Vibration of nonlocal Timoshenko beams

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Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams (2013, methodology): “Wang, Zhang, and He (2007) derived the governing equations and boundary conditions using Hamilton’s principle for the vibration of nonlocal Timoshenko beams and analytically obtained the vibration frequenc ies of beams with various end conditions.”
A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams (2012, background): “The material properties of SWCNT are [13]: 5.”
On nonconservativeness of Eringen’s nonlocal elasticity in beam mechanics: correction from a discrete-based approach (2014, background): “2 that the small length scale effect has a softening influence in case of the self-adjoint nonlocal elasticity model, whereas surprisingly, a stiffening effect is noticed with the nonself-adjoint nonlocal elasticity mode ([22,23] or [24]).”
Assessment of timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics (2009, methodology): “[18] derived the governing equations and boundary conditions for the free vibration of nonlocal Timoshenko beams via Hamiltonian’s principle.”