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In this article, using a (γ ,a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extending several discrete inequalities and their corresponding continuous analogues. We say that symmetry plays an essential role in determining the correct methods with which to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

This article explores the application of the reduced differential transform method (RDTM) for the computational solutions of two fractional-order cancer tumor models in the Caputo sense: the model based on cancer chemotherapeutic effects which explain the relation between chemotherapeutic drugs, tumor cells, normal cells, and immune cells using a fractional partial differential equations, and the model that describes the different cases of killing rate K of cancer cells (the killing percentage of cancer cells K (I) is dependent on the number of cells, (II) is a function of time only, and (III) is a function of space only). The solutions are presented using Mathematica software as a convergent power series with elegantly computed terms using the suggested technique. The proposed method gives new series form results for various values of gamma. To clarify the complexity of the models, we plot the two- and three-dimensional and contour graphics of the obtained solutions at varied values of fractional-order gamma and the selected system parameters. The solutions are analyzed with fractional and reduced differential transform methods to obtain an idea of invariance regarding the computed solution of the designed mathematical model. The obtained results demonstrate the efficiency and preciseness of the proposed method to achieve a better understanding of chemotherapy effects. It is observed that chemotherapy drugs boost immunity against the specific cancer by decreasing the number of tumor cells, and the killing rate K of cancerous cells depend on the cells concentration. [ABSTRACT FROM AUTHOR]

This article is focused on investigating the convective magneto-hydrodynamic single-phase flow for comparative analysis of two different base fluids above an exponentially stretchable porous surface under the effect of the chemical reaction. The Buongiorno fluid model is incorporated to observe the Thermophoresis and Brownian diffusion in this study. Boussinesq approximation for temperature and concentration are accounted for flow to be naturally convective. In this study, water and ethanol are assumed for comparative analysis. Additionally, to achieve the outcomes of the designed three-dimensional flow boundary value, problem technique is employed to simulate the problem in MATLAB. Increase in the magnetic field, thermophoresis diffusion, temperature exponent, and Prandtl number expand thermal boundary, whereas contraction is observed with an increase in porosity. Shear stress rates in respective directions have decreased with an increase in the stretching ratio of the surface. Moreover, through comparison, reasonably enhanced Nusselt number is observed for water under influence of study parameters while the Nusselt number abruptly decreases for ethanol. High mass coefficients are observed for both examined fluids. [ABSTRACT FROM AUTHOR]

Within this work, the radial Proportional Derivative (PD-) controller along with the eight-poles electro-magnetic actuator are introduced as a novel control strategy to suppress the lateral oscillations of a non-linear Jeffcott-rotor system. The proposed control strategy has been designed such that each pole of the magnetic actuator generates an attractive magnetic force proportional to the radial displacement and radial velocity of the rotating shaft in the direction of that pole. According to the proposed control mechanism, the mathematical model that governs the non-linear interactions between the Jeffcott system and the magnetic actuator has been established. Then, an analytical solution for the obtained non-linear dynamic model has been derived using perturbation analysis. Based on the extracted analytical solution, the motion bifurcation of the Jeffcott system has been investigated before and after control via plotting the different response curves. The obtained results illustrate that the uncontrolled Jeffcott-rotor behaves like a hard-spring duffing oscillator and responds with bi-stable periodic oscillation when the rotor angular speed is higher than the system's natural frequency. It is alsomfound that the system, before control, can exhibit stable symmetric motion with high vibration amplitudes in both the horizontal and vertical directions, regardless of the eccentricity magnitude. In addition, the acquired results demonstrate that the introduced control technique can eliminate catastrophic bifurcation behaviors and undesired vibration of the system when the control parameters are designed properly. However, it is reported that the improper design of the controller gains may destabilize the Jeffcott system and force it to perform either chaotic or quasi-periodic motions depending on the magnitudes of both the shaft eccentricity and the control parameters. Finally, to validate the accuracy of the obtained results, numerical simulations for all response curves have been introduced which have been in excellent agreement with the analytical investigations. [ABSTRACT FROM AUTHOR]

