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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]

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 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]

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]

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]