Search

In the present exploration, the nonlocal stress and strain gradient microscale effects are adopted on the nonlinear dynamical instability feature of functionally graded (FG) piezoelectric microshells under a combination of axial compression, electric actuation, and temperature. To perform this objective, a unified unconventional shell model based on the nonlocal strain gradient continuum elasticity is established to capture the size effects as well as the influence of the geometrical nonlinearity together with the shear deformation along with the transverse direction on the dynamic stability curves. With the aid of an efficient numerical strategy incorporating the generalized differential quadrature strategy and pseudo arc-length continuation technique, the extracted unconventional nonlinear differential equations in conjunction with the associated edge supports are discretized and solved to trace the dynamic stability paths of FG piezoelectric microshells. It is revealed that the nonlocal stress and strain gradient effects result in, respectively, higher and lower values of the nonlinear frequency ratio in comparison with the conventional one due to the stiffening and softening characters associated with the nonlocality and strain gradient size dependency, respectively. In addition, it is observed that within the prebuckling territory, the softening character of nonlocality is somehow more than the stiffening character of strain gradient microsize dependency, while by switching to the postbuckling domain, this pattern becomes vice versa. [ABSTRACT FROM AUTHOR]

• Nonlinear primary resonance of nonlocal nano beams subject to time delay control is investigated. • It is shown that the nonlocal effect on the system is reduced for certain time delay parameters. • An optimal time-delay value for a nonlocal nano beam system exists. The paper is concerned with the nonlinear primary resonance of nano beams with axial load under the velocity time delay control. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The effects of the control gains and time delays on the system stability are then investigated. The analyses illustrated that both delay feedback gain coefficient and velocity time delay control can mitigate the system vibrations properties (e.g. hardening nonlinearity, resonance amplitude and the corresponding width) to an excellent level. The nonlinear primary resonance of nano beam is also discussed with the influences of small scale effect, axial initial load, wave number, Winkler foundation modulus and the ratio of the length to the diameter. This paper establishes the relationship between the time delay controller and vibration properties of a nano beam system which provides the guidance for applying time delayed active control for different types of nano devices in engineering practices. [ABSTRACT FROM AUTHOR]

A scale-dependent continuum model is presented to investigate the effect of initial in-plane edge displacement on the nonlinear vibration and electromagnetic buckling of magneto-electro-elastic (MEE) ultrathin films using the nonlocal continuum mechanics and the von Kármán's theory of large deflections. The coupled nonlinear governing differential equations are solved employing Galerkin's approach and a perturbation method. Analytical relations are obtained to highlight the impact of initial edge displacement on the nonlinear natural frequencies as well as the buckling electric and magnetic potentials. It is shown that the initial edge displacement plays a crucial role in the nonlinear response of MEE nanofilms. [ABSTRACT FROM AUTHOR]

This study presents a size-dependent continuum model for the nonlinear buckling of magneto-electro-elastic (MEE) hybrid nanoshells in thermal environment. The nanocomposite cylindrical shell is composed of a carbon nanotube (CNT), a microtubule (MT) and a MEE nanoscale layer which are coupled by polymer or filament matrix. The hybrid nanostructure is subjected to thermo-electro-magnetic loads. The small scale effect is taken into consideration based on the nonlocal elasticity theory. The Pasternak model is used to simulate the normal and shear behavior of the coupling elastic medium. Using the principle of virtual work and von Karman’s strain-displacement relations, the nonlinear governing differential equations are derived. The non-dimensional postbuckling loads of the hybrid nanoshells are obtained using the Galerkin’s approach. The validity of the present model and method of solution is verified by comparing the results with available experimental data and the molecular dynamics simulation results from the literature. It is found that the nonlinear buckling loads of MEE hybrid nanoshells are strongly sensitive to the small scale coefficient. In addition, the non-dimensional buckling loads decrease with increasing the external electric voltage, while the applied magnetic potential has an increasing effects on the critical buckling loads. [ABSTRACT FROM AUTHOR]

In this paper, a nonlocal continuum plate model is developed for the transverse vibration of double-piezoelectric-nanoplate systems (DPNPSs) with initial stress under an external electric voltage. The Pasternak foundation model is employed to take into account the effect of shearing between the two piezoelectric nanoplates in combination with normal behavior of coupling elastic medium. Size effects are taken into consideration using nonlocal continuum mechanics. Hamilton?s principle is used to derive the differential equations of motion. The governing equations are solved for various boundary conditions by using the differential quadrature method (DQM). In addition, exact solutions are presented for the natural frequencies and critical electric voltages of DPNPS under biaxial prestressed conditions in in-phase and out-of-phase vibrational modes. It is shown that the natural frequencies of the DPNPS are quite sensitive to both nonlocal parameter and initial stress. The effects of in-plane preload and small scale are very important in the resonance mode of smart nanostructures using piezoelectric nanoplates. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear free vibration of the nanotube with damping effects is studied. Based on the nonlocal elastic theory and Hamilton principle, the governing equation of the nonlinear free vibration for the nanotube is obtained. The Galerkin method is employed to reduce the nonlinear equation with the integral and partial differential characteristics into a nonlinear ordinary differential equation. Then the relation is solved by the multiple scale method and the approximate analytical solution is derived. The nonlinear vibration behaviors are discussed with the effects of damping, elastic matrix stiffness, small scales and initial displacements. From the results, it can be observed that the nonlinear vibration can be reduced by the matrix damping. The elastic matrix stiffness has significant influences on the nonlinear vibration properties. The nonlinear behaviors can be changed by the small scale effects, especially for the structure with large initial displacement. [ABSTRACT FROM AUTHOR]

