Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory

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Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics (2018, background): “, strain gradient and couple-stress theories, have been actively developed during the past years [15, 16, 17, 18, 19, 20, 21, 22, 23, 24].”
Free flexural vibration of geometrically imperfect functionally graded microbeams (2016, methodology): “…& Shabani, 2013 ), static bending and free vibration analysis of functionally graded microbeams using a new higher order beam theory by ( ̧S im ̧s ek & Reddy, 2013 ), free flexural vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams by ( Akgöz & Civalek, 2013…”
Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method (2015, background): “Recently several studies have been dealing with the size-dependent functionally graded micro/nano-beams [32-36] and two-dimensional micro/nano-plates.”
Static analyses of FGM beams by various theories and finite elements (2015, methodology): “Moreover, these refined beam models were also used in the static, free-vibration [9] and stability [10] analysis of micro-beams in the modified couple stress theory framework.”