M. R. Bagheri

Bio: M. R. Bagheri is an academic researcher from University of Kashan. The author has contributed to research in topics: Nonlinear system & Equations of motion. The author has an hindex of 2, co-authored 2 publications receiving 115 citations.

Nonlocal vibration and instability of embedded dwbnnt conveying viscose fluid

Abstract: Electro-thermo nonlinear vibration and instability of embedded double-walled Boron Nitride nanotubes (DWBNNTs) conveying viscose fluid is studied in this article based on nonlocal piezoelasticity theory and Euler–Bernoulli beam (EBB) model. Boron Nitride nanotube (BNNT) is surrounded by elastic medium which is simulated as Pasternak foundation. The van der Waals (vdW) forces between the inner and the outer DWBNNTs are taken into account based on the Lennard–Jones model. Using von Karman geometric nonlinearity, Hamilton’s principle and considering charge equation for coupling of electrical and mechanical fields, the nonlinear higher order governing equations are derived. The differential quadrature method (DQM) is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency and critical fluid velocity of fluid-conveying DWBNNTs. Results indicated that the small scale parameter, elastic medium, temperature change and electric potential have significantly effect on the dimensionless natural frequency and critical fluid velocity. Furthermore, the effect of fluid viscosity on the vibration of DWBNNTs may be ignored.

Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory

Abstract: Nonlinear free vibration and instability of fluid-conveying double-walled boron nitride nanotubes (DWBNNTs) embedded in viscoelastic medium are studied in this paper. The effects of the transverse shear deformation and rotary inertia are considered by utilizing the Timoshenko beam theory. The size effect is applied by the modified couple stress theory and considering a material length scale parameter for beam model. The nonlinear effect is considered by the Von Karman type geometric nonlinearity. The electromechanical coupling and charge equation are employed to consider the piezoelectric effect. The surrounding viscoelastic medium is described as the linear visco-Pasternak foundation model characterized by the spring and damper. Hamilton’s principle is used to derive the governing equations and boundary conditions. The differential quadrature method (DQM) is employed to discretize the nonlinear higher-order governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequency and critical fluid velocity of fluid-conveying DWBNNTs with clamped-clamped (C-C) boundary conditions. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, spring and damping constants of surrounding viscoelastic medium and fluid velocity on the nonlinear free vibration, instability and electric potential distribution of DWBNNTs. This study might be useful for the design and smart control of nano devices.

Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model

Abstract: In this article, the free vibration behavior of circular and annular graphene sheet is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets (SLGS) and nonlocal parameter appears into arguments of Bessel functions. Analytical frequency equations for circular and annular graphene sheets are obtained based on different cases of boundary conditions. New version of differential quadrature method has been used to solve the governing equations for circular nanoplate. The results of new version of differential quadrature method are successfully verified with those of the analytical method. The results are subsequently compared with valid results reported in the literature. The effects of the small scale on natural frequencies are investigated considering various parameters such as the radius of the plate, radius ratio, nodal circle, nodal diameter number, boundary conditions and mode numbers.

Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)

Abstract: Longitudinal free vibration analysis of axially functionally graded microbars is investigated on the basis of strain gradient elasticity theory. Functionally graded materials can be defined as nonhomogeneous composites which are obtained by combining of two different materials in order to obtain a new desired material. In this study, material properties of microbars are assumed to be smoothly varied along the axial direction. Rayleigh–Ritz solution technique is utilized to obtain an approximate solution to the free longitudinal vibration problem of strain gradient microbars for clamped–clamped and clamped-free boundary conditions. A parametric study is carried out to show the influences of additional material length scale parameters, material ratio, slenderness ratio and ratio of Young’s modulus on natural frequencies of axially functionally graded microbars.