T. Murmu

Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory

In the present work, nonlocal elasticity theory has been implemented to study the vibration response of single-layered graphene (SLGS) sheets. The nonlocal elasticity theory accounts for the small size effects when dealing with nanostructures. Influence of the surrounding elastic medium on the fundamental frequencies of the SLGS is investigated. Both Winkler-type and Pasternak-type models are employed to simulate the interaction of the graphene sheets with a surrounding elastic medium. On the basis of Hamilton’s principle governing differential equations for the aforementioned problems are derived. The nonlocal small scale coefficients get introduced into the nonlocal theory through the constitutive relations. Differential quadrature method is being employed and numerical solutions for the frequencies are obtained. Numerical results show that the fundamental frequencies of SLGS are strongly dependent on the small scale coefficients. Further, a nonlinear frequency response is observed for the SLGS with lar...

Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity

In this article, nonlocal elasticity theory is applied to investigate the vibration response of nanoplates under uniaxially prestressed conditions. Nonlocal elasticity theory takes into account the small-size effects when dealing with nanostructures. Nonlocal governing equations of the prestressed nanoplate are derived and presented. Differential quadrature method is being utilized and numerical frequency solutions are obtained. Influence of small scale and uniaxial preload on the nonlocal frequency solutions is investigated. It is observed that the frequencies for nanoplates under uniaxially prestressed conditions employing classical plate theory are overestimated compared to nonlocal plate solutions. Considering the nonlocal effects, smaller critical compressive load is required to reach the buckling state of a flexural mode compared to the classical plate theory. The present research work thus reveals that the nonlocal parameter, aspect ratios, boundary conditions, and initial uniaxial prestress have s...

Small-scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

Nonlocal elasticity theory is a growing technique for the mechanical analyses of microelectromechanical (MEMS) and nanoelectromechanical (NEMS) based structures. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to study the vibration response of SWCNT embedded in an elastic medium. Influence of the surrounding elastic medium on the fundamental frequencies of the SWCNT is investigated. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the SWCNT with the surrounding elastic medium. A differential quadrature approach is being utilized and numerical solutions for the natural frequencies are obtained. Influences of nonlocal effects, Winkler modulus parameter, Pasternak shear modulus parameter, and aspect ratio on the frequency of SWCNT are analyzed and discussed. The present study illustr...