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

چکیده مقاله

In this article, nonlocal nonlinear vibration of nano-beam embedded in a Pasternak foundation is investigated using third order shear deformation theory of beam. This model includes rotary inertia and transverse shear deformation in the formulation. Considering Eringen’s theory, the nonlinear governing equations are derived using Hamilton’s principle and discretized based on the differential quadrature method (DQM). The lowest frequencies are determined for clamped-clamped boundary condition. The effects of dimensionless small scale, elastic medium coefficient, on the imaginary and real components of frequency are also taken into account. Results indicate that both normal and shear modulus increase the natural frequency of nano-beam. It is also worth to mention that decreasing nonlocal parameter and presence of Winkler and Pasternak foundation can enlarge the stability region of nano-beam.