Abstract: Abstract Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic scale. At every instant, the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass, the velocity, the internal stress, and the intrinsic angular momentum. The deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density field. It is shown that these microcontinua are endowed with the following unique response features: (i) the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable; (ii) this fundamental dynamic equation and this complex field variable are just the Schrödinger equation and the complex wave function in quantum theory; and, accordingly, (iii) the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered, thus following objective and deterministic response patterns for quantum entities, in which the physical origins and meanings of the wave function and the Schrödinger equation become self-evident and, in particular, any probabilistic indeterminacy becomes irrelevant. PubDate: 2019-12-01

Abstract: Abstract The present study deals with the propagation of a polarized shear horizontal (SH) wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder. The interface of the two media is assumed mechanically imperfect. For obtaining the dispersion relation, the mathematical formulation has been developed and solved by an analytical treatment. The effects of various parameters, i.e., the thickness ratio, the imperfect interface, the initial stress, the reinforcement, and the piezoelectric and dielectric constants, on the dispersion curve are observed prominently. The dispersion curves for different modes have been also plotted. The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices. PubDate: 2019-11-28

Abstract: Abstract This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer, which is also an exact solution to the unsteady Navier-Stokes (NS) equations. The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions. The wall temperature and heat flux have power dependence on both time and spatial distance. The solution domain, the velocity distribution, the flow field, and the temperature distribution in the fluids are studied for different controlling parameters. These parameters include the Prandtl number, the mass transfer parameter at the wall, the wall moving parameter, the time power index, and the spatial power index. It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems. The heat transfer solutions are given by the confluent hypergeometric function of the first kind, which can be simplified into the incomplete gamma functions for special conditions. The wall heat flux and temperature profiles show very complicated variation behaviors. The wall heat flux can have multiple poles under certain given controlling parameters, and the temperature can have significant oscillations with overshoot and negative values in the boundary layers. The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified. The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed. Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations, which can be used as a benchmark problem for numerical code validation. PubDate: 2019-11-28

Abstract: Abstract In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail. PubDate: 2019-11-20

Abstract: Abstract Vibration energy harvesting is to transform the ambient mechanical energy to electricity. How to reduce the resonance frequency and improve the conversion efficiency is very important. In this paper, a layer-separated piezoelectric cantilever beam is proposed for the vibration energy harvester (VEH) for low-frequency and wide-bandwidth operation, which can transform the mechanical impact energy to electric energy. First, the electromechanical coupling equation is obtained by the Euler-Bernoulli beam theory. Based on the average method, the approximate analytical solution is derived and the voltage response is obtained. Furthermore, the physical prototype is fabricated, and the vibration experiment is conducted to validate the theoretical principle. The experimental results show that the maximum power of 0.445 □W of the layer-separated VEH is about 3.11 times higher than that of the non-impact harvester when the excitation acceleration is 0.2 g. The operating frequency bandwidth can be widened by increasing the stiffness of the fundamental layer and decreasing the gap distance of the system. But the increasing of operating frequency bandwidth comes at the cost of reducing peak voltage. The theoretical simulation and the experimental results demonstrate good agreement which indicates that the proposed impact-driving VEH device has advantages for low-frequency and wide-bandwidth. The high performance provides great prospect to scavenge the vibration energy in environment. PubDate: 2019-11-20

Abstract: Abstract In this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton’s principle and derive the governing differential equations. Then, we use Navier’s solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the side-tothickness ratio, and the nanoplate shape on natural frequencies are investigated. PubDate: 2019-11-16

Abstract: Abstract The nonlinear convective flow of an Oldroyd-B fluid due to a nonlinear stretching sheet with varying thickness is examined. The salient features of the random movement and thermophoresis are described. Formulation is made with the nonlinear thermal radiation and heat generation/absorption. Further, the convective conditions and double stratification are taken into account. The resulting flow problems are tackled by the optimal homotopy analysis method (OHAM). The resulting nonlinear problems are solved for the velocity, temperature, and concentration fields. The temperature and concentration gradients are numerically discussed. The total residual error is calculated. The Nusselt number is an increasing function of the radiation parameter. The Sherwood number increases with the increase in the solutal stratification or the Schmidt number. The main outcomes are presented in conclusions. This study has a wide range of applications such as thermal stratification of oceans, reservoirs, and rivers, density stratification of atmosphere, hydraulic lifts, and polymer processing. PubDate: 2019-11-13

