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This study is focused on the application of 3D-printed elements and conventional elements to create a prototype of a custom-made exoskeleton for lower limb rehabilitation. The 3D-printed elements were produced by using Fused Deposition Modeling technology and acrylonitrile butadiene styrene (ABS) material. The scope of this work involved the design and construction of an exoskeleton, experimental testing of the ABS material and numerical research by using the finite element method. On the basis of the obtained results, it was possible to deduce whether the load-bearing 3D-printed elements can be used in the proposed mechanical construction. The work contains full data of the material models used in FEM modeling, taking into account the orthotropic properties of the ABS material. Various types of finite elements were used in the presented FE models. The work is a comprehensive combination of material testing issues with the possibility of implementing the obtained results in numerical strength models of machine parts. [ABSTRACT FROM AUTHOR]

On the basis of the analysis of thermoelastic motion, the current research develops a novel model of modified thermoelasticity. The rotating long hollow cylinders with fixed surfaces are considered in a generalized Moore–Gibson–Thompson thermoelastic model (MGTTE) framework, including the modified Ohm's law. The cylinders are made of a thermoelastic material that rotates at a uniform rotational speed and is elastic in the transverse direction. The set of equations for the MGT heat conduction in the new model is built under the influence of the electromagnetic field by including a delay time in the context of Green–Naghdi of the third kind (GN-III). The inner boundary of the hollow cylinder is not only restricted but also sensitive to heat loading. The outer surface, on the other hand, is also restricted but insulates the heat. The Laplace transform method is utilized to deal with the differential equations produced in the new domain and transfer the problem to the space domain. The Dubner and Abate method is used to compute dynamically and graphically depict the theoretical findings for an isotropic transverse material. After comparing the results of several thermoelastic theories, the implications for the electromagnetic field are discussed. [ABSTRACT FROM AUTHOR]

We established some new α -conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of α -conformable Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy's inequality for several functions of α -conformable calculus. Our results are proved by using two-dimensional dynamic Jensen's inequality and Fubini's theorem on time scales. When α = 1 , then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we derived Hardy's inequality for T = R , T = Z and T = h Z . Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

10.3390/app12052333 23 Hong J., Jiang L., Wang Y., Su Z., Ma Y. Nonlinear Dynamics of an Elastic Stop System and Its Application in a Rotor System. Nonlinear phenomena occur in engineering structures, biological systems, social processes, and in economics. Particle weight adjustment can ensure the stability, tracking efficiency, and continuity of the particle filter control process. Xu et al. [[8]] develop a particle filter design scheme for a robust nonlinear control system of an uncertain heat exchange process against noise and communication delay. [Extracted from the article]

The main purpose of this research is to propose a new methodology to observe a class of time-fractional generalized fifth-order Korteweg–de Vries equations. Laplace transform along with a homotopy perturbation algorithm is utilized for the solution and analysis purpose in the current study. This extended technique provides improved and convergent series solutions through symbolic computation. The proposed methodology is applied to time-fractional Sawada–Kotera, Ito, Lax's, and Kaup–Kupershmidt models, which are induced from a generalized fifth-order KdV equation. For validity purposes, obtained and existing results at integral orders are compared. Convergence analysis was also performed by computing solutions and errors at different values in a fractional domain. Dynamic behavior of the fractional parameter is also studied graphically. Simulations affirm the dominance of the proposed algorithm in terms of accuracy and fewer computations as compared to other available schemes for fractional KdVs. Hence, the projected algorithm can be utilized for more advanced fractional models in physics and engineering. [ABSTRACT FROM AUTHOR]

