Hierarchical theories for the free vibration analysis of functionally graded beams

By Gaetano Giunta, Daniela Crisafulli, S. Belouettar, Erasmo Carrera. 2011

127 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a39cf1b77a39bed37a1246e003446ea339df87d5

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In Civil and Structural Engineering

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Free vibration analysis of rotating composite blades via Carrera Unified Formulation (2013, background): “As far as composite beams are concerned, interesting analyses are presented in [36–39].”
Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories (2012, methodology): “via the use of a unified formulation) [25-27].”
Geometrically nonlinear free vibration analysis of axially functionally graded taper beams (2015, background): “[11] worked with several axiomatic refined theories and derived the governing differential equations by variationally imposing the equilibrium through the principle of virtual displacements.”
Static and vibration analysis of functionally graded beams using refined shear deformation theory (2013, background): “Although there are many references available on static [12–17] and vibration [18–23], the research on the displacements and natural frequencies of FG beams in a unitary manner is limited.”
Modeling and analysis of functionally graded sandwich beams: a review (2019, methodology): “[66, 67] also applied these refined theories for the analysis of mono-layer and sandwich FG beams using unified formulation.”
Free vibration of FGM layered beams by various theories and finite elements (2014, unknown): “EBBT [30] 3.”
Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams (2015, methodology): “The crosssectional dimensions, the material constitution of the bottom and top surfaces of the FGB are kept the same as used in Ref [5].”
Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory (2013, background): “[10–12] presented static and vibration analysis of functionally graded beams using this beam model.”
Free vibration of functionally graded beams and frameworks using the dynamic stiffness method (2018, methodology): “Foremost amongst these are the applications of direct analytical procedure using the governing differential equations of motion [5-19], finite element [20-22], Rayleigh-Ritz [23], finite volume [24-26], differential quadrature [27], differential transformation [27, 28] and transfer function [29, 30]”
Recent developments on refined theories for beams with applications (2015, unknown): “Functionally graded material beams have been investigated via closed-form (Giunta et al., 2010, 2011) and FE (Mashat et al., 2014) solutions.”
Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams (2015, methodology): “The free vibration analysis of FG beams via several axiomatic refined theories was presented by Giunta et al (2011) based on Navier type solution.”