Abstract: Abstract The definitions of the third-order elastic, piezoelectric, and dielectric constants and the properties of the associated tensors are discussed. Based on the energy conservation and coordinate transformation, the relations among the third-order constants are obtained. Furthermore, the relations among the third-order elastic, piezoelectric, and dielectric constants of the seven crystal systems and isotropic materials are listed in detail. These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials. It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups, while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material. The reason is that some of the point groups are centrally symmetric, and the other point groups are high symmetry. These results provide the foundation to measure these constants, to choose material, and to research nonlinear problems. Moreover, these results are helpful not only for the study of nonlinear elastic and piezoelectric problems, but also for the research on flexoelectric effects and size effects. PubDate: 2019-11-11

Abstract: Abstract In this study, the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional (3D) theoretical model. The complete nonlinear governing equations are discretized via Galerkin’s method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm. Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions. A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio, the flow velocity, and the gravity parameter on the post-buckling behavior of the pipe. Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter. It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached. Just beyond the critical flow velocity, the pipe would lose stability by static divergence via a pitchfork bifurcation, and two possible nonzero equilibrium positions are generated. It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter. Unlike a pipe with two immovable ends, however, the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors. The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity. In addition, the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end. PubDate: 2019-11-11

Abstract: Abstract A novel vibration isolation device called the nonlinear energy sink (NES) with NiTiNOL-steel wire ropes (NiTi-ST) is applied to a whole-spacecraft system. The NiTi-ST is used to describe the damping of the NES, which is coupled with the modified Bouc-Wen model of hysteresis. The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer (TET) to concentrate the energy locally on the nonlinear oscillator, and then dissipates it through damping in the NES with NiTi-ST. The generalized vibration transmissibility, obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions (NOFRFs), is first used as the evaluation index to analyze the whole-spacecraft system in the future. An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs. Finally, the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption. The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system, without changing its natural frequency. Moreover, the NES with NiTi-ST can be directly used in practical engineering applications. PubDate: 2019-11-09

Abstract: Abstract Modal parameter identification is a mature technology. However, there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination. This paper proposes a new time-frequency method based on intrinsic chirp component decomposition (ICCD) to address these issues. In this method, a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction. The effectiveness and accuracy of the proposed method are illustrated using three examples: a cantilever beam structure with intensive noise contamination or environmental interference, a four-degree-of-freedom structure with two closely spaced modes, and an impact test on a cantilever rectangular plate. By comparison with the identification method based on the empirical wavelet transform (EWT), it is shown that the presented method is effective, even in a high-noise environment, and the dynamic characteristics of closely spaced modes are accurately determined. PubDate: 2019-11-08

Abstract: Abstract The vibroimpact systems with bilateral barriers are often encountered in practice. However, the dynamics of the vibroimpact system with bilateral barriers is full of challenges. Few closed-form solutions were obtained. In this paper, we propose a novel method for random vibration analysis of single-degree-of-freedom (SDOF) vibroimpact systems with bilateral barriers under Gaussian white noise excitations. A periodic approximate transformation is employed to convert the equations of the motion to a continuous form. The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov (FPK) equation. The closed-form stationary probability density function (PDF) of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow. Finally, the versatility of the proposed approach is demonstrated by its application to two typical examples. Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods. PubDate: 2019-11-08