In the present article, we prove some new generalizations of dynamic inequalities of Hardy-type by utilizing diamond- α dynamic integrals on time scales. Furthermore, new generalizations of dynamic inequalities of Hardy-type in two variables on time scales are proved. Moreover, we present Hardy inequalities for several functions by using the diamond- α dynamic integrals on time scales. The results are proved by using the dynamic Jensen inequality and the Fubini theorem on time scales. Our main results extend existing results of the integral and discrete Hardy-type inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this article, we introduce bipolar neutrosophic (BN) aggregation operators (AOs) as a revolutionary notion in aggregation operators (AOs) by applying Einstein operations to bipolar neutrosophic aggregation operators (AOs), with its application related to a real-life problem. The neutrosophic set is able to drawout the incomplete, inconsistent and indeterminate information pretty efficiently. Initially, we present essential definitions along with operations correlated to the neutrosophic set (NS) and its generalization, the bipolar neutrosophic set (BNS). The Einstein aggregation operators are our primary targets, such asthe BN Einstein weighted average (BNEWA), BN Einstein ordered weighted average (BNEOWA), BN Einstein hybrid average (BNEHA), BN Einstein weighted geometric (BNEWG), BN Einstein ordered weighted geometric (BNEOWG) and BN Einstein hybrid geometric (BNEHG), as well as their required properties. The most important benefit of using the suggested approaches is that they provide decision-makers with complete sight of the issue. These techniques, when compared to other methods, provide complete, progressive and precise findings. Lastly, by means of diverse types of newly introduced aggregation operators and a numerical illustration by an example, we suggest an innovative method to be used for multi-criteria community decision-making (DM). This illustrates the utility and applicability of this new strategy when facing real-world problems. [ABSTRACT FROM AUTHOR]

In this paper, a unique overview of intelligent machines and mathematical methods designed and developed to measure and to control the water level in industrial or laboratory setups of coupled and cascaded configurations of tanks is made. A systematized and concise overview is made of the mechatronic systems used in the measurement, identification, and control of the water level enumerates, the software used in the associated scientific research, modern techniques and sensors, and mathematical models, as well as analysis and control strategies. The broad overview of applications of the last decade is finalized by a proposition of a control system that is based on a parameter estimation of a new experimental setup, an integral dynamic model of the system, a modern mechatronic machine such as the Watson-Marlow peristaltic pump, the Anderson Negele sensor of level, the NI cRIO-9074 controller, and LabVIEW virtual instrumentation. The results of real experimental tests, exploiting a hybrid proportional control, being improved by a numerically predicted water level, are obtained using a few tools, i.e., the static characteristics, the classical step response, and a new pyramid-shaped step function of a discontinuous path-following reference input, being introduced to evaluate the effectiveness and robustness of the regulation of the level height. [ABSTRACT FROM AUTHOR]

We use two parameters for functions whose second (q, ω)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on (q, ω)-Hahn difference operator. Furthermore, we procure some q-integral and continuous inequalities as special cases of the main results as well these generalizations. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this research, a numerical analysis is accomplished aiming to investigate the effects of adding a new design fins arrangement to a vertical triplex tube latent heat storage system during the melting mechanism and evaluate the natural convection effect using Ansys Fluent software. In the triplex tube, phase change material (PCM) is included in the middle tube, while the heat transfer fluid (HTF) flows through the interior and exterior pipes. The proposed fins are triangular fins attached to the pipe inside the PCM domain in two different ways: (1) the base of the triangular fins is connected to the pipe, (2) the tip of the triangular fins is attached to the pipe and the base part is directed to the PCM domain. The height of the fins is calculated to have a volume equal to that of the uniform rectangular fins. Three different cases are considered as the final evaluation toward the best case as follows: (1) the uniform fin case (case 3), (2) the reverse triangular fin case with a constant base (case 12), (3) the reverse triangular fin case with a constant height (case 13). The numerical results show that the total melting times for cases 3 and 12 increase by 4.0 and 10.1%, respectively, compared with that for case 13. Since the PCM at the bottom of the heat storage unit melts slower due to the natural convection effect, a flat fin is added to the bottom of the heat storage unit for the best case compared with the uniform fin cases. Furthermore, the heat storage rates for cases 3 and 12 are reduced by 4.5 and 8.5%, respectively, compared with that for case 13, which is selected as the best case due to having the lowest melting time (1978s) and the highest heat storage rate (81.5 W). The general outcome of this research reveals that utilizing the tringle fins enhances the thermal performance and the phase change rate. [ABSTRACT FROM AUTHOR]

