جستجوی مقالات مرتبط با کلیدواژه « nanorod » در نشریات گروه « مکانیک »

This paper investigates the free longitudinal vibrations of functionally graded nanorods with constant cross-section on the basis of nonlocal strain gradient theory. Functionally graded nanostructures can be defined as nonhomogeneous composites which are obtained by combining two different materials with different elasticity moduli and mass densities. Due to the special properties of the functionally graded materials (FGM), the changes of physical properties (such as the elasticity modulus and mass density along the axis of functionally graded nanorods) are expressed by an exponential relation in terms of the location and constant ratios of the material properties. In this paper, numerical results related to these changes are shown. Galerkin solution technique is utilized to obtain an approximate solution to the free longitudinal vibration of FGM nanorods with clamped–clamped boundary conditions. A parametric study is carried out to show the influences of nonlocal parameters on the fundamental natural frequencies such as location-dependent nonlocal parameter and material length scale parameter as well as the physical parameters such as the elasticity modulus and mass density of different material composition.

In the present paper, free axial vibration behavior of functionally graded nanorods is studied using the surface elasticity theory. For modelling of free axial vibration of nanorods, the Simple theory of rods is implemented. Besides using the Simple theory of rods, the surface elasticity theory is used for considering the surface energy parameters in the governing equations and boundary conditions. The surface energy parameters are the surface elasticity, the surface density, and the surface residual stress. The surface and bulk material properties of nanorod are considered to vary in the length direction according to the power law distribution. Then, the governing equation of motion and boundary conditions of nanorod are derived using the Hamilton’s principle. Due to considering the surface energy parameters, the obtained governing equation of motion becomes non-homogeneous. But in none of the previous researches, for example investigation of free transverse vibration of nanobeams and free torsional vibration of nanorods in presence of the surface energy, the surface energy parameters do not cause the non-homogeneity of the governing equation or the boundary conditions. To extract the natural frequencies of the nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using Galerkin method. In order to have a comprehensive research, effects of various parameters like the length and radius of nanorod on axial frequencies of functionally graded nanorod is investigated.

In this work, axial vibration of nanorod was analyzed based on two phase integro-differential nonlocal elasticity theory using isogeometric method. Two phase integro-differential nonlocal elasticity theory not only shows the nonlocal property in an integrated manner based on kernel weight function, but also combines local and nonlocal linear curvature for a two phase nonlocal elastic material. The new isogeometric approach combines finite element method with computational geometry and can present an accurate geometric model for the problem. Also, using b-spline basis functions with arbitrary continuity order, it can be a better alternative for classical finite element methods. The obtained results indicated that isogeometric approach was superior to finite element method in term of speed and convergence quality. Moreover, in this model, the effects of phase and nonlocal parameters on the natural frequencies of the nanorod were investigated and it was shown that increase of parameters of local phase and nonlocal length scale, respectively, increased and decreased the values of natural frequencies of nanorods. Finally, for two special cases, asymptotic frequencies for a single type of nonlocal rod, two phase integro-differential was obtained and the results were compared with corresponding available differential Eringen results.

In this paper, the longitudinal vibration of nanorod based on Eringen’s nonlocal elasticity theory was studied using Rayleigh-Ritz method. A non-uniform nano-rod with variable cross-sectional area, density and Young’s modulus were considered. In the present work, boundary polynomials with orthogonal polynomials were used as shape functions in the Rayleigh-Ritz method which causes the vibrational analysis to be computationally efficient and imposing of boundary conditions to be easier. Using the mentioned polynomials the convergence rate of the obtained results was increased. All of the equations used in this study were made to have no dimensional to reduce the number of effective parameters in the solution. The influence of the nonlocal and in-homogeneity parameters on the vibrational behavior of nanorod was investigated. The results were compared to available results in the literature and a good agreement has been achieved. The results showed that nanorod frequencies were depended to the small scale effect, non-uniformity, and boundary conditions. For instance, an increase in frequency ratio causes the scale coefficient in all vibration modes to be increased, especially in higher modes. In addition, the frequencies were increased by increasing in the length of the nanorod.