Abstract: Based on the nonlocal continuum theory, the nonlinear primary resonance of nano beam with the axial initial load is investigated. The amplitude–frequency response for the primary resonance is derived with the multiple scale method and the stability is analyzed. The nonlinear primary resonance of nano beam is discussed with the influences of small scale effect, axial initial load, mode number, Winkler foundation modulus and the ratio of the length to the diameter. From the results, the typical hardening nonlinearity can be observed. Moreover, some significant and interesting nonlinear phenomena can be found for the primary resonance of nano beam. This work is expected to be useful for the design and analysis for the nonlinear dynamic behaviors of structures at nano scales. [Copyright &y& Elsevier]

Abstract: The natural frequencies of the flapwise bending vibrations of a nonuniform rotating nanocantilever has been calculated, considering the true spatial variation of the axial force due to the rotation. The area of the nanobeam cross-section is assumed to change linearly. The problem has been formulated using the nonlocal Eringen elasticity theory and it was solved by a pseudo-spectral collocation method based on Chebyshev polynomials. The effect of the nonlocal small-scale, angular speed, nonuniformity of the section and hub radius on the vibration behavior of the nanocantilever is discussed. [Copyright &y& Elsevier]

Micro/nano-components often exhibit size effects in micro-electro-mechanical systems. A torsional vibration model of micro circular shafts is established based on nonlocal elasticity theory in this paper. Concrete examples are presented for three kinds of boundary conditions. It is shown that according to nonlocal elasticity theory the predicted natural frequencies of the torsional vibration decrease in comparison with the results based on classical continuum mechanics, and the differences are much larger with a smaller external characteristic scale (such as radius of cross section ) or for higher modal frequencies. Vibration frequencies decrease and the nonlocal scale effects disappear gradually with the increase of cross section radius. Vibration mode functions and relative rotation angles are also observed, of which the former are consistent with those predicted by classical continuum theory. Furthermore the selection of internal characteristic scale is discussed. A numerical example proves that lattice constant of material is very close to the scale mentioned, which may he approximately adopted as the internal characteristic scale in micro/nano-mechanics. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, the effects of the viscous fluid on the propagation characteristics of elastic waves in carbon nanotubes are studied. Based on the nonlocal continuum theory, the small scales effects are also considered. The equations of wave motion are derived and the dispersion relation is presented. Numerical simulations are performed with the consideration of different scale coefficients to discuss the influence of the viscous fluid. From the results, it can be observed that the dispersion relation can be changed by the fluid viscosity obviously. Moreover, due to the fluid viscosity, the wave frequency will be reduced to a low region and the elastic wave behaviors can be significantly influenced by the viscous fluid velocity. [Copyright &y& Elsevier]

Abstract: In this article, a single nonlocal beam model is developed and applied to investigate the flapwise bending–vibration characteristics of a rotating nanocantilever. A rotating nanocantilever is found as blades of a nanoturbine. Employing Eringen’s nonlocal elasticity theory, the governing differential equations for the abovementioned problem are derived. Differential quadrature method (DQM) is being utilized and nondimensional nonlocal frequencies are obtained. The effects of the small-scale, angular velocity and hub radius are examined and discussed. It is shown that small-scale effects play a significant role in the vibration response of a rotating nanocantilever. Further as rotational angular velocity increases, the small-scale effect on the frequency response is increased for first modes of vibration while it is decreased for higher modes of vibration. [Copyright &y& Elsevier]

Abstract: In this paper, the propagation characteristics of the elastic wave in fluid-conveying double-walled carbon nanotubes are investigated. The nonlocal continuum theory is applied to discuss the dispersion relation with small scale effects. The interaction of the double tubes is considered with the van der Waals interaction pressure and the equation of the flexural wave for the double-walled Euler–Bernoulli beam model is derived. The properties of the frequency and the amplitude ratio are proposed with different wave numbers and fluid velocities. From this work, it can be observed that the small scale effects should be considered in the investigation of the elastic wave propagation in fluid-conveying double-walled nanotubes. [Copyright &y& Elsevier]

Abstract: Variational principles are derived for multi-walled carbon nanotubes undergoing buckling using the semi-inverse method. Derivations are based on the continuum modelling of nanotubes taking into account small scale effects via the nonlocal theory of elasticity. Natural and geometric boundary conditions for multi-walled nanotubes are derived which leads to a set of coupled boundary conditions. [Copyright &y& Elsevier]