<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Toufik Benmansour</style></author><author><style face="normal" font="default" size="100%">Abdelhak Sekhri</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Simplified Method Using Homogenization Approch for Non Linear Dynamic Analysis of Dissipative Energy in Multilayered Beams</style></title><secondary-title><style face="normal" font="default" size="100%">Arab Journal of Science and Engineering</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s13369-014-1036-4	</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">39</style></volume><pages><style face="normal" font="default" size="100%">5073-5084</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Based on known theoretical developments in linear dynamics of homogeneous beams, two homogenization&lt;br&gt;approaches of composite beams are developed further to an&amp;nbsp;anterior work using two equivalent properties: the physical and the mechanic–geometrical properties. Further to the&amp;nbsp;assumption of Euler–Bernoulli beams, dynamic parameters&amp;nbsp;are needed. Equations of a given beam structure subjected&amp;nbsp;to free un-damped and/or damped vibration are established.&amp;nbsp;The natural frequency responses of the first five modes are&amp;nbsp;obtained from both approaches, and then compared with&amp;nbsp;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&amp;nbsp;equivalent physical parameter homogenization method using&amp;nbsp;the behaviour law in nonlinear state is presented here. Thus,&amp;nbsp;the homogenization is extended to an elastically equivalent&amp;nbsp;model elaboration for a system having an elastic–plastic and&amp;nbsp;bilinear behaviour. The aim is to use analytical expressions&amp;nbsp;from an elastically equivalent model for a nonlinear system&amp;nbsp;of multilayer beam type to obtain the new corrected dynamic&lt;br&gt;parameter. Based on the ductility factor method combined&amp;nbsp;with the secant method that uses a substitute structure and&amp;nbsp;secant stiffness to account for nonlinear behaviour, we developed a formula using global&amp;nbsp;
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	effective&amp;nbsp;Es∗,&amp;nbsp;the equvalent mass density ρ∗, as well as the two types of&amp;nbsp;viscous damping parameter (these types include a viscous&amp;nbsp;resistance to transverse&amp;nbsp;
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	displacement C∗ of the beam anda viscous resistance to straining of the beam material CS∗)&amp;nbsp;which can be&amp;nbsp;
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	incorporated into the formula without difficulty.&amp;nbsp;The&amp;nbsp;
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	nonlinear analysis shows that the degradation of&amp;nbsp;
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	rigidity decreases the frequencies response curve,&amp;nbsp;
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	which tends to&amp;nbsp;increase the vibration periods giving an additional storage&amp;nbsp;space for the structure capacity to accumulate displacements&amp;nbsp;of a higher degree&amp;nbsp;
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	compared to those of the elastic case.&amp;nbsp;The&amp;nbsp;
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	importance of the nonlinearity assumption is shown,&amp;nbsp;
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	which fits better with the real mechanical&amp;nbsp;
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	performances of the&amp;nbsp;structure. &amp;nbsp;
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	&amp;nbsp;
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</style></abstract><issue><style face="normal" font="default" size="100%">06</style></issue></record></records></xml>