The Application of the Modified Lindstedt-Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations

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dc.authorid0000-0002-5968-3382en_US
dc.authorid0000-0001-7678-6351en_US
dc.contributor.authorAvey, Mahmure
dc.contributor.authorTornabene, Francesco
dc.contributor.authorAslanova, Nigar Mahar
dc.contributor.authorSofiyev, Abdullah H.
dc.date.accessioned2024-03-22T08:02:00Z
dc.date.available2024-03-22T08:02:00Z
dc.date.issued2024en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractThe solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated.en_US
dc.identifier.doi10.3390/math12050749en_US
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-85187886014en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.urihttps://hdl.handle.net/11467/7175
dc.identifier.urihttps://doi.org/10.3390/math12050749
dc.identifier.volume12en_US
dc.identifier.wosWOS:001180993900001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMDPIen_US
dc.relation.ispartofMathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectcomposites; inhomogeneity; NL equations; NL vibration; plates; ground effect; NL frequenciesen_US
dc.titleThe Application of the Modified Lindstedt-Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundationsen_US
dc.typeArticleen_US

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