Abstract: Abstract The behavior of large deformations of cellular tissues is usually affected by the local properties of cells and their interactions, resulting in folding which acts as an important role in the embryonic development, as well as growing and spreading of a tumor, which can rapidly promote the stereo complexity of the architecture of the tissues. In the present study, a cylindrical vertex model is constructed to explore the morphology of the tubular cell sheets subject to an embedded contractile ring. It is found that an inner region of the contractile ring in equilibrium will protrude from the tube wall, and it will suddenly collapse when the contractile strength exceeds a threshold, indicating the occurrence of a bifurcation. These results on the effect of embedded contraction in the tubular shell are quite different from the planar cases, which can reveal the importance of the interaction between the geometric and material non-linearity in cylindrical geometry. The dependence of the large deformation on the bending modulus parameters and contraction strength is also analyzed for the cylindrical cell shell. PubDate: 2019-11-07

Abstract: Abstract Motivated by the study of regularization for sparse problems, we propose a new regularization method for sparse vector recovery. We derive sufficient conditions on the well-posedness of the new regularization, and design an iterative algorithm, namely the iteratively reweighted algorithm (IR-algorithm), for efficiently computing the sparse solutions to the proposed regularization model. The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length. Finally, we present numerical examples to illustrate the features of the new regularization and algorithm. PubDate: 2019-11-05

Abstract: Abstract The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied. PubDate: 2019-11-01

Abstract: Abstract Application of dielectric elastomers (DE) has remarkably increased in mechatronics because they are suitable candidates for energy harvesting due to their low cost, light weight, and high energy density. The dielectric elastomer generators (DEGs) exhibit high performance regardless of the applications scale. However, functioning as a generator, a DE may lose its efficiency due to several failure modes including material rupture, loss of tension (LT), electrical breakdown (EB), and electromechanical instability (EMI). The failure modes confine the area of allowable states for generation process. Dielectric constant and dielectric strength of such elastomers depend on the amount of applied deformation and also working temperature, which are often ignored in theoretical simulations. In this paper, variations of the above-mentioned parameters are considered in mechanical and electrical modellings to investigate their effects on energy density and efficiency of generators. Obtained results show that, ignoring the variations of material dielectric constant and dielectric strength leads to overestimation of the specific energy. Furthermore, it is shown that, for an acrylic-based generator, the specific energy sharply decreases with temperature rise. PubDate: 2019-11-01

Abstract: Abstract This paper numerically studies the aerodynamic performance of a bird-like bionic flapping wing. The geometry and kinematics are designed based on a seagull wing, in which flapping, folding, swaying, and twisting are considered. An in-house unsteady flow solver based on hybrid moving grids is adopted for unsteady flow simulations. We focus on two main issues in this study, i.e., the influence of the proportion of down-stroke and the effect of span-wise twisting. Numerical results show that the proportion of down-stroke is closely related to the efficiency of the flapping process. The preferable proportion is about 0.7 by using the present geometry and kinematic model, which is very close to the observed data. Another finding is that the drag and the power consumption can be greatly reduced by the proper span-wise twisting. Two cases with different reduced frequencies are simulated and compared with each other. The numerical results show that the power consumption reduces by more than 20%, and the drag coefficient reduces by more than 60% through a proper twisting motion for both cases. The flow mechanism is mainly due to controlling of unsteady flow separation by adjusting the local effective angle of attack. These conclusions will be helpful for the high-performance micro air vehicle (MAV) design. PubDate: 2019-10-12

Abstract: Abstract A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient. The numerical solutions are obtained by a finite difference scheme method. The stability of this finite difference scheme method is discussed. The distributions of the velocity and phase difference are given numerically and graphically. The effects of the Reynolds number, relaxation time, and aspect ratio of the cross section on the oscillatory flow are investigated. The results show that when the relaxation time of the Maxwell model and the Reynolds number increase, the resonance phenomena for the distributions of the velocity and phase difference enhance. PubDate: 2019-10-10

Abstract: Abstract A sophisticated theoretical and mathematical model is proposed. It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux, thermal radiation, and viscous dissipation. Despite the fact that some properties of the fluid do not depend on the temperature, the fluid thermal conductivity is assumed to depend on the temperature. Based on accelerating the fluid elements, some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena. The contribution in this study is that a similar solution is obtained, in spite of the high nonlinearity of the Carreau model, especially, with the heat flux, variable conductivity, and viscous dissipation phenomena. Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number. Likewise, the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter. Finally, the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results. PubDate: 2019-10-09