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In this study, nonlinear vibration and stability of a pipe conveying fluid, with axially moving supports, immersed in an external fluid is studied. The equation of motion is derived with the aid of the Newtonian method via employing the Euler–Bernoulli beam theory and plug flow assumption. Considering the stretching effect, the nonlinear equation of motion is obtained, and it is discretized via the Galerkin method. Afterward, the stability of the system is investigated using two different approaches, and their results are compared. Numerical simulations show the system has complex dynamic behavior. To unveil the dynamics of the system, various analysis techniques such as bifurcation diagram of Poincaré map, phase portrait, power spectrum, and time trajectories are used. Limit cycle, period-n, quasi-periodic, and chaotic regime are observed. It is found that pipe can flutter around the trivial solution or post-buckling equilibrium points. Moreover, the influences of some system parameters on the chaotic behavior of the pipe are discussed. [ABSTRACT FROM AUTHOR]

The solitary wave solutions of the (2 + 1) -dimensional nonlinear Chiral Schrödinger ((2 + 1) -D CNLS) equation by making use of the modern extended direct algebraic approach are investigated in this paper. Such a nonlinear model's different categories of solitary waves solutions are found. The division of semi-dark solitons, singular dark-pitch solitons, single solitons of type 1 along with 2, intermixed hyperbolically, trigonometrically and rational solitons are developed and evaluated using software tools for numerical calculations. Detailed graphical interpretation of results with deliberation is also discussed. This paper effectively depicts 3D- and 2D-contour plots to provide further detail about the physical characteristics of the obtained solutions. We compare our solutions to previously reported findings along with study motivation and future directions. The fractional quantum hall effect's edge states are defined by the discussed model. [ABSTRACT FROM AUTHOR]

The purpose of this research is to analyze the general equations of double diffusive magneto-free convection in a rate type fluid presented in non-dimensional form, and apply to a moving heated vertical plate as in the boundary layer flow up, with existence of externally magnetic fields which are either moving or fixed consistent with the plate. Thermal transport phenomenon is discussed in the presence of constant concentration coupled with first-order chemical reaction with exponential heating. An innovative definition in power law (CF) and Mittag-Leffler (ABC) kernels form time fractional operators are implemented to hypothecate the constitutive mass, heat and momentum equations. The results based on special functions are obtained by using the technique of Laplace transformation to tackle the non-dimensional equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid is presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not to be zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations along with some special cases for the movement of the plate which are also studied. [ABSTRACT FROM AUTHOR]

This work focuses on analyzing the dynamical behavior of a mechanical system consisting of a double spatial pendulum in contact with a movable obstacle. The pendulum's ability to move in space is achieved by the use of special Cardan–Hook joints as the links of the pendulum. The mechanical system is equipped with a special movable obstacle, i.e. a rotating circular plate situated below the pendulum, which limits the space of admissible positions. A significant part of this work is devoted to the modeling of the contact between the pendulum and the obstacle. In this regard, a special class of reduced models is derived with the resultant friction force and moment acting on the finite size of the contact area along with a compliant model of impact based on the Hertz stiffness. Finally, the effective model suitable for fast and realistic numerical simulations is obtained. The contact model is tested numerically and the effect of its parameters on the system bifurcation dynamics is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we studied both kinematic and dynamic models of a mammal-like octopod robot. To control robot legs, we employed a simple gait generator based on a sine function and we proposed modified generators of gait. The introduced generators allowed us to obtain better kinematic and dynamic properties of motion of the whole robot during walking. By changing the length and the height of a single robot step, it is possible to use one model to control the initial, regular, and final phases of the robot gait without the need of generating additional control signals. The simulation parameters were estimated based on the prototype designed in Inventor software. In turn, for numerical research, we used a simulation model implemented in Mathematica. The obtained results were presented in the form of time histories of basic kinematic and dynamic quantities of the robot gait as well as the configuration of the robot legs at the chosen time moments. The presented method allows us to precisely control the robot position in the vertical direction, which is also presented in this paper. As a result, we obtained better stability of the whole robot during walking and performing tasks, also on slippery terrains, i.e. on terrains with relatively low coefficient of friction between the ground and the robot feet. [ABSTRACT FROM AUTHOR]

A parametric pendulum excited by a discrete wave-modulated step function of length is subjected to a mathematical analysis and numerical modeling. We observe an existence of almost periodic solutions of ordinary differential equations with linear boundary value conditions. An exemplary oscillator subject to both an almost periodic step elongation and forcing synchronizes with the forcing, tending to almost periodic motions like stable limit cycles. Conditions for that synchronization as well as trajectories of numerical solutions on time history plots and phase planes are shown to confirm correctness of the analytical derivations and dedicated numerical modeling. [ABSTRACT FROM AUTHOR]

