Narrow Results

This paper presents an analysis of wave dispersion behavior in electrode–piezoelectric–electrode sandwich structures, considering surface effects (SE). The sandwich structure was situated atop an orthogonally anisotropic viscoelastic substrate. This paper aims to explore the surface effects on the dispersion characteristics of piezoelectric sandwich nanoplates embedded with viscoelastic substrates, integrating frequency-wave number curves and phase velocity-wave number curves. The displacement field of the nanoplate was derived using the sinusoidal shear deformation theory, and governing equations were established through Hamilton’s principle and surface constitutive equations. Subsequently, equations of motion were obtained based on the nonlocal strain gradient theory (NSGT), and characteristic equations were developed using harmonic solutions. The study thoroughly examined the effects of scale, viscoelasticity, and surface properties on wave propagation characteristics. The results reveal that scale effects significantly influence the dispersion curves of nanoplates, depending on the wave number, and emphasize the necessity of considering the surface effects of electrode layers. Notably, a reduction in thickness leads to an upward trend in both frequency and phase velocity curves. Furthermore, the Winkler modulus and shear modulus play a pivotal role in enhancing frequency stiffness, while increases in the damping coefficient and voltage result in a decrease in both frequency and phase velocity.

Atomistic molecular dynamics simulations have been used, apparently for the first time, to investigate the anchoring behavior of a liquid crystal at the interface with an amorphous polymer. The simulations studied a system consisting of the nematogen 5CB at the surface of amorphous polyethylene, and used the simple Dreiding II force field. The simulations indicate a preference for nonplanar anchoring. Two distinct microscopic paths have been identified by which the liquid crystal changes orientation at the surface. In one case, only one or a few of the 5CB molecules are rotating at any particular time. In the other case, a substantial fraction of the molecules rotate simultaneously.

Applying surface piezoelectricity theory and plane wave expansion (PWE) method to the model of Kirchhoff plate, the calculation method of band structure of a piezoelectric phononic crystal (PC) nanoplate with surface effects is proposed and formalized. In order to investigate the bandgap properties of first order in the nanoplate in detail, the corresponding influence rules of thermo-electro-mechanical coupling fields, surface effects and geometric parameters on bandgaps are studied. During the researches, temperature variation, electrical voltage and external axial force are picked as the influencing parameters corresponding to thermo-electro-mechanical coupling fields. Residual surface stress and material intrinsic length are chosen as the influencing parameter related to surface effects. Lattice constant, radius of PZT-4 hole and thickness of nanoplate are picked as the influencing parameters of geometric parameters. All the results are expected to be helpful for the design of micro and nanodevices based on piezoelectric periodic nanoplates.

The catalyst surface was processed in the high-voltage electrical discharge device in oxygen environment. Continuous active oxide centers formed on the surface and complete filling of the surface with oxygen occur, and its thermo-physical properties, thermo-luminescence curves, scanning electron microscope and ESR spectrometers were studied. It was determined that the activity of the catalyst at values of the absorbed dose $D\le 21$kGy is many times higher than that of conventional catalysts. Thus, due to the sorption volume of the surface, the volume of the product formed in the liquid phase increases by 1.6 times.

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

In the present paper, the vibrational and buckling characteristics of nanotubes with various boundary conditions are investigated considering the coupled effects of nonlocal elasticity and surface effects, including surface elasticity and surface tension. The nonlocal Eringen theory is adopted to consider the effect of small scale size, and the Gurtin–Murdoch model the surface effect. Hamilton’s principle is employed to formulate the governing equation and differential transformation method (DTM) is utilized to obtain the natural frequency and critical buckling load of nanotubes with various boundary conditions. The results obtained match the available ones in the literature. Detailed mathematical derivations are presented and numerical investigations are performed. The emphasis is placed on the effects of several parameters, such as the nonlocal parameter, surface effect, aspect ratio, mode number and beam size, on the normalized natural frequencies and critical buckling loads of the nanotube. It is explicitly shown that the vibration and buckling of a nanotube is significantly influenced by these effects. Numerical results are presented which may serve as benchmarks for future analysis of nanotubes.

In this paper, the buckling characteristic of FGM plate considering the surface effect is studied based on general third-order plate theory and non-local theory. The surface effect of FGM plate is captured by the surface elasticity theory. The Kirchhoff hypothesis is released by employing parabolic variation of transverse shear strains. By using Navier solution technique, analytical solutions of buckling loads of FGM plate with surface effect are given, and detailed parametric studies are presented to show the relationship between surface effects and the plate thickness, power-law index, surface residual stress, surface moduli and non-local parameter. Furthermore, the surface effect on the buckling characteristic of FGM plate is also discussed.

This paper aims to investigate the imperfection sensitivity of the post-buckling behavior and the free vibration response under pre- and post-buckling of nanoplates with various edge supports in the thermal environment. Formulation is based on the higher-order shear deformation plate theory, von Kármán kinematic hypothesis including an initial geometrical imperfection and Gurtin–Murdoch surface stress elasticity theory. The discretized nonlinear coupled in-plane and out-of-plane equations of motion are simultaneously obtained using the variational differential quadrature (VDQ) method and Hamilton’s principle. To this end, the displacement vector and nonlinear strain–displacement relations corresponding to the bulk and surface layers are matricized. Also, the variations of potential strain energies, kinetic energies and external work are obtained in matrix form. Then, the VDQ method is employed to discretize the obtained energy functional on space domain. By Hamilton’s principle, the discretized quadratic form of nonlinear governing equations is derived. The resulting equations are solved employing the pseudo-arc-length technique for the post-buckling problem. Moreover, considering a time-dependent small disturbance around the buckled configuration, the vibrational characteristics of pre- and post-buckled nanoplates are determined. The influences of initial imperfection, thickness, surface residual stress and temperature rise are examined in the numerical results.

This paper investigates the nonlinear vibration of a size-dependent doubly clamped nanoresonator based on modified indeterminate couple-stress theory and Euler–Bernoulli beam theory. Surface effects, dispersion Casimir force, and fringing field effects are considered in the nonlinear model. The electrostatic actuation is a combination of DC and AC voltages and imposed on the nanobeam through one electrode. The governing differential equation of motion is derived using the extended Hamilton’s principle and discretized to a nonlinear ODE using Galerkin’s procedure. The multiple time scale method is applied to the reduced-order model in order to obtain the nanobeam frequency-response curves analytically under small AC voltage loads. The influences of the mentioned parameters are investigated on the primary resonance characteristics of the nanoresonator. It is shown that the application of non-classical continuum theory results in a softening effect on the dynamic response of the system near primary resonance. Moreover, it is concluded that the influence of surface energy on the system dynamic behavior depends on the value of DC voltage load.

We present results of first principle calculations of the Casimir force between Si films of nanometric size, which show that it depends significantly upon the configuration of the surface atoms, and give evidence of the importance of surface states.