Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory

Microsystem Technologies - In this article, a cylindrical functionally graded shell model is developed in the framework of nonlocal strain gradient theory for the first time. For this purpose, the...     

Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment

Microsystem Technologies - This article presented a numerical method for discovering the free vibration of a spinning bi-dimensional functionally graded materials (FGM) micro circular plate exposed...     

Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate

Microsystem Technologies - In this paper, the free vibration of a rotating variable thickness two-directional FG circular microplate is studied. The governing equations of motion for the microplate...     

Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment

In this article, transverse vibration of rotary functionally graded size-dependent tapered Bernoulli–Euler nanobeam in thermal environment at low temperature has been investigated based on Eringen's nonlocal theory for cantilever and propped cantilever boundary conditions. Material properties of FG nanobeam are supposed to be temperature dependant and vary continuously along the thickness according to the power-law form. The axial force is also included in the model as the true spatial variation due to the rotation. The nonlocal equations of motion are derived through Hamilton's principle and they are solved by the differential quadrature method. Validations are done by comparing available literatures and obtained results, which reveal the accuracy of the applied method. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters, such as angular velocity, material distribution profile, different boundary conditions, small-scale parameter and rate of cross-section change on the first three nondimensional natural frequencies of the rotary FG nanobeam in detail. Numerical results are presented to serve as benchmarks for the application and the design of nanoelectronic, nanodrive devices and nanomotor, in which nanobeams act as basic elements. They can also be useful as valuable sources for validating other approaches and approximate methods.The results of this article are suitable in designation of micromachines, such as micromotors and micro-rotors.     

Size-dependent effects on critical flow velocity of a SWCNT conveying viscous fluid based on nonlocal strain gradient cylindrical shell model

This article investigates vibration and instability analysis of a single-walled carbon nanotube (SWCNT) conveying viscous fluid flow. For this purpose, the first-order shear deformation shell model is developed in the framework of nonlocal strain gradient theory (NSGT) for the first time. The proposed model is a conveying viscous fluid in which the external force of fluid flow is applied by the modified Navier–Stokes relation and considering slip boundary condition and Knudsen number. The NSGT can be reduced to the nonlocal elasticity theory, strain gradient theory or the classical elasticity theory by inserting their specific nonlocal parameters and material length scale parameters into the governing equations. Comparison of above-mentioned theories suggests that the NSGT predicts the greatest critical fluid flow velocity and stability region. The governing equations of motion and corresponding boundary conditions are discretized using the generalized differential quadrature method. Furthermore, the effects of the material length scale, nonlocal parameter, Winkler elastic foundation and Pasternak elastic foundation on vibration behavior and instability of a SWCNT conveying viscous fluid flow with simply supported and clamped–clamped boundary conditions are investigated.