DISSIPATIVE OSCILLATORS’ POWER CHARACTERISTIC NON-SYMMETRY DYNAMIC EFFECT

The features of motion of a non-linear oscillator under the instantaneous force pulse loading are studied. The elastic characteristic of the oscillator is given by a polygonal chain consisting of two linear segments. The focus of the paper is on the influence of the dissipative forces on the possibility of occurrence of the elastic characteristic non-symmetry dynamic effect, studied previously without taking into account the influence of these forces. Four types of drag forces are considered, namely linear viscous friction, Coulomb dry friction, position friction, and quadratic viscous resistance. For the cases of linear viscous friction and Coulomb dry friction the analytical solutions of the differential equation of oscillations are found by the fitting method and the formulae for computing the swings are derived. The conditions on the parameters of the problem are determined for which the elastic characteristic non-symmetry dynamic effect occurs in the system. The conditions for the effect to occur in the system with the position friction are derived from the energy relations without solving the differential equation of motion. In the case of quadratic viscous friction the first integral of the differential equation of motion is given by the Lambert function of either positive or negative argument depending on the value of the initial velocity. The elastic characteristic non-symmetry dynamic effect is shown to occur for small initial velocities, whereas it is absent from the system when the initial velocities are sufficiently large. The values of the Lambert function are proposed to be computed by either linear interpolation of the known data or approximation of the Lambert function by elementary functions using asymptotic formulae which approximation error is less than 1%. The theoretical study presented in the paper is followed up by computational examples. The results of the computations by the formulae proposed in the paper are shown to be in perfect agreement with the results of numerical integration of the differential equation of motion of the oscillator using a computer.

Track Model with Nonlinear Elastic Characteristic of the Rubber Rail Pad

This paper presents a new basic nonlinear track model consisting of an infinite Euler-Bernoulli beam (rail) resting on continuous foundation with two elastic layers (rail pad and ballast bed) and intermediate inertial layer (sleepers). The two elastic layers have bilinear elastic characteristic obtained from the load-displacement characteristic of the rail pad and ballast. A time-varying load with two components - time-constant one and harmonic other, representing the wheel/rail contact force is considered as the track model input. Rail deflection due to the time-constant component of the load is obtained solving the nonlinear equations of the balance position. Subsequently, the structure of the nonhomogeneous foundation is determined. Dynamic rail response in terms of receptance due to the harmonic component of the load is calculated using the linearised track model with nonhomogeneous elastic characteristic. Influence of the time-constant component and the reflected waves due to the nonhomogeneous foundation are presented.

DYNAMICS FEATURES OF A VIBRATING MACHINE WITH ELASTIC ELEMENT HAVING EXPONENTIAL CHARACTERISTIC OF RESILIENT FORCE

The article analyzes the possibility of using nonlinear elastic elements as a suspension of the working element of resonant vibrating machines with two unbalance vibration exciters is analyzed. The elastic characteristic of the suspension is described by an exponential law, which ensures that the natural frequency remains unchanged regardless of the system mass. Static characteristics of the vibration exciter motors are taken into account. A system of differential equations describing movement of the system depending on the processed material mass is obtained. Amplitude-frequency characteristics depending on the power supply voltage, as well as on the debalance rotational speed are obtained for different values of material mass. The stability of the obtained periodic solutions is analyzed. The constancy of resonant amplitude and frequency of the working element vibrations at various values of material mass is shown. The results obtained confirm the advisability of using an equalfrequency suspension of the working element for resonant vibrating machines.

Vibration analysis of nonlinear and linear elastic systems

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

Thermodeformation properties of dynamically volcanized thermoplastic elastomers based on random polypropylene and nitrile butadiene rubber

The paper presents the results of a study of the thermodefomational characteristics of dynamically vulcanized thermoplastic elastomers based on random polypropylene and nitrile butadiene rubber (SKN). In order to improve the compatibility of polymer mixtures, Exxelor PO1200, a grafted copolymer of polypropylene with maleic anhydride, was used as a compatibilizer. The concentration of maleic anhydride in the composition of the grafted copolymer was 3.0 wt. %. It was shown that as a result of the loading of the compatibilizer, it seemed possible to improve the compatibility of bipolar mixtures, in which there was no separation between the components of the mixture. It was found that with the load of 30 wt. % SKN-18, as well as 40 wt. % SKN-26 or SKN-40 into the composition of random polypropylene, the polymer composition exhibits the properties of thermoplastic elastomers, as a result of which plastic deformation is replaced by a highly elastic characteristic for rubbers. The temperature regions of the solid, highly elastic, and viscous flowing states are determined. In order to give polymer blends greater elasticity, they were vulcanized using crosslinking agents such as dicumyl peroxide and sulfur. It is shown how, in the process of increasing the concentration of dicumyl peroxide from 0.25 to 1.0 wt. %, the thermomechanical properties of dynamically vulcanized thermoplastic elastomers significantly change. It was found that with the introduction of dicumyl peroxide in an amount equal to 1.0 wt. %, the melt flowability of vulcanized materials almost completely lose their ability to flow, and pass from a highly elastic state to a glassy one. With the load of sulfur in an amount of 1.0 to 10 wt. %, the melt flowability of the vulcanized thermoplastic elastomers is preserved.

