BENDING, BUCKLING AND FREE VIBRATION ANALYSES OF NANOBEAM-SUBSTRATE MEDIUM SYSTEMS

This study presents a newly developed size-dependent beam-substrate medium model for bending, buckling, and free-vibration analyses of nanobeams resting on elastic substrate media. The Euler-Bernoulli beam theory describes the beam-section kinematics Winkler-foundation represents interaction between its underlying medium. reformulated strain-gradient elasticity possessing three non-classical material constants is employed to address beam-bulk small-scale effect. first second associated with couple-stress effects, respectively while third constant related velocity-gradient Gurtin-Murdoch surface adopted account surface-free energy. To obtain system governing equation as well corresponding boundary conditions, Hamilton’s principle called for. Three numerical simulations are presented characterize influences effect, surface-energy surrounding free vibration responses nanobeam-substrate systems. simulation focuses bending response shows ability proposed eliminate paradoxical characteristic inherent nanobeam models in literature. perform sensitivity investigation parameters buckling load natural frequency, respectively. All analytical results reveal that both effects consistently stiffen effect weakens response. Furthermore, these sized-scale more pronounced when becomes softer.