Small Scale Parameter Research Articles

Analytical buckling and post-buckling characteristics of Mindlin micro composite plate with central opening by use of nonlocal elasticity theory

The effect of central opening on the buckling and nonlinear post-buckling response of carbon nanotubes (CNTs) reinforced micro composite plate embedded in elastic medium is considered in this paper. It is assumed that the system is surrounded by elastic medium, therefore; the influence of Pasternak foundation on buckling and post-buckling behavior are analyzed. In order to derive the basic formulations of plate the Mindlin plate theory is applied. Furthermore, nonlocal elasticity theory is applied to consider the size-dependent effect. Analytical approach and Newton-Raphson iterative technique are utilized to calculate the impact of cut out on the buckling and nonlinear post-buckling response of micro composite plate. The variation of buckling and post-buckling of micro composite cut out plate based on some significant parameters such as volume fraction of CNTs, small scale parameter, aspect ratio, square cut out and elastic medium were discussed in details. According to the results, it is concluded that the aspect ratio and length of square cut out have negative effect on buckling and post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the buckling and post-buckling behavior of plate. Meanwhile, considering elastic medium increases the buckling and post-buckling load of system.

Nonlocal mixed variational formula for orthotropic nanoplates resting on elastic foundations

This paper deals with the examination of orthotropic nanoplates utilizing nonlocal mixed variational formula. For this model, the displacement and stress fields are considered to be arbitrary and it includes the impact of transverse normal stress which does not exist in numerous theories. The orthotropic nanoplates are thought to be refreshed on elastic foundations. The mixed theory is utilized to get the governing differential equations as per Eringen’s nonlocal elasticity model. The governing equations incorporate the small-scale effect as well as foundations and mechanical impacts. Analytical solutions of bending response for simply supported orthotropic nanoplates are derived. The present outcomes are compared well with those being in the literature. The effects played by elastic foundation parameters, small-scale parameter, aspect and thickness nanoplate ratios are examined. The present study can be used as benchmarks for future comparisons with other investigators applying models containing the transverse shear and normal strains.

On the dynamic response of porous functionally graded microbeam under moving load

In this article, the dynamic behavior of functionally graded (FG) microbeams with different porosity distributions and acted by a moving harmonic load is studied. A bi-dimensional FG microbeam with its material properties changing gradually along both the length and thickness directions in a power-law distribution form is presented. Besides, the porosities are distributed evenly and unevenly in the body of microbeams, and the small-scale effect is captured with the help of the modified couple stress theory. The equations describing the motions of the FG microbeam are obtained in the framework of Hamilton's principle in conjunction with the parabolic shear deformation theory. These equations are solved by employing the finite element formulation, which is validated by comparing the fundamental frequency and dynamic response with previous works. The effects of several key factors such as two grading indexes, small scale parameters, porous distribution pattern and volume fraction, as well as moving speed and motivation frequency of the acted load are investigated in detail. It is concluded that the bi-dimensional FG parameters and porous parameter play significant roles in the dynamic response of microbeams subjected to a moving load, which is helpful for the multi-functional and optimal design of microsystems.

Size-dependent dynamics of a FG Nanobeam near nonlinear resonances induced by heat

This study explores heat-induced nonlinear vibration of a functionally graded (FG) capacitive nanobeam within the framework of nonlocal strain gradient theory (NLSGT). The elastic FG beam, which is firstly deflected by a DC voltage, is driven to vibrate about its deflected position by a periodic heat load. The nano-structure, which consists of a clamped-clamped nanobeam, is modeled assuming Euler–Bernoulli beam assumption which accounts for the nonlinear von-Karman strain and the electrostatic and intermolecular forcing. To simulate the static and dynamic responses, a model reduction procedure is carried out by employing the Galerkin method. The method of Averaging as a regular semi-analytic perturbation method is applied to obtain governing equations of the steady-state responses. With the purpose of establishing the validity of the solution, a Shooting technique in conjunction with the Floquet theory is used to capture the periodic motions and then examine their stability. The nonlinear resonance frequency of the FG nanobeam near its fundamental natural frequency (primary resonance) and near principal parametric resonance is investigated while the emphasis is placed on studying the effect of various parameters including DC voltage, amplitude of the periodic heat source, material index, damping ratio, and small scale parameters. The main objective of this study is to model a miniature structure which can be used as either a sensitive remote temperature sensor or a high-efficiency thermal energy harvester.

