Transverse vibration of a hanging nonuniform nanoscale tube based on nonlocal elasticity theory with surface effects

Instability analysis of quasicrystal nano‐switch with thermal effect and surface distributed forces

“…Nondimensional electrostatic voltage and maximum deflection of nanobeams with different boundary conditions are presented via analytical model by the shooting method and finite element modeling (FEM) in Table 3. Results in the Tables 3 and 4 are obtained under the C-C/S-S/C-F boundary conditions (24). It is shown that the voltage and displacement are maximum under the C-C boundary condition, smaller under the S-S boundary, and minimum for the C-F boundary.…”

“…When we solve the cantilever beam, we first extract an independent quantity λ from the electrostatic force according to the load of the problem, and then set an initial undetermined parameter D 0 . We substitute λ and D 0 into the corresponding Equations ( 4), (31), and ( 33) to find out whether the boundary condition (24) at the fixed end is satisfied. If not, an increment will be added to D 0 .…”

“…Because differential Equations ( 22) and ( 23) constitute two-point boundary values, that is, there are strong nonlinearity and mutual coupling between variables, it is difficult to obtain its analytical solution under boundary condition (24).…”

“…They observed that the nonlocal effect increased the fundamental frequency. The nonlocal elastic theory has recently developed to consider surface effects such as surface elasticity, surface stress and surface density [24]. These effects are related to the scale of nanomaterials [25].…”