabian Journal for Science and Engineering. 39:5073-5084 |
| ISSN: | 2191-4281 1319-8025 |
| Popis: | Based on known theoretical developments in linear dynamics of homogeneous beams, two homogenization approaches of composite beams are developed further to an anterior work using two equivalent properties: the physical and the mechanic–geometrical properties. Further to the assumption of Euler–Bernoulli beams, dynamic parameters are needed. Equations of a given beam structure subjected to free un-damped and/or damped vibration are established. The natural frequency responses of the first five modes are obtained from both approaches, and then compared with those obtained from a finite element model approach, taking into account different slenderness and boundary conditions. The result shows good agreement. An extension to the equivalent physical parameter homogenization method using the behaviour law in nonlinear state is presented here. Thus, the homogenization is extended to an elastically equivalent model elaboration for a system having an elastic–plastic and bilinear behaviour. The aim is to use analytical expressions from an elastically equivalent model for a nonlinear system of multilayer beam type to obtain the new corrected dynamic parameter. Based on the ductility factor method combined with the secant method that uses a substitute structure and secant stiffness to account for nonlinear behaviour, we developed a formula using global effective flexural modulus \({E_{\rm s}^*}\) , the equivalent mass density ρ*, as well as the two types of viscous damping parameter (these types include a viscous resistance to transverse displacement C* of the beam and a viscous resistance to straining of the beam material \({C_{\rm S}^{*})}\) which can be incorporated into the formula without difficulty. The nonlinear analysis shows that the degradation of rigidity decreases the frequencies response curve, which tends to increase the vibration periods giving an additional storage space for the structure capacity to accumulate displacements of a higher degree compared to those of the elastic case. The importance of the nonlinearity assumption is shown, which fits better with the real mechanical performances of the structure. |
| Databáze: | OpenAIRE |
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