This paper presents a novel model-based structural optimization approach for the efficient electromechanical development of hexapod robots. First, a hexapod-design-related analysis of both optimization objectives and relevant parameters is conducted based on the derived dynamical model of the robot. A multi-objective optimization goal is proposed, which minimizes energy consumption, unwanted body motion and differences between joint torques. Then, an optimization framework is established, which utilizes a sophisticated strategy to handle the optimization problems characterized by a large set of parameters. As a result, a satisfactory result is efficiently obtained with fewer iterations. The research determines the optimal parameter set for hexapod robots, contributing to significant increases in a robot's walking range, suppressed robot body vibrations, and both balanced and appropriate motor loads. The modular design of the proposed simulation model also offers flexibility, allowing for the optimization of other electromechanical properties of hexapod robots. The presented research focuses on the mechatronic design of the Szabad(ka)-III hexapod robot and is based on the previously validated Szabad(ka)-II hexapod robot model. [ABSTRACT FROM AUTHOR]

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) and a servo-controlled linear actuator (SCLA), were applied to suppress the undesired oscillations of the harmonically-excited car. 2D and 3D graphical plots are included based upon the equations resulting from the harmonic balance method. Moreover, a numerical simulation was established using the fourth order Rung–Kutta technique in order to confirm the overall controlled behavior of the studied model. [ABSTRACT FROM AUTHOR]

In recent times, the loss of useful energy and solutions to those energy challenges have a wide scope in different areas of engineering. This work focuses on entropy analysis for unsteady viscoelastic fluids. The momentum boundary layer and thermal boundary layer are described under the effects of a magnetic field in the absence of an induced magnetic field. The study of a fractional model of Maxwell nanofluid by partial differential equation using Caputo time differential operator can well address the memory effect. Using transformations, the fractional ordered partial differential equations (PDEs) are transfigured into dimensionless PDEs. Numerical results for fractional Maxwell nanofluids flow and heat transfer are driven graphically. The Bejan number is obtained following the suggested transformation of dimensionless quantities like entropy generation. A mathematical model of entropy generation, Bejan number, Nusselt number and skin friction are developed for nanofluids. Effects of different physical parameters like Brickman number, Prandtl number, Grashof number and Hartmann number are illustrated graphically by MAPLE. Results depict that the addition of nanoparticles in base-fluid controls the entropy generation that enhances the thermal conductivity and application of magnetic field has strong effects on the heat transfer of fractional Maxwell fluids. An increasing behavior in entropy generation is noticed in the presence of source term and thermal radiation parameter. [ABSTRACT FROM AUTHOR]

The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This phenomenon is investigated in this contribution using a model of a 2D FitzHugh–Nagumo neuron coupled with a 3D Hindmarsh–Rose neuron through a multistable memristive synapse. The investigation of the equilibria revealed that the coupled neuron model is equilibrium free and, thus, displays a hidden dynamics. Some traditional nonlinear analysis tools are used to demonstrate that the heterogeneous neuron system is able to exhibit the coexistence of an infinite number of electrical activities involving both periodic and chaotic patterns. Of particular interest, a noninvasive control method is applied to suppress all the periodic coexisting activities, while preserving only the desired chaotic one. Finally, an electronic circuit of the coupled neurons is designed in the PSpice environment and used to further support some results of the theoretical investigations. [ABSTRACT FROM AUTHOR]

Nonhomogeneous systems governed by second-order linear differential equations with pure delay are considered. As an application, the exact solutions of these systems and their delayed matrix functions are used to obtain the finite-time stability results. Our results extend and improve some previous results by removing some restrictive conditions. Finally, an example is provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Within this work, an advanced control algorithm was proposed to eliminate the non-linear vibrations of the rotor electro-magnetic suspension system. The suggested control algorithm is known as the Adaptive Linear Integral Positive Position Feedback controller (ALIPPF-controller). The ALIPPF-controller is a combination of first-order and second-order filters that are coupled linearly to the targeted non-linear system in order to absorb the excessive vibratory energy. According to the introduced control strategy, the dynamical model of the controlled rotor system was established as six non-linear differential equations that are coupled linearly. The obtained dynamical model was investigated analytically applying the asymptotic analysis, where the slow-flow equations were extracted. Based on the derived slow-flow equations, the bifurcation behaviors of the controlled system were explored by plotting the different bifurcation diagrams. In addition, the performance of the ALIPPF-controller in eliminating the rotor lateral vibrations was compared with the conventional Positive Position Feedback (PPF) controller. The acquired results illustrated that the ALIPPF-controller is the best control technique that can eliminate the considered system's lateral vibrations regardless of the angular speed and eccentricity of the rotating shaft. Finally, to demonstrate the accuracy of the obtained analytical results, numerical validation was performed for all obtained bifurcation diagrams that were in excellent agreement with the analytical solutions. [ABSTRACT FROM AUTHOR]