The change in mechanical properties of the femoral bone tissue surrounding hip endoprosthesis stems during the post-operative period is one of the causes of implant instability, and the mathematical description of this phenomenon is the subject of much research. In the present study, a model of bone adaptation, based on isotropic Stanford theory, is created for further computer investigation. The results of implementation of such a mathematical model are presented regarding the choice of cement mantle rational thickness in cemented hip arthroplasties. The results show that for cement mantle thicknesses ranging from 1–1.5 mm, a peak stress value in the proximal part of the mantle exceeds the limit of durability of bone cement. Moreover, results show that high reduction in the bone density of distal and proximal regions was observed in cases of cement mantle thicknesses varying from 1–3 mm. No significant changes in bone density of the abovementioned regions were obtained for 4 mm and 5 mm. The outcome of numerical investigations can be treated as valuable and will lead to the improvement of cemented hip replacement surgery results. [ABSTRACT FROM AUTHOR]

Results of the simulations of vibrations of collecting electrode system of dry electrostatic precipitator (ESP) are reported. The system of nine electrodes 16m long, suspension beam (upper beam) and anvil beam (bottom beam) is analyzed. First, the variants regarding differ position of the anvil beam are analyzed. Second, the differ position of a point of the impulse force as well as direction of the impulse force are investigated (in this case the anvil beam is in a 'classic' position). Discretization of both beams and electrodes is carried out employing the modified rigid finite element method (RFEM). It allows to study an influence of the mass distribution and geometric properties of the analyzed system. Moreover, the method is convenient for the introduction of additional lumped mass parameters modeling the joints that fasten the electrodes to the suspension beam, distance-marking bushes, riveted and screw joints, etc. Position of the anvil beam and position/direction of the point of impulse force application can have essential influence on tangent and normal accelerations at different points of the plates, and thus on the effectiveness of the dust removal process. We aim to find optimal position of an anvil beam, which guaranties the maximum amplitudes of vibrations and their proper distribution in the plates. [ABSTRACT FROM AUTHOR]

The paper is focused on the kinematic, dynamic and power consumption analysis of the constructed prototype of the hexapod robot walking with tripod gait on a flat and hard ground. The movements of the robot legs are controlled by different well known oscillators working as central pattern generators (CPGs). The mentioned models, as well as those proposed in our previous paper, are employed and compared from the viewpoint of fluctuations of the robot gravity center both in vertical and movement direction, contact forces between the robot legs and the ground as well as energy demand of the whole robot during walking process. Time histories of the key kinematic and dynamic quantities describing locomotion of the robot are numerically studied and experimentally verified. Power consumption of the whole robot is experimentally investigated based on the current consumption in the applied servo motors which drive the robot legs. We show that the proposed CPG model is more efficient regarding acceleration/deceleration of the whole robot, contact forces and overload acting on the robot legs as well the energy demand during walking of the robot. The appropriate choice of the robot leg movements, depending on the actual situation, can have a positive influence on the investigated issues, i.e. avoid unnecessary acceleration/deceleration of the robot, decrease the contact forces between the legs and the ground and reduce energy demand of the whole robot. Consequently, it also allows to improve structural stability of the robot during walking process. [ABSTRACT FROM AUTHOR]

The (G′/G)-expansion scheme is used to execute many wave results for the partial differential equation, namely, the nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation which plays a significant role in mathematical physics, and this equation is accomplished in quantum electron–positron–ion magneto plasmas. The Lie approach is used to find the infinitesimal generators, and group invariant solutions, and help us to reduce the considered PDEs into ODEs. Then a planer dynamical system approach is used to see the existence of closed-form solutions. All possible phase portraits are obtained and the existence of electrostatic wave potentials is reported. Meantime, periodic and super-nonlinear electrostatic wave potentials are found for different initial value conditions with the help of the Runge–Kutta method. Moreover, new traveling wave patterns of the considered models are constructed and presented graphically. Then, the conserved vectors of the given physical model with the use of the multiplier scheme are presented. [ABSTRACT FROM AUTHOR]

