A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup $TF_{n}$ of all
order-preserving transformations on an $n$-element zig-zag ordered set. We determine the rank of $TF_{n}$ and provide a minimal generating set for $TF_{n}$. Moreover, a formula for the number of idempotents in $TF_{n}$ is given.

An optical experimental procedure for evaluating the J-Integral from full-field displacement fields under dynamic loading is proposed in this work. The methodology is applied to measure the J-integral in the dynamic compressive loading of fiber-reinforced composites and to calculate the dynamic fracture toughness associated with the propagation of a kink-band. A modified J-Integral that considers inertia effects is calculated over the full-field measurements obtained by digital image correlation, for double edge-notched specimen of IM7-8552 laminates dynamically loaded in a split-Hopkinson pressure bar (SHPB). A sensibility study is conducted to address the influence of the speckle parameters. The results show good agreement with experimental observations obtained by using a different data reduction method, suggesting the existence of a rising R-curve for the studied material under dynamic loading. Furthermore, it was noticed that the inertia effect can be negligible, indicating a state of dynamic equilibrium in which quasi-static approaches may comfortably be used.

The high strain rate compressive behaviour of Pinus pinaster Ait. wood along the radial and tangential material axes was addressed in this work. Both quasi-static and dynamic tests were considered for comparation purposes. The quasi-static compression tests were performed on rectangular prismatic specimens along the radial and tangential directions coupled with digital image correlation. The high strain rate tests were carried out using a classical split-Hopkinson pressure bar coupled with a high-speed imaging system allowing independent kinematic measurements through digital image correlation. From these tests and material symmetry orientations, the constitutive curves were determined from which the Young modulus, Poisson’s ratio and yield stress were evaluated and compared over the two different regimes over the strain rate spectrum. The mechanical properties observed for this species under quasi-static compression loading agree with reference values. A qualitative comparison between quasi-static and high strain rate regimes reveals a significant increase of some mechanical properties by increasing the strain rate. Quantitatively, by comparing mean values at the two strain rates, it was found that, in the radial direction, the modulus of elasticity increased by 6.3%, the yield stress showed an increase of 130.3% and the Poisson’s ratio is slightly higher by 3.0%. Furthermore, in the tangential direction, it was found that the modulus of elasticity increased by 21.9% while the value of the yield stress showed an increase of 111.8%, and finally the Poisson‘s ratio presented a reduction of 24.3%.

Physics Letters B, 795 (2019) 682–688. 10.1016/j.physletb.2019.06.069

Problem of the reliability increasing of the vehicles electric drives is discussed in context of the reduction of the electric motor heating during variable character of movement. Opportunities of the induction motor stator winding heating reduction by means of the control of the vehicles electric drives in transient and steady state modes of movement are shown. Analytical expressions for dynamic torque, optimal on minimal of the winding temperature rise during acceleration, as well as expressions for dynamic torque and value of the motor torque limitation, optimal on energy consumption during acceleration are presented. It is shown that desire to reduce the stator winding temperature rise by means of dynamic torque optimal value selection or motor torque limitation can lead to the rise of energy consumption. Results of the modeling are presented.

This paper presents a wireless energy transfer system operating at the frequency values of kHz order: modeling, simulation, and comparison with prototype measurement results. Wireless energy transfer system model using finite element method was carried out to simulate the electric field and the magnetic flux density for different air gap sizes between the transmitter and the receiver coils. Results are presented and compared with the electromagnetic emission measurements radiated by the wireless energy transfer system prototype. The electric field comparison between the simulated and the prototype measurement values shows an error of roughly 8.7{%}. In the recent years, the interest in the wireless energy transfer technology, especially for electric vehicles batteries charging, is rapidly increasing. As a result of the increasing application of this technology in the industrial and consumer electronic products, more concerns are raised about the electromagnetic compatibility, since the wireless energy transfer systems produce electromagnetic emissions in the surrounding environment.