This article investigates heat and mass transport enrichment in natural convection fractionalized nanofluid flow inside a channel with isothermal and ramped wall conditions under the effects of chemical reactions, radiation, heat absorption, and the Soret effect. To obtain the fractional model, the Caputo time-fractional derivative definition is used, and analytical results are obtained by the Laplace transform. In two base fluids, water and glycerin, the impacts of two nanoparticles, single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs), are investigated. The comparison of six distinct fluids, including water, water–SWCNT, water–MWCNT, glycerin, glycerin–SWCNT and glycerin–WMCNT, is explored graphically. Physical parameters' effects on isothermal and ramped conditions are graphically depicted and explained in depth. For isothermal wall conditions, the variation in concentration, temperature and velocity is exponential, while for ramped wall conditions, the variation is steady. Finally, the results of skin frictions, Nusselt numbers and Sherwood numbers and for both ramped wall and isothermal wall conditions are evaluated in tabular form for various values of volume fraction. Moreover, it is observed that the temperature, velocity, Nusselt numbers and skin frictions increase by increasing the volume fraction of CNTs. [ABSTRACT FROM AUTHOR]

The present work discusses the dynamical analysis of the superharmonic resonance in a mass-damper-spring model controlled by a cubic-position negative-velocity feedback (CPNV) controller. Thanks to the harmonic balance technique, the approximate solution of the studied model can be extracted and then checked for stability using Floquet exponents. The cubic-position control gain is adjusted in order to suppress the model's steady oscillations. In addition, the negative-velocity control gain is adjusted in order to shrink the period of the transient oscillations. Several plots are included to relate the car's oscillatory amplitude with the model's different parameters pre- and post-control so that we can determine the optimum conditions for running the model safely. [ABSTRACT FROM AUTHOR]

In this study, an adaptive nonsingular terminal sliding mode control technique according to the barrier function is designed for the performance improvement and robust stability of nonlinear systems with outdoor disturbances. For this reason, a novel nonlinear sliding surface is presented based on the states of the system. The nonlinear sliding surface forces the states of the system to converge from initial conditions to zero. Subsequently, a non-singular terminal sliding control scheme is advised for the purpose of finite-time stability of the nonlinear switching surface. Finite-time stabilization of the non-singular terminal sliding surface is verified by the Lyapunov theory. For improvement of the system performance against exterior perturbation, the barrier function adaptive technique is employed to estimate the unknown upper bounds of the exterior disturbance. Finally, the advantage and productivity of the recommended control method is investigated based on the simulation results. In the simulation part, the plasma torch jerk chaotic system is considered as a case study, such that the obtained results are given in different scenarios. [ABSTRACT FROM AUTHOR]

A cubic-position negative-velocity (CPNV) feedback controller is proposed in this research in order to suppress the nontrivial oscillations of the 1 / 3 order subharmonic resonance of a mass-damper-spring model. Based on the Krylov–Bogoliubov (KB) averaging method, the model's equation of motion is approximately solved and tested for stability. The nontrivial solutions region is plotted to determine where these solutions occur and try to quench them. The controller parameters can play crucial roles in eliminating such regions, keeping only the trivial solutions, and improving the transient response of the car's oscillations. Different response curves and relations are included in this study to provide the reader a wide overview of the control process. [ABSTRACT FROM AUTHOR]

In this recent work, the continuous dependence of double diffusive convection was studied theoretically in a porous medium of the Forchheimer model along with a variable viscosity. The analysis depicts that the density of saturating fluid under consideration shows a linear relationship with its concentration and a cubic dependence on the temperature. In this model, the equations for convection fluid motion were examined when viscosity changed with temperature linearly. This problem allowed the possibility of resonance between internal layers in thermal convection. Furthermore, we investigated the continuous dependence of this solution based on the changes in viscosity. Throughout the paper, we found an "a priori estimate" with coefficients that relied only on initial values, boundary data, and the geometry of the problem that demonstrated the continuous dependence of the solution on changes in the viscosity, which also helped us to state the relationship between the continuous dependence of the solution and the changes in viscosity. Moreover, we deduced a convergence result based on the Forchheimer model at the stage when the variable viscosity trends toward a constant value by assuming a couple of solutions to the boundary-initial-value problems and defining a difference solution of variables that satisfy a given boundary-initial-value problem. [ABSTRACT FROM AUTHOR]