Thermal processes occurring in the mechanical clutch or brake systems have a great influence on the strength of elements of these systems as well as on their dynamics. The contact problems exhibited by such systems include heat generated by dry friction contact surfaces. The contact dynamics in general depends on many system parameters, and it attracted attention of many researches focused on analysis of the mentioned phenomena in different kinds of mechanical systems like clutches, brakes, and others. In this work a mathematical model describing the processes of heat generation and its propagation in the mechanical friction clutch is presented. The presented model takes into account the unequal distribution of flux density of produced heat in the clutch, the thermal conductivity of materials of friction linings, and the heat transfer between the friction linings of clutch and its environments. The analyzed object is described by a set of algebraic linear homo- and heterogeneous equations, and it is derived using a computer numerical method. Many interesting numerical and experimental results are obtained, illustrated and discussed. Presented numerical results coincide with experimental data. [ABSTRACT FROM AUTHOR]

Calculations of nonlinear displacements and vibrations of inhomogeneous loaded shells with developable principal surface by means of different analytical methods are represented. It is shown that solutions to these methods are the expansions of exact solution in the Taylor series for an independent variable, and in the particular case - for the powers of a natural parameter. A method that provides a polynomial asymptotic approximation of the exact solution of the general form and its meromorphic continuation based on 1D and 2D Padé approximations is proposed. Calculations of nonlinear deformation and stability of elastic flexible circular cylindrical shell under uniform external pressures and of free oscillations of simply supported stringer shell demonstrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, the complete set of Tangens hyperbolicus approximations of model of dry friction coupled with rolling resistance for circular contact area between interacting bodies is proposed. The developed approximations are compared with corresponding Padé approximants of the first and second order well known from the literature and with the numerical solution of the exact integral model as well. It is shown that Tangens hyperbolicus approximants are closest to the exact solution. Then the approximated models are applied to the celtic stone dynamics, however with the significant simplifying assumption of circular contact between stone and the table, presenting differences between them again. Certain specific approximations and regularizations of the friction and rolling resistance models enabling and facilitating their application to the real problem are shown. The analysis of the response dependence on initial conditions is performed by the use of a special kind of diagram. [ABSTRACT FROM AUTHOR]

No abstract received. [ABSTRACT FROM AUTHOR]

A weakly nonlinear 2-DOF system, parametrically and externally excited, is studied. An intensive energy transfer between modes of vibrations is discovered. Multiple scales method is used for recognizing resonances occurring in the system. The amplitude response functions for some chosen cases of resonances are obtained and studied. Many of the engineering systems can be investigated in the presented way. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a real plane and periodically forced triple pendulum is investigated experimentally and numerically. Mathematical modeling includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have also been reported, and a novel approach of the rolling bearings friction modeling is proposed, among other. [ABSTRACT FROM AUTHOR]

A boundary value problem associated with filtering governed by differential equations with time dependent coefficients and exhibiting a weak nonlinearity is solved. Namely, the boundary value problem is split into two independent boundary problems, i.e., that of Goursat for the concentration of a sorbate and that absorbed by a sorbent. Then each of the formulated problems is solved separately applying the Riemann transformation. [ABSTRACT FROM AUTHOR]

The triple physical pendulum with barriers is used to model a piston — connecting rod — crankshaft system of a mono-cylinder combustion engine. Among other results, a peculiar motion of the piston — connecting rod — crankshaft model is reported, i.e. six sliding stages of the piston along the cylinder per one engine cycle are illustrated. In spite of its simplicity, the introduced model can serve as the first step in a more advanced modeling taking into account various technological details. In particular, the proposed model can be considerably useful for the investigations of impacts between the piston and the cylinder aiming at the reduction or total elimination of this source of harmful noise. [ABSTRACT FROM AUTHOR]

A self-excited friction pair is modeled by a mechanical system of two degrees-of-freedom with a normal force varying during the block displacement. Two different friction coefficients are used, and a normal force pressing the sliding body to a belt depending on an angle bar motion of the analyzed system is applied. In addition, the numerical analysis is supported by the investigation of a real laboratory object modeling the feedback reinforcement of friction forces acting on the block. Both numerical and experimental results are compared showing good agreement. [ABSTRACT FROM AUTHOR]

In this work a triple pendulum with damping, external forcing and impacts is investigated. We integrate the obtained system of governing equations between two successive impacts, and the discontinuity points are detected (by halving time step until the required precision is obtained). For each impact time, the state of the system is transformed using the extended restitution coefficient rule. The theory of Aizerman and Gantmakher is used to calculate the fundamental solution matrices in the analyzed system exhibiting discontinuities. Fundamental matrices are used during calculation of Lyapunov exponents, in stability analysis of periodic solution (Floquet multipliers) and in shooting method of finding periodic orbits. Then some examples for three coupled identical rods with horizontal barrier are shown. [ABSTRACT FROM AUTHOR]

Introduces the articles published in the June 2005 issue of the "International Journal of Bifurcation and Chaos."