This article is an attempt to explore the heat transfer features of the steady three-dimensional rotating flow of magneto-hydrodynamic hybrid nanofluids under the effect of nonlinear radiation over the bi-directional stretching surface. For this purpose, two different nano-particles, namely silver (Ag) and molybdenum di-sulfide (MoS2), were selected. Three different conventional base fluids were utilized to form desired hybrid nanofluids such as water (H2O), engine oil (EO), and ethylene glycol (EG). We obtained steady three-dimensional highly nonlinear partial differential equations. These highly nonlinear partial differential equations cannot be solved analytically, so these equations were handled in MATLAB with the BVP-4C technique with convergence tolerance at 10−6. The graph depicts the effect of the magnetization effect, thermal radiation, and stretching ratio on rotating hybrid nanofluids. Additionally, the impact of thermal radiation on the heat coefficient of three different hybrid nanofluids is being investigated. The augmentation in magnetization decreases the primary velocity, whereas the increment in radiation enhances the primary velocity. The stretching ratio and the presence of higher magnetic forces increase the temperature profile. The concentration profile was enhanced with an increment in the magnetic field, stretching, and rotation ratio. The maximum Nusselt number was achieved for the Ag-MoS2/EO hybrid nanofluid. It was concluded that augmentation in nonlinear radiation enhances the heat transfer coefficient for the examined cases (I) and (II) of the hybrid nanofluids. The Nusselt number doubled for both the examined cases under nonlinear radiation. Moreover, it was discovered that Ag-MoS2/water produced the best heat transfer results under nonlinear radiation. Therefore, the study recommends more frequent exploration of hybrid nanofluids (Ag-MoS2/water) when employing nonlinear radiation to analyze the heat transfer coefficient. [ABSTRACT FROM AUTHOR]

Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture different physical situations such as thin film flows and waves on shallow water surfaces. In this work, a new approach for predicting and analyzing nonlinear time-fractional coupled KdV systems is proposed based on Laplace transform and homotopy perturbation along with Caputo fractional derivatives. This algorithm provides a convergent series solution by applying simple steps through symbolic computations. The efficiency of the proposed algorithm is tested against different nonlinear time-fractional KdV systems, including dispersive long wave and generalized Hirota–Satsuma KdV systems. For validity purposes, the obtained results are compared with the existing solutions from the literature. The convergence of the proposed algorithm over the entire fractional domain is confirmed by finding solutions and errors at various values of fractional parameters. Numerical simulations clearly reassert the supremacy and capability of the proposed technique in terms of accuracy and fewer computations as compared to other available schemes. Analysis reveals that the projected scheme is reliable and hence can be utilized with other kernels in more advanced systems in physics and engineering. [ABSTRACT FROM AUTHOR]

In the present paper, some new generalizations of dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales are established. Some integral and discrete Gronwall–Bellman–Pachpatte-type inequalities that are given as special cases of main results are original. The main results are proved by using the dynamic Leibniz integral rule on time scales. To highlight our research advantages, several implementations of these findings are presented. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations. [ABSTRACT FROM AUTHOR]

We prove new Hardy–Copson-type (γ , a) -nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller's chain rule, the integration by parts formula, and the dynamic Hölder inequality on time scales. When γ = 1 , then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous and discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

As a new usage of Leibniz integral rule on time scales, we proved some new extensions of dynamic Gronwall–Pachpatte-type inequalities on time scales. Our results extend some existing results in the literature. Some integral and discrete inequalities are obtained as special cases of the main results. The inequalities proved here can be used in the analysis as handy tools to study the stability, boundedness, existence, uniqueness and oscillation behavior for some kinds of partial dynamic equations on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation. [ABSTRACT FROM AUTHOR]

Nonlinear vibration control of the twelve-poles electro-magnetic suspension system was tackled in this study, using a novel control strategy. The introduced control algorithm was a combination of three controllers: the proportional-derivative (P D) controller, the integral resonant controller (I R C) , and the positive position feedback (P P F) controller. According to the presented control algorithm, the mathematical model of the controlled twelve-poles rotor was established as a nonlinear four-degree-of-freedom dynamical system coupled to two first-order filters. Then, the derived nonlinear dynamical system was analyzed using perturbation analysis to extract the averaging equations of motion. Based on the extracted averaging equations of motion, the efficiency of different control strategies (i.e., P D ,   P D + I R C ,   P D + P P F ,   and   P D + I R C + P P F ) for mitigating the rotor's undesired vibrations and improving its catastrophic bifurcation was investigated. The acquired analytical results demonstrated that both the P D and P D + I R C controllers can force the rotor to respond as a linear system; however, the controlled system may exhibit the maximum oscillation amplitude at the perfect resonance condition. In addition, the obtained results demonstrated that the P D + P P F controller can eliminate the rotor nonlinear oscillation at the perfect resonance, but the system may suffer from high oscillation amplitudes when the resonance condition is lost. Moreover, we report that the combined control algorithm ( P D + I R C + P P F ) has all the advantages of the individual control algorithms (i.e., P D ,   P D + I R C ,   P D + P P F ), while avoiding their drawbacks. Finally, the numerical simulations showed that the P D + I R C + P P F controller can eliminate the twelve-poles system vibrations regardless of both the excitation force magnitude and the resonant conditions at a short transient time. [ABSTRACT FROM AUTHOR]