This research focuses on the nonlinear vibration control of a self-excited single-degree-of-freedom system. The integral resonant controller (IRC) is introduced to stabilize the unstable motion and suppress nonlinear oscillations of the considered system. The nonlinear dynamical equations that govern the vibratory behaviors of the proposed closed-loop control system are investigated using perturbation analysis, where loop delays have been included in the studied model. The system bifurcation behaviors have been visualized in both the two and three-dimensional spaces, and corresponding dynamical behaviors have been explored numerically using the bifurcation diagrams, Poincaré map, time-response, zero-one chaotic test algorithm, and frequency spectrum. The obtained analytical investigations revealed that the uncontrolled system can oscillate with one of four vibration modes depending on the excitation frequency, which are mono-stable periodic motion, bi-stable periodic motion, periodic and quasi-period motion, and quasi-periodic motion only. In addition, it is found that the existence of time delays in the control loop can either improve or degrade the control performance. Therefore, an objective function has been introduced to design the optimum control parameters. Based on the derived objective function, it is found that the performance of the proposed control strategy is proportional to the product of the control and feedback gains and inversely proportional to the internal loop feedback gain when the loop delays are neglected. Moreover, it is reported that the controller performance is a periodic function of the total sum of the loop delays. Accordingly, the optimal operating conditions of the time-delayed integral resonant controller have been explained. Finally, numerical validations for all obtained analytical results have been performed, where an excellent correspondence between the analytical and numerical investigations has been demonstrated. [ABSTRACT FROM AUTHOR]

The main purpose of this research was to use the comparison approach with a first-order equation to derive criteria for non-oscillatory solutions of fourth-order nonlinear neutral differential equations with p Laplacian operators. We obtained new results for the behavior of solutions to these equations, and we showed their symmetric and non-oscillatory characteristics. These results complement some previously published articles. To find out the effectiveness of these results and validate the proposed work, two examples were discussed at the end of the paper. [ABSTRACT FROM AUTHOR]

The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient F = 0 and the case of the Taylor-Darcy number τ = 0 . For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories. [ABSTRACT FROM AUTHOR]

In this paper, we have shown an electronic circuit equivalence of a mechanical system consisting of two oscillators coupled with each other. The mechanical design has the effects of the magnetic spring force resistance force, and the spring constant of the system is periodically varying. We have shown that the system's state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractors to the chaotic attractors through the periodic and quasi-periodic oscillations. We have verified those numerically obtained phenomena using the analog electronic circuit of this mechanical system. [ABSTRACT FROM AUTHOR]

In this article, a simple prototype and control system of a lower limb exoskeleton driven by stepper motors was proposed. To study kinematic parameters of the device, a general, three-dimensional simulation model of the exoskeleton was developed. Moreover, a gait pattern was modeled for hip, knee, and ankle joints. It represents sagittal plane angular positions of joints during normal gait and consists of three piecewise-defined sine-square-based functions. It is based on the experimental gait data recorded with an optoelectronic motion capture system for a healthy subject walking on a treadmill. Although the developed pattern is intended to be implemented in a control system of a lower limb exoskeleton for gait rehabilitation, it can be used to control bipedal robots as well. Last but not least, the control approach was tested with the exoskeleton prototype. [ABSTRACT FROM AUTHOR]