Nonlocal dynamic stability analysis of a Timoshenko nanobeam subjected to a sequence of moving nanoparticles considering surface effects

In this study, the dynamic stability of a Timoshenko nanobeam under the intermittent movement of nanoparticles is investigated considering surface effects. Simply-supported boundary conditions are assumed for a rectangular cross-section beam. The elastic foundation is modeled as a Pasternak elastic foundation. Also, the role of the nanoparticle inertia is considered. The nanoparticles move over the beam continuously with a constant velocity, and the friction between particles, and the beam is ignored. Governing equations are derived by Hamilton's principle in conjunction with nonlocal and Gurtin-Murdoch theories. Dynamic stability analysis of the nanobeam under induced excitation of moving nanoparticles is carried out, and the stability and instability regions are derived by incremental harmonic balance method (IHBM). The stability of the system is described in the plane (mass-velocity). A detailed study is conducted to examine the effects of various parameters such as the small scale parameter, surface constants, Pasternak foundation coefficients, and nanoparticles inertia on the dynamic instability region (DIR) of the nanobeam. The results show that considering surface theory has a negligible effect on the DIR of the nanobeam under the intermittent passage of nanoparticles. Pasternak and Winkler spring constants increase the stiffness and stability of the nanobeam. Also, considering moving mass inertia and small scale parameter shifts the DIR to the lower frequency zone.

Nonlinear dynamic analysis of temperature-dependent functionally graded magnetostrictive sandwich nanobeams using different beam theories

In the present study, nonlinear dynamic analysis of an embedded functionally graded sandwich nanobeam (FGSNB) integrated with magnetostrictive layers is investigated. The core layer of FGSNB, which is subjected to a time-dependent transverse load, is made of a two-constituent functionally graded material that the material properties of the functionally graded nanobeam are temperature dependent and assumed to vary in the thickness direction. The modified couple stress theory is taken into account so as to consider the small-scale effects. The surrounding elastic medium is simulated as visco-Pasternak foundation to study the effects of damping, shear and elastic effects of surrounded medium. Using energy method and Hamilton’s principle, the governing motion equations and related boundary conditions are obtained for different beam theories. Finally, the differential quadrature as well as Newmark-β methods are employed to obtain the nonlinear dynamic response of the functionally graded magnetostrictive sandwich nanobeam (FGMSNB), and therefore deflection-response curves are plotted to study the effects of small-scale parameter, surrounding elastic medium, magnetostrictive layers, geometrical parameters, material compositions of core layer, environment temperature and boundary conditions and nonlinear terms graphically. The results indicate that the magnetostrictive layers play a key role on the dynamic behavior of the FGMSNB. Moreover, comparing results with those obtained in Ghorbanpour Arani and Abdollahian (Mech Adv Mater Struct, 2017. https://doi.org/10.1080/15376494.2017.1387326 ) shows the importance of the nonlinear terms. The obtained results in this paper can be used as sensor and actuator in the sensitive applications.

A Fully Time-dependent Ab Initio Cosmic-Ray Modulation Model Applied to Historical Cosmic-Ray Modulation

Abstract Cosmogenic nuclide records can in principle allow for the estimation of the behavior of the heliospheric magnetic field (HMF) in the distant past. This requires careful modeling of cosmic-ray transport in a manner that is as realistic as possible, taking into account as many of the factors affecting the transport of cosmic-rays (CRs) as possible. The present study presents a 3D time-dependent ab initio CR modulation code that utilizes as inputs simple theoretically and observationally motivated temporal profiles to model large-scale (such as the tilt angle) and small-scale (such as the magnetic variance) parameters relevant to CR transport. Galactic CR proton differential intensities computed using this model for the period 1977–2001 are in reasonable to good agreement with spacecraft observations, reproducing the major salient features of the observed CR intensity temporal profile. To investigate pre-space-age cosmic-ray modulation, and to test conclusions previously drawn regarding the relative importance of drift effects on said modulation, historic estimates of the past HMF presented by McCracken & Beer were used as inputs for the model. The resulting CR temporal intensity profile displays clear evidence of drift effects, with a sharp peak in intensities during the Dalton Minimum.

Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions

Thermoelastic dynamic analysis of micro-/nano-beams is essential in the field of micro-/nano-electro-mechanical systems (MEMSs/NEMSs). However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro-/nano-beams must be considered in their thermoelastic vibrations. This work originally explores analytical solutions of coupled thermoelastic forced vibrations of micro-/nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory. The heat conductivity equation is obtained by using the type Ⅲ Green-Naghdi theory. Coupled thermoelastic dynamic equations are decoupled by use of Green's function method and expressions of displacements, temperature fields, and thermal moments of micro-/nano-beams are derived. Furthermore, movement behaviors of an “ice core” of the temperature field are used to explain dynamic phenomena of the coupled system. Results from finite element analysis are compared with analytical solutions for verification purposes. This work primarily discusses influences of a small-scale parameter on coupled displacement and temperature fields and those of other important physical parameters, such as heating positions and height-to-length ratios of micro-/nano-beams, on system responses.

