Dynamic Characteristics of Mixture Unified Gradient Elastic Nanobeams

Abstract

The mixture unified gradient theory of elasticity is invoked for the rigorous analysis of the dynamic characteristics of elastic nanobeams. A consistent variational framework is established and the boundary-value problem of dynamic equilibrium enriched with proper form of the extra non-standard boundary conditions is detected. As a well-established privilege of the stationary variational theorems, the constitutive laws of the resultant fields cast as differential relations. The wave dispersion response of elastic nano-sized beams is analytically addressed and the closed form solution of the phase velocity is determined. The free vibrations of the mixture unified gradient elastic beam is, furthermore, analytically studied. The dynamic characteristics of elastic nanobeams is numerically evaluated, graphically illustrated, and commented upon. The efficacy of the established augmented elasticity theory in realizing the softening and stiffening responses of nano-sized beams is evinced. New numerical benchmark is detected for dynamic analysis of elastic nanobeams. The established mixture unified gradient elasticity model provides a practical approach to tackle dynamics of nano-structures in pioneering MEMS/NEMS.

Pull-down plateau of a Toda-like fractal-fractional oscillator and its application in grass carp’s roes’ agglomeration

“…The vibration of roes' agglomeration can be described as a particle system with nonlinear spring connections as shown in Figure 3, similar to a nanobeam system. 8,[29][30][31] It consists of a roe with mass m, which is connected to other roes by springs. It is also adsorbed by the entire system.…”

“…Its particularly important property is the instability motion, which is an inherent property for a nonlinear system with even nonlinearity, 7 just like pull-in phenomenon in a MEMS system. 8 Much literature has conducted extensive analysis on the dynamic pull-in of MEMS models because it is important for the efficient operation and reliability of the device. [9][10][11][12] For example, Anjum et al proposed a variational iteration method for predicting the pull-in instability condition.…”

“…Its particularly important property is the instability motion, which is an inherent property for a nonlinear system with even nonlinearity, 7 just like pull-in phenomenon in a MEMS system. 8…”

Stability analysis of a time-delayed Van der Pol–Helmholtz–Duffing oscillator in fractal space with a non-perturbative approach

“…As essential components of micro-and nano-electromechanical systems (MEMS/NEMS), micro-and nano-sensors have found a wide range of applications in cuttingedge engineering systems [9]. The latest development in fractal MEMS theory incorporates fractal geometry into MEMS design to enhance performance, sensitivity, and efficiency.…”

Free Vibration of Single-Walled Carbon Nanotubes Using Nonlocal Truncated Timoshenko-Ehrenfest Beam Theory

“…Further applications of the nonlocal elasticity theory have been used in the study of the buckling problem and vibration problems in CNTs by applying Euler-Bernoulli beam, plate and shell theories and Timoshenko beam theory [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The wave dispersion response of elastic nano-sized beams was analytically addressed and the closed-form solution of the phase velocity was determined in [28]. Still based on the nonlocal elasticity beam theory, the effects of the spatial variation of the nonlocal parameter on free frequencies of nanoplates were discussed in [29].…”