Rotating Nanorod with Clamped Ends

Abstract

This paper presents an analytical investigation on the buckling and post-buckling behavior of rotating nanorods subjected to axial compression and clamped at both ends. The nonlinear governing equations are derived based on the classical Euler–Bernoulli theory and Eringen's nonlocal elasticity model. The critical load parameters such as angular velocity and compressive axial force are determined for given values of nonlocality parameter. The validity, convergence and accuracy of the solutions are established by comparing them with known classical solutions. The numerical results show that an increase in the nonlocality parameter gives rise to an increase in post-buckling deformation.

Nano- and viscoelastic Beck’s column on elastic foundation

“…By introducing non-local constitutive equation, the critical load and frequency decrease with the increase of non-locality parameter, as depicted in Figure 2. This effect of non-locality parameter on stability boundary was also shown to hold true for static problems of various conservative loading configurations and boundary conditions in [5,12,33]. Here it is shown that reduction in critical load also occurs for non-conservative problems when nonlocal constitutive equation is adopted.…”

Bifurcation analysis of the rotating axially compressed nano‐rod with imperfections

“…System of equations (7), subject to (8), can be reduced to a single equation, represented by the action of a non-linear operator on deflection y equated with zero. The operator is obtained either as the integro-differential operator of the second order, or as the differential operator of the fourth order.…”

“…The buckling problem of a rotating compressed rod, described by the elastic moment-curvature constitutive equation, is considered in [3,10,17,20], while in [5,7] the rod is allowed to have variable cross section and extensible axis, and in [19] there are additional rigid bodies attached to the rod. Static stability problem of a non-local rotating compressed rod, described by the Eringen stress gradient constitutive model, is studied in [8,9] for the clamped-clamped and clamped-free rod, while in [1] a non-local clamped-free rod rotating about the axis perpendicular to rod's axis is considered. The application of non-local theory in the static and dynamic stability problems of different types of rods is quite extensive, see the review articles [2,13,18] and book [12].…”

Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints

“…36 Often collectively referred to as enriched micro-continuum theories, 37 these theories enhance the assessment of the implication of size-speci¯c phenomenological traits on the mechanical responses of micron-scale structural elements. A select category of these theories include the strain gradient theory (SGT), 38 the micropolar and nonlocal elasticity theories, [39][40][41][42][43] the couple stress theory of elasticity, 44 the modi¯ed couple stress theory (MCST) 45,46 and the modi¯ed SGT. 47,48 The MCST o®ers a direct framework to deal with the inclusion of internal material length scale of one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) micron-scale structures, 32,49,50 and is the theory adopted in the current study.…”