Characterization of path loss model for wireless communication channel modelling

PurposeWireless communication channel provides a wide area of applications in the field of communication, distributed sensor network and so on. The prominence of the wireless communication channel is because of its robust nature and the sustainability for the precise ranging and the localization. The precision and accuracy of the wireless communication channel largely depend on the localization. The development of the wireless communication channel with improved benefits needs the accurate channel model.Design/methodology/approachThis paper characterizes the tangential path loss model in the WINNER based wireless communication channel model. The measurements taken in the WINNER channel model are compared with the tangential path loss characterized WINNER Channel model.FindingsThe model operates well over the varying antenna orientations, measurement condition and the propagation condition. The proposed tangential path loss model is performing well over the various outdoor scenarios.Originality/valueThe proposed characterization shows change in the small-scale parameters (SSP), such as power, delay, angle of arrival and angle of departure as well as the large-scale parameters (LSP), such as RMS delay spread, shadowing, path loss and Ricean factor associated with the model.

Effects of surface energy and surface residual stresses on vibro-thermal analysis of chiral, zigzag, and armchair types of SWCNTs using refined beam theory

In this article, vibration characteristics of three different types of Single-Walled Carbon Nanotubes (SWCNTs) such as armchair, chiral, and zigzag carbon nanotubes have been investigated considering the effects of surface energy and surface residual stresses. The nanotubes are embedded in the elastic substrate of the Winkler type and are also exposed to low and high-temperature environments. A new refined beam theory namely, one-variable shear deformation beam theory has been combined with Hamilton’s principle to develop the governing equations of the proposed model. The size-dependent behavior of the SWCNTs is addressed by Eringen’s nonlocal elasticity theory whereas the model is investigated analytically by employing Navier’s technique. Also, a parametric study has been conducted to analyze the effects of various scaling parameters such as small scale parameter, temperature change, thermal environments, Winkler modulus, and length of the beam. The results are also validated with previously published articles in special cases witnessing robust agreement.

Size-dependent hydroelastic vibration of FG microplates partially in contact with a fluid

This work focuses on the hydroelastic vibration of vertical functionally graded (FG) microplates partially in contact with a fluid. The nonlocal Lam strain gradient theory is here proposed to include small-scale effects, with the introduction of three higher-order material constants within the formulation. This non-classical model would revert to the modified couple stress theory (MCST) or the classical continuum model (CCM) for a vanishing value of two or three length scale parameters, respectively. A fifth-order shear deformation theory is employed to capture the transverse shear stresses and rotary inertia effects. An ideal fluid is also assumed to simplify the dynamic problem, where the continuity equation is enforced to determine the fluid velocity potential associated with bulging and sloshing modes. Once the kinetic and potential energy are calculated for the both of structure and interacting fluid, the Rayleigh-Ritz method is employed to determine the wet frequencies of the system. After a preliminary validation of the proposed model, a systematic investigation is performed to check effects of different mechanical and/or geometrical parameters on the vibrational characteristics of the microplate, namely, the small-scale parameters, the aspect ratio, the thickness ratio and the fluid dimensions contacting with the microstructure.

Nonlinear Vibration and Stability Analysis of Thermally Postbuckled Double-Layered Graphene Sheet under 1:1 and 3:1 Internal Resonance

In the present research, vibration behavior is presented for a thermally postbuckled double layered graphene sheet (DLGS). The DLGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on Kirchhoff’s plate theory and nonlinearity of von Karman type is considered in strain–displacement relations. The thermal effects, van der Waals forces between layers and chirality are also included, and some of the material properties are assumed to be temperature-dependent. A coupled system of equations is derived and a new semi-analytical solution is obtained using multiple time-scale methods. The effects of variation of small-scale parameter on the natural frequencies, deflections and response curve of DLGS are analyzed, and the numerical results are obtained from the nonlocal plate model; also, molecular dynamics (MD) simulations are used to investigate different vibration behaviors of DLGS and calibration of the small-scale coefficient. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLGS in thermal environments such as scale parameter, environmental damping, length and thermal load are presented. The stability and occurrence of internal resonance between vibration modes around a stable buckled configuration are investigated.