To meet the current challenges concerning the removal of dyes from wastewater, an environmentally friendly and efficient treatment technology is urgently needed. The recalcitrant, noxious, carcinogenic and mutagenic compound dyes are a threat to ecology and its removal from textile wastewater is challenge in the current world. Herein, biochar-mediated zirconium ferrite nanocomposites (BC-ZrFe2O5 NCs) were fabricated with wheat straw-derived biochar and applied for the adsorptive elimination of Tartrazine dye from textile wastewater. The optical and structural properties of synthesized BC-ZrFe2O5 NCs were characterized via UV/Vis spectroscopy, Fourier transform Infra-red (FTIR), X-Ray diffraction (XRD), Energy dispersive R-Ray (EDX) and Scanning electron microscopy (SEM). The batch modes experiments were executed to explore sorption capacity of BC-ZrFe2O5 NCs at varying operative conditions, i.e., pH, temperature, contact time, initial dye concentrations and adsorbent dose. BC-ZrFe2O5 NCs exhibited the highest sorption efficiency among all adsorbents (wheat straw biomass (WSBM), wheat straw biochar (WSBC) and BC-ZrFe2O5 NCs), having an adsorption capacity of (mg g−1) 53.64 ± 0.23, 79.49 ± 0.21 and 89.22 ± 0.31, respectively, for Tartrazine dye at optimum conditions of environmental variables: pH 2, dose rate 0.05 g, temperature 303 K, time of contact 360 min and concentration 100 mg L−1. For the optimization of process variables, response surface methodology (RSM) was employed. In order to study the kinetics and the mechanism of the adsorption process, kinetic and equilibrium mathematical models were used, and results revealed 2nd order kinetics and a multilayer chemisorption mechanism due to complexation of hydroxyl, Fe and Zr with dyes functional groups. The nanocomposites were also recovered in five cycles without significant loss (89 to 63%) in adsorption efficacy. This research work provides insight into the fabrication of nanoadsorbents for the efficient adsorption of Tartrazine dye, which can also be employed for practical engineering applications on an industrial scale as efficient and cost effective materials. [ABSTRACT FROM AUTHOR]

Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler–Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler–Maruyama and stochastic Runge–Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis. [ABSTRACT FROM AUTHOR]

Concerns about the environment, the cost of energy, and safety mean that low-energy cold-mix asphalt materials are very interesting as a potential replacement for present-day hot mix asphalt. The main disadvantage of cold bituminous emulsion mixtures is their poor early life strength, meaning they require a long time to achieve mature strength. This research work aims to study the protentional utilization of waste and by-product materials as a filler in cold emulsion mixtures with mechanical properties comparable to those of traditional hot mix asphalt. Accordingly, cold mix asphalt was prepared to utilize paper sludge ash (PSA) and cement kiln dust (CKD) as a substitution for conventional mineral filler with percentages ranging from 0–6% and 0–4%, respectively. Test results have shown that the incorporation of such waste materials reflected a significant improvement in the mixture's stiffness and strength evolution. The cementitious reactivity of PSA produces bonding inside the mixtures, while CKD is used as an additive to activate the hydration process of PSA. Therefore, based on the results, it will be easier to build cold mixtures by shortening the amount of time needed to reach full curing conditions. [ABSTRACT FROM AUTHOR]

