Auxetic honeycomb structures are promising metamaterials with outstanding mechanical properties, and can be potentially used in energy absorption applications. In this study, a novel modified re-entrant hybrid auxetic metamaterial inspired by Islamic motif art is designed by integrating four-pointed double re-entrant motifs with symmetric semi-hexagonal unit cells to achieve a high energy absorption capacity (EAC). Theoretical analyses and numerical simulations are performed to examine the dynamic crushing behavior of the four-pointed double re-entrant combined structure (FDRCS). The developed finite element models (FEMs) are validated by the experiments under quasi-static compression. The deformation mode and stress-strain curves are further studied under low, medium, and high crushing velocities. The theoretically predicted plateau stress of the FDRCS under different crushing velocities is consistent with the numerical simulation results. The crushing stress and the EAC of the FDRCS are influenced by the geometric parameters and crushing velocities. The FDRCS exhibits a negative Poisson's ratio (NPR), owing to the four-point re-entrant structure (RES). Moreover, the specific energy absorption (SEA) of these structures is higher than that of nonauxetic hexagonal and auxetic re-entrant structures, owing to the generation of more plastic hinges that dissipate more energy during dynamic crushing.

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied. The pipes are installed in parallel and fixed at their ends, and are restrained by clips to one bracket at their middle points. The pipe subjected to the basement excitation at the left end is named as the active pipe, while the pipe without excitation is called the passive pipe. The clips between the two pipes are the bridge for the vibration energy. The adjacent natural frequencies will enhance the vibration coupling. The governing equation of the coupled system is deduced by the generalized Hamilton principle, and is discretized to the modal space. The modal correction is used during the discretization. The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket. The harmonic balance method (HBM) is used to study the responses in the adjacent natural frequency region. The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket, while the locations of them are not node points. The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes. The stiffness of the clip and bracket can release the vibration coupling. It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough. In this way, the vibration energy is reflected by the almost rigid bracket, and is hard to transfer to the passive pipe via a soft clip. The best choice is to set the clips at the pipe node points. The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.

The propagation of an elastic wave (EW) in a piezoelectric semiconductor (PSC) subjected to static biasing fields is investigated. It is found that there exist two coupling waves between electric field and charge carriers. One is stimulated by the action of the polarized electric field in the EW-front on charge carriers (EFC), and the other is stimulated by the action of initial electric field in biasing fields on dynamic carriers (IEC). Obviously, the latter is a man-made and tunable wave-carrier interaction. A careful study shows that IEC can play a leading role in remaking dynamic performance of the wave-front and an inter-medium role in transferring energy from biasing fields to EW-fronts. Hence, a method is proposed to reform the EW performance by biasing-fields: reforming the dispersivity of EW-fronts by promoting competition between IEC and EFC and inverting the dissipation by the IEC to transfer energy from biasing fields to EW-fronts. The corresponding tuning laws on the phase-frequency characteristics of an EW show that the wave velocity can be regulated smaller than the pure EW velocity at a low-frequency and larger than the pure piezoelectric wave velocity at a high-frequency. As for regulating the amplitude-frequency characteristics of the EW by the IEC, analyses show that EWs can obtain amplification only for those with relatively high vibration frequencies (small wave lengths). The studies will provide guidance for theoretical analysis of waves propagating in PSCs and practical application and design of piezotronic devices.

DNA nanotubes (DNTs) with user-defined shapes and functionalities have potential applications in many fields. So far, compared with numerous experimental studies, there have been only a handful of models on the mechanical properties of such DNTs. This paper aims at presenting a multiscale model to quantify the correlations among the pre-tension states, tensile properties, encapsulation structures of DNTs, and the surrounding factors. First, by combining a statistical worm-like-chain (WLC) model of single DNA deformation and Parsegian's mesoscopic model of DNA liquid crystal free energy, a multiscale tensegrity model is established, and the pre-tension state of DNTs is characterized theoretically for the first time. Then, by using the minimum potential energy principle, the force-extension curve and tensile rigidity of pre-tension DNTs are predicted. Finally, the effects of the encapsulation structure and surrounding factors on the tensile properties of DNTs are studied. The predictions for the tensile behaviors of DNTs can not only reproduce the existing experimental results, but also reveal that the competition of DNA intrachain and interchain interactions in the encapsulation structures determines the pre-tension states of DNTs and their tensile properties. The changes in the pre-tension states and environmental factors make the monotonic or non-monotonic changes in the tensile properties of DNTs under longitudinal loads.