POST-IMPACT VIBRATIONS OF A SQUARE NONLINEAR DISPATIVE OSCILLATOR

An oscillator damped by viscous linear resistance, due to the instantaneous increase in its mass after impact, can become a dissipative oscillatory system under the action of dry or positional friction. In the article describes the oscillations of a dissipative oscillator with an asymmetric quadratically nonlinear elastic characteristic and dry Coulomb friction, arising as a result of an inelastic vertical impact of a rigid body on it. In the article, the Cox model is used, which does not take into account local deformations of solid bodies subjected to impact. The paper establishes the dependences on the impact velocity and the values of other parameters at which the effect of asymmetry of the elastic characteristic of the system may appear or may not appear. The conditions are derived when the dynamic effect of asymmetry of the power characteristic is manifested in the system. It consists in the fact that the maximum displacement of the oscillator (oscillation range) in the direction of the shock pulse is less than the opposite extreme displacement (range) after the shock oscillations. The existence of such a critical value of the shock impulse is established, the excess of which leads to the loss of motion stability. The second integral of the oscillation equation describes the movement of the oscillator in time, expressed in terms of Jacobi elliptic functions. An approximate formula for their calculation is proposed. Formulas are also derived to determine the time to reach extreme deviations of the system from the equilibrium position. This time is expressed in terms of elliptic integrals of the first kind, which refer to the tabulated functions. Examples of calculations are considered, where, in addition to using the derived formulas, numerical computer integration of the original nonlinear differential equation of motion is carried out. A comparison of the results obtained for the displacement values of a quadratically nonlinear oscillator with dry friction expressed in terms of Jacobi elliptic functions and obtained by numerical integration is carried out. Good consistency of the calculation results in two ways confirmed the adequacy of the obtained analytical solutions of the nonlinear Cauchy problem.

The Stability, Microstructure, and Microrheological Properties of Monascus Pigment Double Emulsions Stabilized by Polyglycerol Polyricinoleate and Soybean Protein Isolate

Monascus pigment is a natural food pigment and is commonly used for coloring and as antiseptic of cured meat products, confectionery, cakes, and beverages. However, Monascus pigment is sensitive to environmental conditions. The main aim of this study was to investigate the effect of polyglycerol polyricinoleate (PGPR) and soy protein isolate (SPI) on the particle size, zeta potential, physical stability, microstructure, and microrheological properties of Monascus pigment double emulsions. The effects of ionic strength, heating, and freeze thawing treatment on the stabilities of Monascus pigment double emulsions were also characterized. It was found that the optimum PGPR and SPI concentrations for fabricating Monascus pigment double emulsion were 3.6 and 3.0 wt%, respectively. The fabricated Monascus pigment double emulsion was composed of fine particles with narrow and uniform size distributions. Microrheological property results suggested that the elastic characteristic of the Monascus pigment double emulsion was dominated with increasing PGPR and SPI contents. It was mainly due to the increased collision and interaction between the droplets during the movement resulting in force increasing. Monascus pigment double emulsions with <5 mM CaCl2 prevented calcium to destroy the physical stability of emulsions, while Monascus pigment double emulsions with more than 10 mM CaCl2 formed creaming. After freeze thawing treatment, creaming occurred in Monascus pigment double emulsion. However, it was stable against heating treatment due to heating leading to a dense network structure. It could be contributed to the practical applications of Monascus pigment double emulsions in food products.

Rheological behavior and antiarthritic activity of Pterodon pubescens nanoemulsion

Pterodon pubescens, popularly known as "sucupira", it is traditionally used as anti-inflammatory agent. This work aimed to evaluate the in vivo antiarthritic properties of a P. pubescens oil nanoemulsion and the rheological behavior of the developed system. The viscoelastic properties, creep and recovery were evaluated by dynamic oscillatory tests. The antiarthritic activity of the nanoemulsion was evaluated by the zymozan-induced arthritis model, at three different doses (25, 50 and 125 mg/kg/day). P. pubescens oil nanoemulsion has been shown to decrease cell recruitment to a joint cavity and increased cartilaginous regeneration at the end of treatment of the dose of 50 mg/kg. The evaluation of the behaviour of deformation allowed to observe that the P. pubescens nanoemulsion presents predominantly elastic characteristic. These findings demonstrate the potential of P. pubescens and nanotechnology in the development of new antiarthritic drugs.

A Numerical Method for Calculating the Nonlinear Elastic Characteristic of Longitudinal-Transverse Transducers

This paper presents a numerical method for studying the stress-strain state of longitudinal-transverse transducers and obtaining their nonlinear elastic characteristic. The authors propose a mathematical model that uses a direct numerical solution of the boundary value problem based on the plain curved rod equations in MATLAB. The stress-strain state and the nonlinear elastic characteristic of the system are obtained using a method of successive loading based on linearized equations of the curved rod. The proposed model can be considered as an initial approximation to the solution of the spatial problem of the longitudinal-torsional transducer.