Heat transfer at industrial levels has been revolutionized with the advancement of nanofluid and hybrid nanofluid. Keeping this development in view, this article aims to present the rate of heat transfer for conventional and hybrid nanofluids, incorporating the Hall Effect over a stretchable surface. The flow governing equations are obtained with the help of suitable assumptions, and the problem is attempted with the boundary value problem technique in MATLAB. The highly non-linear partial differential equations are transformed into non-dimensional forms using suitable similarity transforms. The criterion of convergence for solution or tolerance of a problem is adjusted to 10−7. Water is considered as a base fluid; copper (Cu) and silver (Ag) nanoparticles are mixed to obtain nanofluid. This novel work is incorporated for conventional and hybrid nanofluid with the effect of Hall current above the stretching/shrinking surface. Increasing the Stefan blowing parameter reduces the flow rate; it increases the heat transfer rate and nano-particle concentration of conventional and hybrid nanofluid. Both velocity components decreases by increasing the magnetic field. The Hall Effect also decreases the velocity of nanofluid. The outcomes are compared to previously published work, demonstrating that the existing study is legitimate. The heat transfer rate of the hybrid nanofluid is higher than the convential nanofluid. This study suggests more frequent use of hybrid nanofluid because of high heat transfer rates and reduced skin friction. [ABSTRACT FROM AUTHOR]

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]

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, 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]

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]

Featured Application: A high fidelity aeroelastic model of a typical fin–actuator system is established, in which the friction model is more accurate. The influence of freeplay and friction on the system stability is analyzed using the time-domain method and frequency-domain method, and some suggestions for flutter suppression design are put forward. Both the dynamic characteristics and structural nonlinearities of an actuator will affect the flutter boundary of a fin–actuator system. The actuator models used in past research are not universal, the accuracy is difficult to guarantee, and the consideration of nonlinearity is not adequate. Based on modularization, a high-fidelity modeling method for an actuator is proposed in this paper. This model considers both freeplay and friction, which is easy to expand. It can be directly used to analyze actuator characteristics and perform aeroelastic analysis of fin–actuator systems. Friction can improve the aeroelastic stability, but the mechanism of its influence on the aeroelastic characteristics of the system has not been reported. In this paper, the LuGre model, which can better reflect the friction characteristics, was integrated into the actuator. The influence of the initial condition, freeplay, and friction on the aeroelastic characteristics of the system was analyzed. The comparison of the results with the previous research shows that oversimplified friction models are not accurate enough to reflect the mechanism of friction's influence. By changing the loads, material, and geometry of contact surfaces, flutter can be effectively suppressed, and the power loss caused by friction can be minimized. [ABSTRACT FROM AUTHOR]

Adaptive tracking control of the speed of a very elastically attached circular load driven by a direct current motor accompanied with an adaptive conventional and a fractional-order Proportional Integral Derivative (PID) controller is studied. It refers to improving the closed-loop control system response of elastically coupled components of drivelines. The motor and the load mechatronic models and the block diagrams are constructed. Parameters of the PID controller in the model reference control are both constant, as well as vary in time. The adaptive control method is improved by the application of a new closed-loop control structure canceling error dynamics. A few competing control strategies are tested based on the application of two types low and high frequency stepwise increasing variations of loading torque and damping coefficient of motion. Moreover, the performance of the control strategies is verified by Integral Time-Weighted Absolute Error (ITAE) index, since their robustness is evaluated by applying a sine modulated triangle waves of selected electric parameters. Therefore, a dynamic forcing and parameter uncertainty is applied. Simulation results are compared for checking the proposed methods. [ABSTRACT FROM AUTHOR]

The aim of the paper was to analyze the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method, Rosenstein method, Kantz method, the method based on the modification of a neural network, and the synchronization method) for the classical problems governed by difference and differential equations (Hénon map, hyperchaotic Hénon map, logistic map, Rössler attractor, Lorenz attractor) and with the use of both Fourier spectra and Gauss wavelets. It has been shown that a modification of the neural network method makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyperchaos, and others. The aim of the comparison was to evaluate the considered algorithms, study their convergence, and also identify the most suitable algorithms for specific system types and objectives. Moreover, an algorithm of calculation of the spectrum of Lyapunov exponents based on a trained neural network has been proposed. It has been proven that the developed method yields good results for different types of systems and does not require a priori knowledge of the system equations. [ABSTRACT FROM AUTHOR]

In this part of the paper, the theory of nonlinear dynamics of flexible Euler-Bernoulli beams (the kinematic model of the first-order approximation) under transverse harmonic load and colored noise has been proposed. It has been shown that the introduced concept of phase transition allows for further generalization of the problem. The concept has been extended to a so-called noise-induced transition, which is a novel transition type exhibited by nonequilibrium systems embedded in a stochastic fluctuated medium, the properties of which depend on time and are influenced by external noise. Colored noise excitation of a structural system treated as a system with an infinite number of degrees of freedom has been studied. [ABSTRACT FROM AUTHOR]