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The purpose of this paper is to develop a modeling method for the analysis of low-frequency metamaterials (MTMs) and their near-field applications.

The Euler–Lagrange method is introduced. An MTM is modeled as a multi-degree-of-freedom system without homogenization. The properties and the responses of the MTM in a near-field device are readily and rigorously studied through the motion equation derived from the Lagrange equations. The resonance frequencies and the corresponding resonance modes are solved from the characteristic equation.

The numerical results of the proposed method show good agreement with the experimental ones. A measurement of MTM-core coil resistance and inductance shows high accuracy of the proposed method.

The proposed Euler–Lagrange method provides a new study perspective and enables more flexible, rigorous and straightforward analysis of low-frequency MTMs in near-field applications. Consequently, the presented work greatly facilitates further explorations and studies on various novel MTM-based low-frequency near-field devices and systems.

The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete.

The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well.

Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented.

The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

Aims to realize the high accurate contour control with high‐speed motion of articulated robot manipulator (ARM) with interference.

Proposes a new contour control method by using Gaussian neural network (GNN) to solve the problem of the deterioration of the contour control performance due to the interference between robot links. The construction of the GNN controller and the approximation of the interference are based on the Euler‐Lagrange model of ARM. The actual input/out data about the motion of ARM are used for training the GNN to accurately represent the inverse dynamics of ARM with interference. With the Lyapunov function, the stability and the robustness of the GNN controller are discussed. Through the simulation and experiment, it verified that the precision of the contour control has been improved, and illustrated the good features of the proposed method.

Finds that the actual data about the motion of ARM, which is easily obtained from the working field, can express the real features of ARM, and the GNN controller can improve the precision of the contour control with good features.

The proposed method provides an effective method for realizing high accurate contour control of ARM with interference. It can be extended to the ARMs with more than two links and concerning more factors affecting the precision of the contour control, such as friction or gravity.

Proposes a new GNN controller for realizing high accurate contour control of ARM with interference, which is significant for industry.

Nanofluids’ properties made them interesting for various areas like engineering, medicine or cosmetology. Discussed here, research pertains to specific problem of heat transfer enhancement with application of the magnetic field. The main idea was to transfer high heat rates with utilization of nanofluids including metallic non-ferrous particles. The expectation was based on changed nanofluid properties. However, the results of experimental analysis did not meet it. The heat transfer effect was smaller than in the case of base fluid. The only way to understand the process was to involve the computational fluid dynamics, which could help to clarify this issue. The purpose of this research is deep understanding of the external magnetic field effect on the nanofluids heat transfer.

In presented experimental and numerical studies, the water and silver nanofluids were considered. From the numerical point of view, three approaches to model the nanofluid in the strong magnetic field were used: single-phase Euler, Euler–Euler and Euler–Lagrange. In two-phase approach, the momentum transfer equations for individual phases were coupled through the interphase momentum transfer term expressing the volume force exerted by one phase on the second one.

Therefore, the results of numerical simulation predicted decrease of convection heat transfer for nanofluid with respect to pure water, which agreed with the experimental results. The experimental and numerical results are in good agreement with each other, which confirms the right choice of two-phase approach in analysis of nanofluid thermo-magnetic convection.

The Euler–Lagrange exhibit the best matching with the experimental results.

The purpose of this paper is to establish analytical and numerical solutions of a navigational law to estimate displacements of hyper-static multi-legged mobile robots, which combines: monocular vision (optical flow of regional invariants) and legs dynamics.

In this study the authors propose a Euler-Lagrange equation that control legs’ joints to control robot's displacements. Robot's rotation and translational velocities are feedback by motion features of visual invariant descriptors. A general analytical solution of a derivative navigation law is proposed for hyper-static robots. The feedback is formulated with the local speed rate obtained from optical flow of visual regional invariants. The proposed formulation includes a data association algorithm aimed to correlate visual invariant descriptors detected in sequential images through monocular vision. The navigation law is constrained by a set of three kinematic equilibrium conditions for navigational scenarios: constant acceleration, constant velocity, and instantaneous acceleration.

The proposed data association method concerns local motions of multiple invariants (enhanced MSER) by minimizing the norm of multidimensional optical flow feature vectors. Kinematic measurements are used as observable arguments in the general dynamic control equation; while the legs joints dynamics model is used to formulate the controllable arguments.

The given analysis does not combine sensor data of any kind, but only monocular passive vision. The approach automatically detects environmental invariant descriptors with an enhanced version of the MSER method. Only optical flow vectors and robot's multi-leg dynamics are used to formulate descriptive rotational and translational motions for self-positioning.

The variational principle views a complex problem in an energy way, it gives good physical understanding of an iteration method, and the variational-based numerical methods always have a conservation scheme with a fast convergent rate. The purpose of this paper is to establish a variational principle for a fractal nano/microelectromechanical (N/MEMS) system.