This article contains theoretical analysis and experimental study of the original mechatronics system with flexible characteristics which we can adapt to changing needs and external interference. The main purpose of our research is to find a solution that allows tailoring the desired characteristics of systems regardless of changing conditions without their mechanical interference. The system consists of the guide endowed with mass suspended in the air by the linear aerostatic bearing. Linear mechanical spring is attached to the one side of the guide whereas the neodymium magnet is fixed to the other side. Magnet-magnet and magnet-coil interactions have been investigated. The magnet-magnet interaction plays the role of the nonlinear magnetic spring while the magnet-coil interaction plays the role of the electromagnetic spring or electromagnetic damper in terms of the coil current signal. Static and dynamic characteristics of mechanical, magnetic and electromagnetic springs have been analyzed. A new physical model of the magnet-magnet interaction has been presented, the validity of which is confirmed experimentally. In addition, modern IT (information technology) techniques have been used to control the system behavior. The reliable results of the entire system and its springs are obtained by conducting tests on specially constructed laboratory setup. The main benefit of the fabricated setup concerns an elimination of dry friction effects though the frictions is viscous with identifiable movement resistance. [ABSTRACT FROM AUTHOR]

In this article, the impact of Newtonian heating in addition to slip effects was critically examined on the unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid near an infinitely vertical plate. The functional effects such as the retardation and relaxation of materials can be estimated for magnetized permeability based on the relative decrease or increase during magnetization. From this perspective, a new mathematical model was formulated based on non-slippage and slippage postulates for the Oldroyd-B fluid with magnetized permeability. The heat transfer induction was also examined through a non-fractional developed mathematical model for the Oldroyd-B fluid. The exact solution expressions for non-dimensional equations of velocity and temperature were explored by employing Laplace integral transformation under slipping boundary conditions under Newtonian heating. The heat transfer rate was estimated through physical interpretation by considering the limits on the solutions induced by the Nusselt number. To comprehensively discuss the dynamics of the considered problem, the physical impacts of different parameters were studied and reverberations were graphically highlighted and deliberated. Furthermore, in order to validate the results, two limiting models, namely the Maxwell model and the second grade model, were used to compare the relevant flow characteristics. Additionally, in order to perform the parametric analysis, the graphical representation was portrayed for non-slipping and slipping solutions for velocity and temperature. [ABSTRACT FROM AUTHOR]

The active magnetic bearings system plays a vital role in high-speed rotors technology, where many research articles have discussed the nonlinear dynamics of different categories of this system such as the four-pole, six-pole, eight-pole, and sixteen-pole systems. Although the twelve-pole system has many advantages over the eight-pole one (such as a negligible cross-coupling effect, low power consumption, better suspension behaviors, and high dynamic stiffness), the twelve-pole system oscillatory behaviors have not been studied before. Therefore, this article is assigned to explore the effect of the magneto-electro-mechanical nonlinearities on the oscillatory motion of the twelve-pole system controlled via a proportional derivative controller for the first time. The normalized equations of motion that govern the system vibrations are established by means of classical mechanics. Then, the averaging equations are extracted utilizing the asymptotic analysis. The influence of all system parameters on the steady-state oscillation amplitudes is explored. Stability charts in a two-dimensional space are constructed. The stable margin of both the system and control parameters is determined. The obtained investigations reveal that proportional gain plays a dominant role in reshaping the dynamics and motion bifurcation of the twelve-pole systems. In addition, it is found that stability charts of the system can be controlled by simply utilizing both the proportional and derivative gains. Moreover, the numerical simulations showed that the twelve-poles system can exhibit both quasiperiodic and chaotic oscillations besides the periodic motion depending on the control parameters' magnitude. [ABSTRACT FROM AUTHOR]

Energy harvesting is becoming more and more essential in the mechanical vibration application of many devices. Appropriate devices can convert the vibrations into electrical energy, which can be used as a power supply instead of ordinary ones. This study investigated a dynamical system that correlates with two devices, namely a piezoelectric device and an electromagnetic one, to produce two novel models. These devices are connected to a nonlinear damping spring pendulum with two degrees of freedom. The damping spring pendulum is supported by a point moving in a circular orbit. Lagrange's equations of the second kind were utilized to obtain the equations of motion. The asymptotic solutions of these equations were acquired up to the third approximation using the approach of multiple scales. The comparison between the approximate and the numerical solutions reveals high consistency between them. The steady-state solutions were investigated, and their stabilities were checked. The influences of excitation amplitudes, damping coefficients, and the different frequencies on energy-harvesting device outputs are examined and discussed. Finally, the nonlinear stability analysis of the modulation equations is discussed through the stability and instability ranges of the frequency response curves. The work is significant due to its real-life applications, such as a power supply of sensors, charging electronic devices, and medical applications. [ABSTRACT FROM AUTHOR]

