The performance of a piecewise-stressed ZnO piezoelectric semiconductor nanofiber is studied with the multi-field coupling theory. The fields produced by equal and opposite forces as well as sinusoidally distributed forces are examined. Specific distributions of potential barriers, wells, and regions with effective polarization charges are found. The results are fundamental for the mechanical tuning on piezoelectric semiconductor devices and piezotronics.
The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.
A parallel nonlinear energy sink (NES) is proposed and analyzed. The parallel NES is composed of a vibro-impact (VI) NES and a cubic NES. The dynamical equation is given, and the essential analytical investigation is carried out to deal with the cubic nonlinearity and impact nonlinearity. Multiple time-scale expansion is introduced, and the zeroth order is derived to give a rough outline of the system. The underlying Hamilton dynamic equation is given, and then the optimal stiffness is expressed. The clearance is regarded as a critical factor for the VI. Based on the periodical impact treatment by analytical investigation, the relationships of the cubic stiffness, the clearance, and the zeroth-order attenuation amplitude of the linear primary oscillator (LPO) are obtained. A cubic NES under the optimal condition is compared with the parallel NES. Harmonic signals, harmonic signals with noises, and the excitation generated by a second-order filter are considered as the potential excitation forces on the system. The targeted energy transfer (TET) in the designed parallel NES is shown to be more efficient.
An algorithm is presented to analyze the free vibration in a system composed of a cable with discrete elements, e.g., a concentrated mass, a translational spring, and a harmonic oscillator. The vibrations in the cable are modeled and analyzed with the Lagrange multiplier formalism. Some fragments of the investigated structure are modeled with continuously distributed parameters, while the other fragments of the structure are modeled with discrete elements. In this case, the linear model of a cable with a small sag serves as a continuous model, while the elements, e.g., a translational spring, a concentrated mass, and a harmonic oscillator, serve as the discrete elements. The method is based on the analytical solutions in relation to the constituent elements, which, when once derived, can be used to formulate the equations describing various complex systems compatible with an actual structure. The numerical analysis shows that, the method proposed in this paper can be successfully used to select the optimal parameters of a system composed of a cable with discrete elements, e.g., to detune the frequency resonance of some structures.
A dynamic model for an inclined carbon fiber reinforced polymer (CFRP) cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments. The steady-state solutions of the nonlinear equations are obtained by the multiple scale method (MSM) and the Newton-Raphson method. The frequency- and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal (between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode, the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude, and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.
Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation fields, a new semi-analytical approach is developed to predict the swelling induced finite bending for a functionally graded (FG) layer composed of a pH-sensitive hydrogel, in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference, the initial state is mapped into the deformed configuration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the finite element method (FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement confirms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress fields are studied. Furthermore, the tangential free-stress axes are illustrated in deformed configuration.
The bifurcations of penetrative Rayleigh-Bénard convection in cylindrical containers are studied by the linear stability analysis (LSA) combined with the direct numerical simulation (DNS) method. The working fluid is cold water near 4℃, where the Prandtl number Pr is 11.57, and the aspect ratio (radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter θm. The relationship between the normalized critical Rayleigh number (Rac(θm)/Rac(0)) and θm is formulated, which is in good agreement with the stability results within a large range of θm. The aspect ratio has a minor effect on Rac(θm)/Rac(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system. Moreover, two kinds of qualitatively different steady axisymmetric solutions are identified.
The two-dimensional (2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.
The effects of air dissociation on flat-plate hypersonic boundary-layer flow instability and transition prediction are studied. The air dissociation reactions are assumed to be in the chemical equilibrium. Based on the flat-plate boundary layer, the flow stability is analyzed for the Mach numbers from 8 to 15. The results reveal that the consideration of air dissociation leads to a decrease in the unstable region of the first-mode wave and an increase in the maximum growth rate of the second mode. High frequencies appear earlier in the third mode than in the perfect gas model, and the unstable region moves to a lower frequency region. When the Mach number increases, the second-mode wave dominates the transition process, and the third-mode wave has little effect on the transition. Moreover, when the Mach number increases from 8 to 12, the N-factor envelope becomes higher, and the transition is promoted. However, when the Mach number exceeds 12, the N-factor envelope becomes lower, and the transition is delayed. The Nfactor envelope decreases gradually with the increase in the altitude or Mach number.
Numerical simulations are performed to examine the packing behavior of human red blood cells (RBCs). A combined finite-discrete element method (FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clarified, and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the flat or thick cells used in this study. Such information is beneficial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.