A comparison of the Bolotin and incremental harmonic balance methods in the dynamic stability analysis of an Euler–Bernoulli nanobeam based on the nonlocal strain gradient theory and surface effects

This study addresses the dynamic stability of an Euler–Bernoulli nanobeam under time-dependent axial loading based on the nonlocal strain gradient theory (NSGT) and considering the surface stress effects. The studied nanobeam cross-section was rectangular, and simply-supported boundary conditions were assumed. Moreover, a uniform thermal gradient was applied to the nanobeam. The elastic medium was modeled based on the Pasternak theory. The strain–displacement relations were derived using the Von Kármán equations. The governing equations were obtained by the energy method and applying the Hamilton's principle. Furthermore, the Bolotin and Incremental Harmonic Balance (IHB) methods were used to solve the differential equations. This study investigates the impact of such parameters as the small-scale parameter, the material length scale, surface effects, elastic medium parameters, temperature variations, geometry, and the static loading factor on the Dynamic Instability Region (DIR). The results are suggestive of the shift of the DIR to lower frequency zone by increasing the small-scale Eringen's nonlocal theory parameter, whereas an increase in the material length scale from the strain gradient theory moves the region to higher frequencies. In case the said parameters are equal, the result conforms to the classical beam theory. In addition, assuming a Pasternak medium and taking into account the effects of surface stress (Young's modulus and the residual stress of the surface) shifts the DIR to higher frequencies, whereas applying a compressive static load moves the region to lower frequencies. Moreover, depending on the thermal expansion coefficient of the medium, temperature variations can also displace the DIR.

Natural Frequency of Rotating Single-Walled Carbon Nanotubes with Considering Gyroscopic Effect

This paper investigates the bending vibration of rotating single-walled carbon nanotubes (SWCNTs) based on nonlocal theory. To this end, the rotating SWCNTs system modeled as a beam with a circular cross section and the Euler-Bernoulli beam theory (EBT) is applied with added effects such as rotary inertia, gyroscopic effect and rotor mass unbalance. Using nonlocal theory, two coupled sixth order partial differential equations that govern the vibration of rotating SWCNTs are derived. To obtain the natural frequency and dynamic response of the nanorotor system, the equation of motion for the rotating SWCNTs are solved. It is found that there are two frequencies in the frequency spectrum. The positive rootintroduced as forward whirling mode, while the negative root represents backward whirling mode. The detailed mathematical derivations are presented while the emphasis is placed on investigating the effect of the several parameters such as, tube radius, angular velocity and small scale parameter on the vibration behavior of rotating nanotubes. It is explicitly shown that the vibration of a spinning nanotube is significantly influenced by these effects. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed. To the knowledge of authors, the vibration of rotating SWCNTs considering gyroscopic effect has not investigated analytically yet and then the results generated herein can be served as a benchmark for future works.

Facial Beauty Prediction Based on Lighted Deep Convolution Neural Network with Feature Extraction Strengthened

Convolutionneural network (CNN) has significantly pushed forward machine vision, which has achieved very significant results in face recognition, image classification and objection detection, and provides a new method for facial beauty prediction (FBP). Although the approach is widely applied in FBP, the research progress in FBP is relatively slow compared with face recognition. The first one is that there is less public database for FBP, and experiments for FBP are tested on small-scale database. The second one is that evaluation of facial beauty is subjective and lack of criterion, and CNN model is hard to train. In view of the problems of FBP, we expand Largescale database of Asian women's face database (LSAFBD) with data augmentation. A lighted deep convolution neural network (LDCNN) for FBP including 5650K parameters is constructed by both Inception model of GoogleNet and Max-Feature-Max activation layer, which can extract multi-scale features of an image, get compacted presentation and reduce parameters. Experiments on LSAFBD show that our LDCNN model has advantages of simple structure, small-scale parameters and is suitable for small embedded devices, with the best classification accuracy of 63.5%, which outperforms the other published CNN models for FBP.

Non-local orthotropic elastic shell model for vibration analysis of protein microtubules

Vibrational analysis in microtubules is examined based on the nonlocal theory of elasticity. The complete analytical formulas for wave velocity are obtained and the results reveal that the small scale effects can reduce the frequency, especially for large longitudinal wave-vector and large circumferential wave number. It is seen that the small scale effects are more significant for smaller wave length. The methods and results may also support the design and application of nano devices such as micro sound generator etc. The effects of small scale parameters can increase vibrational frequencies of the protein microtubules and cannot be overlooked in the analysis of vibrating phenomena. The results for different modes with nonlocal effect are checked.

