Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches

The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

Binary-Like Topology Optimization of Piezoelectric Metamaterial Plate with Interface Circuits Using Extended Plane Wave Expansion Method

Piezoelectric metamaterial plate (PMP) is being investigated for structural vibration energy harvesting (SVEH), in which an interface circuit is often used. Thus, it is a challenge to perform bandgap optimization of such an elastic–electro–mechanical coupling system. This paper presents a binary-like topology optimization scheme by dividing the unit cell into identical pieces, where a {0, 1} matrix is optimized to indicate material distribution. Firstly, a unified motion equation is derived for the elastic plate and the piezoelectric patch, and an electromechanical coupling model is built for a self-powered synchronized charge extraction circuit. Then, an extended plane wave expansion method is presented to model the bandgap character of the PMP with interface circuits (PMPICs), and the numerical solution of the dispersion curves is derived based on the Bloch theorem. Next, an extended genetic algorithm is applied for the topology optimization of the PMPIC. In the end, numerical and finite element simulations are performed to validate the proposed method. The results demonstrate that both the structure and the circuit can be optimized simultaneously to obtain the maximum first-order bandgap at a given central frequency. Therefore, the proposed method should provide an effective solution for the topology optimization of a PMPIC for broadband SVEH.

Kerr metric Killing bundles

We provide a complete characterization of the metric Killing bundles (or metric bundles) of the Kerr geometry. Metric bundles can be generally defined for axially symmetric spacetimes with Killing horizons and, for the case of Kerr geometries, are sets of black holes (BHs) or black holes and naked singularities (NSs) geometries. Each metric of a bundle has an equal limiting photon (orbital) frequency, which defines the bundle and coincides with the frequency of a Killing horizon in the extended plane. In this plane each bundle is represented as a curve tangent to the curve that represents the horizons, which thus emerge as the envelope surfaces of the metric bundles. We show that the horizons frequency can be used to establish a connection between BHs and NSs, providing an alternative representation of such spacetimes in the extended plane and an alternative definition of the BH horizons. We introduce the concept of inner horizon confinement and horizons replicas and study the possibility of detecting their frequencies. We study the bundle characteristic frequencies constraining the inner horizon confinement in the outer region of the plane i.e. the possibility of detect frequency related to the inner horizon, and the horizons replicas, structures which may be detectable for example from the emission spectra of BHs spacetimes. With the replicas we prove the existence of photon orbits with equal orbital frequency of the horizons. It is shown that such observations can be performed close to the rotation axis of the Kerr geometry, depending on the BH spin. We argue that these results could be used to further investigate black holes and their thermodynamic properties.

Obtaining an Initial Solution for Facility Layout Problem

The facility layout approaches can generally be classified into two groups, constructive approaches and improvement approaches. All improvement procedures require an initial solution which has a significant impact on final solution. In this paper, we introduce a new technique for accruing an initial placement of facilities on extended plane. It is obtained by graph theoretic facility layout approaches and graph drawing algorithms. To evaluate the performance, this initial solution is applied to rectangular facility layout problem. The solution is improved using an analytical method. The approach is then tested on five instances from the literature. Test problems include three large size problems of 50, 100, and 125 facilities. The results demonstrate effectiveness of the technique especially for large size problems.

INVESTIGATION OF CHARACTERISTIC CURVE FOR STURM–LIOUVILLE PROBLEM WITH NONLOCAL BOUNDARY CONDITIONS ON TORUS

In this paper, we investigate the second-order Sturm–Liouville problem with two additional Nonlocal Boundary Conditions. Nonlocal boundary conditions depends on two parameters. We find condition for existence of zero eigenvalue in the parameters space and classified Characteristic Curves in the plane and extended plane is described as torus. The Characteristic Curve on torus may be of three types only. Some new conclusions about existence and uniqueness domain of solution are presented.

Localized edge states nucleate turbulence in extended plane Couette cells

We study the turbulence transition of plane Couette flow in large domains where localized perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary between laminar and turbulent dynamics we determine invariant structures intermediate between laminar and turbulent flow. In wide but short domains we find states that are localized in spanwise direction, and in wide and long domains the states are also localized in downstream direction. These localized states act as critical nuclei for the transition to turbulence in spatially extended domains.