Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak's foundation

• Published in: European journal of mechanics, A, Solids A, Solids, 2021-01, Vol.85, p.104124, Article 104124
• Main Authors: Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.
• Format: Article
• Language: English
• Subjects: Aspect ratio; Boundary conditions; Comparative studies; Elastic foundations; Exact solutions; Free vibration; FSDT; Functionally graded material; Functionally gradient materials; Galekin-Vlasov; Hamilton's principle; Kinematic equations; Material properties; Parameters; Partial differential equations; Pasternak foundation; Porosity; Shear deformation; Thick plates; Variable thickness; Vibration analysis
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2020.104124

In the paper, free vibration analysis of tapered Functionally Graded Material (FGM) plate with the inclusion of porosity has been performed. The tapered porous FGM plate is considered resting on a two-parameter (Winkler and Pasternak) elastic foundation. The displacement model of the kinematic equation for the plates in the present formulation is based on the First-order shear deformation theory (FSDT). The governing equation for free vibration analysis of FGM plates is obtained using Hamilton's principle. Simple power-law, Exponential Law, and Sigmoid law are used for tailored the material properties in the thickness direction of FGM plates. The solution of the resulting partial differential equation is obtained by using Galerkin-Vlasov's method with different boundary conditions. The solutions for uniform and uniform varying thick plates are investigated, and a comparative study is examined by comparing the results obtained with FSDT and Higher-order shear deformation theory (HSDT). The findings of the comparative study with the present approach provide pertinent outcomes for the vibration analysis of tapered FGM plates. The analytical solution for vibration analysis is presented to reveal the effects of porosity parameter, volume exponent, span ratio, aspect ratio, porosity distribution, and boundary conditions. Also, the elastic foundation parameter on tapered FGM plate increases the non-dimensional frequency, and the Pasternak foundation effect always dominates over the Winkler foundation. •The governing PDEs are solved using Galerkin Vlasov's method to consider plate supported by different boundary conditions.•The tapered porous FGM plate is considered to be resting on a Winkler-Pasternak elastic foundation.•The porosity effect in tapered FGM plate is modelled using two different type of porosities.•The volume fraction distribution across the thickness is modelled based on power law, exponential law and sigmoid law.•The power law and exponential law FGM plate exhibited less overall frequency parameter in comparison to the sigmoid law plate.