Resonances and Synchronization in Two Coupled Oscillators with Stick-Slip Vibrations and Spring Pendulums

We study the dynamical behavior of a system of two coupled mechanical oscillators with spring pendulums and driven by a stick-slip induced vibrations. Each of the oscillator consists of the body placed onto a moving belt/foundation, mechanical coupling associated with the body load pressed the belt depending on the body movement as well as suspended spring pendulum. In addition, the influence of the presence of additional electric/electromagnetic forces acting on the pendulums are analyzed. Different kinds of resonance behavior can be found in the studied system, even if it is simplified to a single degree-of-freedom system. As a result, due to many degrees-of-freedom and strong nonlinearity and discontinuity of the considered system, novel nonlinear dynamical phenomena occur, both near and beyond to the resonance. The motion analysis for different cases is carried out by employing standard numerical methods dedicated for nonlinear systems, including both qualitative and quantitative methods, as well as original animations of the system dynamics created in Mathematica. Understanding the role of coupling, transition between fixed points and energy transition in the considered system can be potentially applied in other similar systems, especially in real electro-mechanical systems, power system or in structural engineering

On the Controlling of Multi-Legged Walking Robots on Stable and Unstable Ground

In this chapter, we developed and investigated numerically a general kinematic model of a multi-legged hybrid robot equipped with a crab-like and/or mammal-like legs. To drive the robot’s limbs, a novel generator of gait was employed and tested. The simulation model developed in Mathematica is suitable for virtual study and visualization of the locomotion process. In contrast to our previous papers, in this study we focused especially on precise control of the position of the robot during walking in different directions. In our study we were able to simultaneously control all six spatial degrees of freedom of the robot’s body, as well as all the robot’s legs. Therefore, the investigated robot can be considered and used as a fully controlled walking Stewart platform. What is more, the used algorithm can also be successfully employed to coordinate and control all limbs of the robot on unstable or vibrating ground. As an example, it can be used to stabilize spatial position of the robot when the supporting ground becomes vibrating or unstable, and it will keep the robot stable and prevent it from falling over. Eventually, the developed simulation algorithms can be relatively simply adopted to control real constructions of different multi-legged robots

Power consumption analysis of different hexapod robot gaits.

The paper is focused on the power consumption analysis of different gaits of our constructed hexapod robot controlled by different Central Pattern Generator (CPG) models. There are a lot of gait patterns in the literature constructed either by different CPG models or using a series of oscillations with adjustable phase lag. The mentioned models, as well as those proposed in our previous paper are used and compared from the viewpoint of energy demand. In general, power consumption of the constructed hexapod robot is experimentally analyzed based on the current consumption in the applied servo motors, which drive the robot limbs. For this purpose the suitable drivers allowing a simple measurement of electric energy consumption of servo motors are used. The obtained experimental results show different energy demand for different robot gaits. Because power consumption is one of the main operational restrictions imposed on autonomous walking robots, we show that the performed energy efficiency analysis and the choice of the appropriate robot gaits depending on the actual situation can reduce the energy costs

Dynamics of two coupled 4-DOF mechanical linear sliding systems with dry friction.

The paper introduces a model of two identical coupled 4-DOF mechanical linear sliding systems with dry friction coupled with each other by a linear torsional spring. The appropriate components (bodies) of the coupled systems are riding on two separated driving belts, which are driven at constant velocities, and stick-slip vibrations can be observed. In this case the physical interpretation of the considered model could be two rows of carriages laying on the guideways and coupled by an elastic shaft, which are moving at constant velocity with respect to the guideways as a foundation. From a mathematical point of view the analyzed problem is governed by eight nonlinear ordinary second order differential equations of motion yielded by the second kind Lagrange equations. Numerical analysis is performed in Mathematica software using the qualitative and quantitative theories of differential equations. Some interesting non-linear system dynamics are detected and reported using the phase portraits and the Poincaré maps. Next, power spectra obtained by the FFT technique are reported. The presented results show periodic, quasi-periodic, chaotic and hyperchaotic orbits. Moreover, synchronization effects between the coupled systems are also detected and studied

Wear Processes in a Mechanical Friction Clutch: Theoretical, Numerical, and Experimental Studies

Mathematical modeling, theoretical/numerical analysis, and experimental verification of wear processes occurring on the contact surface of friction linings of a mechanical friction clutch are studied. In contrast to many earlier papers we take into consideration wear properties and flexibility of friction materials being in friction contact. During mathematical modeling and numerical simulations we consider a general nonlinear differential model of wear (differential wear model) and a model of wear in the integral form (integral wear model). Equations governing contact pressure and wear distributions of individual friction linings, decrease of distance between clutch shields, and friction torque transmitted by the clutch are derived and compared with experimental data. Both analytical and numerical analyses are carried out with the qualitative and quantitative theories of differential and integral equations, including the Laplace transform approach to ODEs. We show that theoretical results and numerical simulations agree with the experimental data. Finally, a numerical analysis of the proposed mathematical models was carried out in a wider range of parameters of the considered system

Reflectivity of Cholesteric Liquid Crystals with an Anisotropic Defect Layer Inside

In this study, first, we numerically investigated the reflectivity of a cholesteric liquid crystal with an anisotropic defect layer inside. To model optical phenomena in the examined system, a 4 × 4 matrix method was employed. The tests were carried out for different thicknesses of the whole system, different thicknesses of the defect layer, as well as different defect layer locations inside the cell. Next, a cholesteric liquid crystal comprising a defect layer and held between two parallel electrical conductors was also considered. In this case, the optical properties of the system could also be adjusted by an external applied electric field. Some interesting simulation results of the reflection coefficient (i.e., the fraction of electromagnetic energy reflected) were obtained, illustrated, and discussed. The simulation results showed a significant influence of both the defect and the external electric field on the selective reflection phenomenon, and the possibility of controlling the shape of the reflection spectrum. Finally, some potential applications of the analyzed optical system were discussed

Thermal Transmission Comparison of Nanofluids over Stretching Surface under the Influence of Magnetic Field

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