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material (FGM) model with transverse isotropy. The FGMs are approximated with $n$-layered materials. Each of the $n$-layered materials is homogeneous and transversely isotropic. The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions. The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties. The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions. Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness. The wheelset is systematized into a one-dimensional (1D) diffusion process by using the stochastic average method, the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system, and the critical speed of stochastic bifurcation is obtained. The stationary probability density and joint probability density are derived theoretically. Based on the topological structure change of the probability density function, the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined. The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed, and the simulation results verify the correctness of the theoretical analysis. The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system, and the left boundary characteristic value $c_{\rm L}=1$ is the critical state of hunting stability. Besides, stochastic D-bifurcation and P-bifurcation will appear in the wheelset system, and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.

In a magnetohydrodynamic (MHD) driven fluid cell, a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined. The energy dissipation of the flow is controlled by the viscosity and linear friction. The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional (3D) MHD experiment in a square bottomed cell. The basic flow in this fluid system is a square eddy flow exhibiting a network of $N^2$ vortices rotating alternately in clockwise and anticlockwise directions. When $N$ is odd, the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows, exhibiting similar characteristics to those observed when $N=3$. For this reason, this study focuses on the instability of the square eddy flow of nine vortices. It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces. Especially, there exist non-real neutral eigenfunctions, which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner. This Hopf bifurcation phenomenon has not been observed in earlier investigations.

The present study aims to perform computational simulations of two-dimensional (2D) hemodynamics of unsteady blood flow via an inclined overlapping stenosed artery employing the Casson fluid model to discuss the hemorheological properties in the arterial region. A uniform magnetic field is applied to the blood flow in the radial direction as the magneto-hemodynamics effect is considered. The entropy generation is discussed using the second law of thermodynamics. The influence of different shape parameters is explored, which are assumed to have varied shapes (spherical, brick, cylindrical, platelet, and blade). The Crank-Nicolson scheme solves the equations and boundary conditions governing the flow. For a given critical height of the stenosis, the key hemodynamic variables such as velocity, wall shear stress (WSS), temperature, flow rate, and heat transfer coefficient are computed.

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations, and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves. The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail. The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied, and the critical values that can describe the magnitude of the dissipation effect are, respectively, found for the two cases of $b_{3}<0$ and $b_{3}>0$ in the equation. The results show that, when the dissipation effect is significant (i.e., $r$ is greater than the critical value in a certain situation), the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution; when the dissipation effect is small (i.e., $r$ is smaller than the critical value in a certain situation), the traveling wave solution to the equation appears as the oscillation attenuation solution. By using the hypothesis undetermined method, all possible solitary wave solutions to the equation when there is no dissipation effect (i.e., $r=0$) and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained; in particular, when the dissipation effect is small, an approximate solution of the oscillation attenuation solution can be achieved. This paper is further based on the idea of the homogenization principles. By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper, and by investigating the asymptotic behavior of the solution at infinity, the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained, which is an infinitesimal amount that decays exponentially. The influence of the dissipation coefficient on the amplitude, frequency, period, and energy of the bounded traveling wave solution of the equation is also discussed.

Epilepsy is believed to be associated with the abnormal synchronous neuronal activity in the brain, which results from large groups or circuits of neurons. In this paper, we choose to focus on the temporal lobe epilepsy, and establish a cortex network of multiple coupled neural populations to explore the epileptic activities under electromagnetic induction. We demonstrate that the epileptic activities can be controlled and modulated by electromagnetic induction and coupling among regions. In certain regions, these two types of control are observed to show exactly reverse effects. The results show that the strong electromagnetic induction is conducive to eliminating the epileptic seizures. The coupling among regions has a conduction effect that the previous normal background activity of the region gives way to the epileptic discharge, owing to coupling with spike wave discharge regions. Overall, these results highlight the role of electromagnetic induction and coupling among the regions in controlling and modulating epileptic activities, and might provide novel insights into the treatments of epilepsy.