Nonlinear Vibration of embedded nanobeam based onnonlocal third order shear deformation theory

In this article, nonlocal nonlinear vibration of nano-beamembedded in a Pasternak foundation is investigatedusing third order shear deformation theory of beam. Thismodel includes rotary inertia and transverse sheardeformation in the formulation. Considering Eringen’stheory, the nonlinear governing equations are derivedusing Hamilton’s principle and discretized based on thedifferential quadrature method (DQM). The lowestfrequencies are determined for clamped-clampedboundary condition. The effects of dimensionless smallscale, elastic medium coefficient, on the imaginary andreal components of frequency are also taken intoaccount. Results indicate that both normal and shearmodulus increase the natural frequency of nano-beam. Itis also worth to mention that decreasing nonlocalparameter and presence of Winkler and Pasternakfoundation can enlarge the stability region of nano-beam.

کلیدواژه ها:

Nonlinear vibration ، Reddy nanobeam ، Nonlocal elasticity theory ، Pasternak foundation