Three-dimensional nonlinear primary resonance of functionally graded rectangular small-scale plates based on strain gradeint elasticity theory

Abstract In this paper, a size-dependent three-dimensional (3D) nonlinear weak formulation is provided to examine the nonlinear primary resonance problem for functionally graded rectangular small-scale plates. The small-scale factors are taken into formulation by choosing the Mindlin's strain gradeint theory (SGT). According to the variational differential quadrature (VDQ) method, first, the displacement field, nonlinear strain-displacement and constitutive relations as well as the potential and kinetic energies are expressed as the vector and matrix forms. Then, by applying the discretized form of differential operators obtained via the generalized differential quadrature (GDQ) method, the discretized form of aforementioned relations is achieved. Finally, Hamilton's principle is employed to access the weak form of 3D nonlinear governing equations of thick rectangular small-scale plates. The achieved formulation is solved via a multi-step numerical technique to address the size-dependent nonlinear primary resonance of considered system under the harmonic lateral force. In addition to reducing the run time, computational effort and CPU usage, the feature of proposed weak form formulation is that one can employ it in other solution approaches such as finite element method. Also, the use of this formulation provides the possibility of recovering models on the basis of other types of size-dependent theories such as modified strain gradient and modified couple stress theories (MSGT and MCST). In the numerical results, the effects of boundary conditions, small-scale parameter, material index and geometry are examined.

Measurement-Based 5G Millimeter-Wave Propagation Characterization in Vegetated Suburban Macrocell Environments

An empirically based analysis of propagation characteristics in two vegetated suburban areas with different types and fractions of vegetation cover in 5G millimeter-wave (mmWave) bands is presented. A basic distance-dependent path loss model with a Gaussian random variance for shadow fading is utilized in accordance with the maximum-power directional and omnidirectional measurement data, therein exploiting significant path loss exponents in the presence of vegetation. In comparison with the existing ITU-R and 3GPP models, the effect of dense-leaved trees on path loss prediction is similar to that of buildings, whereas these standard models are inapplicable for sparse obstacle-line-of-sight (OLoS) links. Consequently, an azimuth-angle-based path loss characterization is proposed considering the antenna pattern, beam misalignment, and blockage effects. Moreover, several composite and cluster-level small-scale channel parameters, such as the number of clusters, delay spread, and angular spread, are extracted. Analysis of the first-arrival cluster in the OLoS setting reveals that forward scattering through foliage is still dominant and is expected to produce a larger azimuth angular spread of the arrival and compact multipath components in the time domain compared with line-of-sight and reflected clusters. The measurement results improve existing 3GPP channel models for suburban macrocell scenarios in mmWave bands.

On the Design of Near-Optimal Sparse Code Multiple Access Codebooks

Sparse code multiple access (SCMA) is one of the competitive non-orthogonal multiple access (NOMA) techniques for the next generation of communication systems. In this paper, a systematic construction procedure for the design of SCMA codebooks under various channel environments is proposed in order to achieve near-optimal designs, especially for cases which consider small-scale SCMA parameters. The procedure includes the rotation angle design, the construction of multi-dimensional codebooks, and the design of labelling rules. The detailed design criteria and the related properties are derived and investigated. A low-complexity construction algorithm is further proposed for the cases of fading channels. Numerical results show that the designed SCMA codebooks provide improvements in error performance for all of the considered channel conditions, when compared to the codebooks presented in the prior literature.

Exponential and harmonic forced torsional vibration of single-walled carbon nanotube in an elastic medium

In this study, free torsional vibration and forced torsional vibration analysis under the time-dependent exponential and harmonic torsional loadings in single-walled carbon nanotube are investigated. The SWCNT is embedded in an elastic medium. Eringen's theory among the small-scale theories is selected. The nonlocal differential constitutive relation and corresponding boundary condition are derived via Hamilton's principle. Clamped–clamped boundary condition is utilized. The assumed modes method is employed for the dynamic torsional vibration in order to discretize the derived governing equations. The novelty of this work is devoted to the analysis of forced torsional vibration of a carbon nanotube embedded in an elastic medium under the various loadings. The angular displacement for the resonance frequency neglecting the elastic medium is illustrated. For the free analysis, the first three nondimensional natural frequencies with various small-scale parameters and stiffness of the elastic medium are calculated. The results are compared with another study for the first 10 mode numbers. The effects of the nonlocal parameter, length of carbon nanotube, stiffness of the elastic medium, thickness, time constant, and excitation frequency on the nondimensional and dimensional angular displacements are investigated, dynamically. For the greater values of the stiffness of the medium, the nonlocal parameter becomes negligible. When a time-dependent exponential torque is applied to the model, the angular displacement becomes greater and then lower by an increase in the value of the length, but the nondimensional angular displacement decreases continuously by increasing the value of the length under the time-dependent harmonic loading. Moreover, the angular displacement for a determined time becomes lower first and then becomes greater by increasing the time constant.