It is well established fact that the functional effects, such as relaxation and retardation of materials, can be measured for magnetized permeability based on relative increase or decrease during magnetization. In this context, a mathematical model is formulated based on slippage and nonslippage assumptions for Oldroyd-B fluid with magnetized permeability. An innovative definition of Caputo-Fabrizio time fractional derivative is implemented to hypothesize the constitutive energy and momentum equations. The exact solutions of presented problem, are determined by using mathematical techniques, namely Laplace transform with slipping boundary conditions have been invoked to tackle governing equations of velocity and temperature. The Nusselt number and limiting solutions have also been persuaded to estimate the heat emission rate through physical interpretation. In order to provide the validation of the problem, the absence of retardation time parameter led the investigated solutions with good agreement in literature. Additionally, comprehensively scrutinize the dynamics of the considered problem with parametric analysis is accomplished, the graphical illustration is depicted for slipping and non-slipping solutions for temperature and velocity. A comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently. [ABSTRACT FROM AUTHOR]

This article aims to explore the oscillatory characteristics of a controlled asymmetric rotor system when subjected to rub and impact forces between the rotor and stator. Four electromagnetic poles are used to control the whirling motion of the rotor system through a linear proportional-derivative control law. The equations of motion that govern the whole system dynamics are derived including the rub and impact forces. The derived mathematical model is analyzed in two basic steps. Firstly, the obtained model is treated as a weakly nonlinear system using perturbation analysis to obtain the slow-flow modulating equations when neglecting the rub and impact forces. Depending on the obtained slow-flow equations, different response curves are plotted to explore the system's periodic vibrations and determine the conditions at which the system can exhibit rub and impact force. Secondly, the whole system model including the rub and impact forces is investigated by using the bifurcation diagrams, Poincare map, frequency spectrums, and temporal oscillations. The obtained results revealed that the applied control law could mitigate the system whirling oscillations and prevent the rub and impact forces if the control gains are tuned properly. However, the system can perform period-n, quasiperiodic, or chaotic motion depending on the shaft spinning speed if the controller fails to eliminate the contact between the rotor and stator. [ABSTRACT FROM AUTHOR]

This is an introductory paper of the Focus Issue Recent advances in modeling complex systems: Theory and applications, where papers presenting new advances and insights into chaotic dynamics, fractional dynamics, complex oscillations, complex traffic dynamics, and complex networks, as well as their applications, are collected. All these different problems share common ideas and methods and provide new perspectives for further progress in the modeling of complex systems. [ABSTRACT FROM AUTHOR]

Guided waves have immense potential for structural health monitoring applications in numerous industries including aerospace. It is necessary to evaluate guided wave dispersion characteristics, i.e., group velocity and phase velocity profiles, for using them effectively. For complex structures, the profiles can have highly irregular shapes. In this work, a direct method for calculating the group velocity profiles for complex, composite, and periodic structures using a wave and finite element scheme is presented. The group velocity calculation technique is easy to implement, highly computationally efficient, and works with the standard finite element formulation. The major contribution is summarised in the form of a comprehensive algorithm for calculating the group velocity profiles. The method is compared with the existing analytical and numerical methods for calculation of dispersion curves. Finally, an experimental study in a multilayered composite plate is conducted and the results are found to be in good agreement. The technique is suitable to be used in all guided wave application areas such as material characterisation, non-destructive testing, and structural health monitoring. [ABSTRACT FROM AUTHOR]

This paper focuses primarily on the mean square consensus problem of a class of nonlinear multi-agent systems suffering from stochastic impulsive deception attacks. The attacks here are modeled by completely stochastic destabilizing impulses, where their gains and instants satisfy all distributions and the Markovian process. Compared with existing methods, which assume that only gains are stochastic, it is difficult to deal with systems with different types of random variables. Thus, estimating the influence of these different types on the consensus problem is a key point of this paper. Based on the properties of stochastic processes, some sufficient conditions to solve the consensus problem are derived and some special cases are considered. Finally, a numerical example is given to illustrate the main results. Our results show that the consensus can be obtained if impulsive attacks do not occur too frequently, and it can promote system stability if the gains are below the defined threshold. [ABSTRACT FROM AUTHOR]