This paper begins with an approximate variational principle in literature for the studied problem, and a genuine variational principle is obtained by the semi-inverse method.

The semi-inverse method is a good mathematical tool to the search for a genuine fractal variational formulation for the N/MEMS system.

The established variational principle can be used for both analytical and numerical analyses of the N/MEMS systems, and it can be extended to some more complex cases.

The variational principle can be used for variational-based finite element methods and energy-based analytical methods.

The new and genuine variational principle is obtained. This paper discovers the missing piece of the puzzle for the establishment of a variational principle from governing equations for a complex problem by the semi-inverse method. The new variational theory opens a new direction in fractal MEMS systems.

Detonation of landmines buried to different depths in water‐saturated sand is analyzed computationally using transient non‐linear dynamics simulations in order to quantify impulse loading. The computational results are compared with the corresponding experimental results obtained using the Vertical Impulse Measurement Fixture (VIMF), a structural mechanical device that enables direct experimental determination of the blast‐loading impulse. The structural‐dynamic/ballistic response of the Rolled Homogenized Armor (RHA) used in the construction of the VIMF witness plate and the remainder of the VIMF and the hydrodynamic response of the TNT high‐energy explosive of a mine and of the air surrounding the VIMF are represented using the standard materials models available in literature. The structural‐dynamic/ballistic response of the sand surrounding the mine, on the other hand, is represented using our recent modified compaction model which incorporates the effects of degree of saturation and the rate of deformation, two important effects which are generally neglected in standard material models for sand. The results obtained indicate that the use of the modified compaction model yields a substantially better agreement with the experimentally‐determined impulse loads over the use the original compaction model. Furthermore, the results suggest that, in the case of fully saturated sand, the blast loading is of a bubble type rather than of a shock type, i.e. the detonation‐induced momentum transfer to the witness plate is accomplished primarily through the interaction of the sand‐over‐burden (propelled by the high‐pressure expanding gaseous detonation by‐products) with the witness plate.

Barge-type offshore floating wind turbine (OFWT) commonly exhibits an under-actuated phenomenon in an offshore environment, which leads to a potential vibration-damping hazard. This article aims to provide a new robust output feedback anti-vibrational control scheme for the novel translational oscillator with rotational actuator (TORA) based five-degrees of freedom (5-DOF) barge-type OFWT in the presence of unwanted disturbances and modeling uncertainties.

In this paper, an active control technique called TORA has been used to design a 5-DOF barge-type OFWT model, where the mathematical model of the proposed system is derived by using Euler–Lagrange's equations. The robust hierarchical backstepping integral nonsingular terminal sliding mode control (HBINTSMC) with an adaptive gain is used in conjunction with extended order high gain observer (EHGO) to achieve system stabilization in the presence of unwanted disturbances and modeling uncertainties. The numerical simulations based on MATLAB/SIMULINK have been performed to demonstrate the feasibility and effectiveness of the proposed model and control law.

The numerical simulation results affirm the accuracy and efficiency of the proposed control law for the TORA based OFWT system. The results demonstrate that the proposed control law is robust against unwanted disturbances and uncertainties. The unknown states are accurately estimated by EHGO which enables the controller to exhibit improved stabilization performance.

A new mathematical model of the 5-DOF barge-type OFWT system based on TORA is the major contribution of this research paper. Furthermore, it provides a new adaptive anti-vibration control scheme by incorporating the EHGO for the proposed model.

The purpose of this study is to investigate the effect of the injection angle α on the spray structures of an air-blast atomizer and help enhance the understanding of droplet-gas mixing process in such atomizers in the engineering domain.

The phenomena in the air-blast atomizer were numerically modelled using the computational fluid dynamics software Fluent 17.2. The Euler-Lagrange approach was applied to model the droplet tracking and droplet-gas interaction in studied cases. The standard k-ε model was used to simulate the turbulent flow. A model with a modified drag coefficient was used to consider the effects of the bending of the liquid column and its penetration in the primary breakup region. The Kelvin-Helmholtz, Rayleigh-Taylor model was applied to consider the secondary breakup of the droplets.

The basic spatial distribution and spray structures of the droplets corresponding to the angled liquid jet (α = 60°) were similar to those reported in liquid jets injected transversely into a gaseous crossflow studies. The injection angle α did not considerably influence the averaged Sauter to mean diameter (SMD) of the cross-sections. However, the spray structures pertaining to α = 30°, α = 60° and α = 90° were considerably different. In the case of the atomizer with multiple injections, a “collision region” was observed at α = 60° and characterized by a higher ci and larger averaged SMD in the central parts of the cross-sections.

The injection angle α is a key design parameter for air-blast atomizers. The findings of this study can help enhance the understanding of the droplet-gas mixing process in air-blast atomizers. Engineers who design air-blast atomizers and face new challenges in the process can refer to the presented findings to obtain the desired atomization performance. The code has been validated and can be used in the engineering design process of the gas-liquid jet atomizer.