Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position

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A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates (2016, methodology): “The increase of FGM applications requires the development of accurate theories to predict their responses (Kar and Panda 2015a, Akbaş 2015, Darılmaz 2015, Ait Atmane et al. 2015, Al-Basyouni et al. 2015, Arefi et al. 2015, Bennai et al. 2015, Meradjah et al. 2015).”
Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position (2015, unknown): “[24] and Bourada et al.”
Free vibration of functionally graded beams and frameworks using the dynamic stiffness method (2018, background): “It should be noted that due to the variation of the material properties through the thickness, the neutral axis would no longer be at the central line of the beam cross-section [42,43].”
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation (2016, background): “…principle can be stated by (Reddy 2007, Draiche et al. 2014, Ait Amar Meziane et al. 2014, Nedri et al. 2014, Mahi et al. 2015, Bourada et al. 2015, Al-Basyouni et al. 2015) t fp dtKUU 0 ) (0 (10) where δUp and δUf are the variations of strain energy of the plate and foundation, respectively;…”