Chaotic vibrations in a regenerative cutting process

We have analysed vibrations generated in an orthogonal cutting process. Using a simple one degree of freedom model of the regenerative cutting, we have observed the complex behaviour of the system. In presence of a shaped cutting surface, the nonlinear interaction between the tool and a workpiece leads the to chatter vibrations of periodic, quasi-periodic or chaotic type depending on system parameters. To describe the profile of the surface machined by the first pass we used a harmonic function. We analysed the impact phenomenon between the tool and a workpiece after their contact loss.     

Analysis of non-deterministic drum scheduling

A non-deterministic drum scheduler reads a file of drum pages in unpredictable order because it selects, at each step, to read the first not previously read page after the reading heads. In this paper bounds are derived for the average latency time of such a scheduler when reading a file uniformly distributed over the drum circumference under the assumption that read requests are issued at uniformly and independently distributed points of the drum circumference.     

Modeling the solidification process in mortar due to internal mass exchange

Aim of the investigation is to model phase transition processes induced by mass transfer in multi-phase and multi-species mixtures. More specific, the innovative concept of using Superabsorbent Polymers (SAPs) as additives in grouting mortars represents a promising practical application, e. g. in mechanized tunneling. In this contribution, we focus on both the driving force for mass transfer as well as the kinetics for water migration, whereas an extension to the classical Theory of Porous Media (TPM) provides a reasonable modeling framework. As a result, the gelation process of the mixture can be described with respect to time. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inverse heat conduction problem in a thin circular plate and its thermal deflection

An inverse problem of transient heat conduction in a thin finite circular plate with the given temperature distribution on the interior surface of a thin circular plate being a function of both time and position has been solved with the help of integral transform technique and also determine the thermal deflection on the outer curved surface of a thin circular plate defined as 0 ? r ? a, 0 ? z ? h. The results, obtained in the series form in terms of Bessel’s functions, are illustrated numerically.     

The half-widths of the bands due to the skeletal vibrations of polyethylene molecules,free and under an applied load

The third-order phonon interactions in free polyethylene chains and polyethylene chains under load have been analyzed to obtain the theoretical temperature dependence of the half-widths of the bands due to the skeletal vibrations potentially active in the absorption and Raman spectra. The problems of the harmonic and anharmonic vibrational analysis of polymers under load are discussed.A. F. Ioffe Order of Lenin Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 3–11, January–February, 1972.     

Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field, where deformations are relatively small, a linear elastic constitutive behavior is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model using a subdomain formulation. The results show that, in the near field, the response of the soil is dominated by a vertically polarized shear wave, whereas in the far field, Rayleigh waves dominate the ground vibration and body waves are importantly attenuated. Finally, the computed ground vibrations are compared with the results of field measurements reported in the literature.     

Analysis of vibrations in large flexible hybrid systems

The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions makes it impossible to find exact analytical solutions. To address the problem, we use the asymptotical method of small parameters together with the numerical method of normal fundamental systems of solutions. These methods allow us to investigate vibrations, and a technique for determination of complex eigenvalues of the considered boundary value problem is developed. The conditions, at which vibration processes of different characteristics take place, are defined. The dependence of the vibration frequencies on the physical parameters of the hybrid system is studied. We show that introduction of different feedbacks into the system allows one to control the frequency spectrum, in which excitation of vibrations is possible.     

On fractal nature of groundwater level fluctuations due to rainfall process

Hourly resolution time series of groundwater level fluctuations are analyzed after removing the seasonal cycle. It is found that fluctuations of groundwater levels have fractal scaling and a persistent behavior. We show also that groundwater level fluctuations exhibit non-Gaussian heavy tailed probability distribution that is well fitted by the Lévy stable distribution. Implications of the present results on the groundwater system modeling as a fractional Lévy motion and the connection with the anomalous diffusion inside the soil are discussed.     

Analysis of an impact damper of vibrations

An analysis of the system with two degrees of freedom, which – provided that its parameters are properly selected – can operate as an impact damper of vibrations, is presented. The investigations have been carried out in two directions. In the first one, it has been assumed that the mass of the system playing the role of a damper is 10 times lower than the mass of the basic system and that this mass is suspended from a spring characterised by low stiffness. In the second case, the damper mass has been assumed to be four times smaller than the basic mass and it is suspended from a spring whose stiffness is four times lower than the stiffness of the basic system spring. Moreover, it has been shown that the impact damper of vibrations operates more efficiently than a classical dynamic vibration damper.     

Self-excited vibrations of deformable multibody systems due to friction: Explanation with the help of two point masses and a belt

The aim of this paper is to present the results of the investigations of the ability of self-excited vibrations due to friction in a planar simplified mechanical model, with a constant coefficient of friction. The Hurwitz criteria is used for the stability analysis and the determination of the critical value of the coefficent of friction. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Temporal and spatial chaos in a van der Waals fluid due to periodic thermal fluctuations

The Mel'nikov technique is applied to prove the existence of deterministic chaos in two problems for a van der Waals fluid. The first problem shows that temporal chaos results as a result of small time periodic fluctuations about a subcritical temperature when the fluid is initially quenched in the unstable spinoidal region. The second problem shows that spatial chaos arises from small spatially periodic flunctions in an infinite tube of fluid if the ambient pressure is appropriately chosen.     

Brownian fluctuations in space-time with applications to vibrations of rods

In this paper Brownian fluctuations in space-time are considered. Time is assumed to run alternately forward and backward, the alternance being marked by a Poisson process with rate λ. It is shown that the law of this motion is a solution of a fourth-order partial differential equation. Furthermore the law of this movement in the presence of an absorbing barrier is derived. The equation ruling the movement analysed, when λ = 0 and is submitted to the change t' = −it, reduces to the equation of vibrations of rods. This fact is exploited to obtain the solution of boundary value problems concerning the equation of vibrating beams by means of Brownian motion techniques.     

Modeling of thermal response and ablation in laminated glass fiber reinforced polymer matrix composites due to lightning strike

Thermal response and ablation of laminated glass fiber reinforced polymer matrix composites subjected to lightning strike are studied. The associated nonlinear time-dependent heat transfer model includes specific features of lightning arcs observed in physical measurements such as lightning channel radius expansion, non-uniform lightning current density, and associated heat flux. Moving spatially and temporally non-uniform lightning-current-induced heat flux boundary and moving boundary due to material phase transition caused by rapid surface ablation are also included. To predict moving phase boundary in the laminated anisotropic composites, an element deletion method is developed and embedded into finite element analysis (FEA), which is performed using ABAQUS. The Umeshmotion + ALE method based on the user subroutine Umeshmotion and arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique is also used, when applicable (i.e., moving phase boundary is confined within a top layer of the composite laminate). Heat transfer analysis is performed for a non-conductive laminated glass fiber reinforced polymer matrix composite panel representing the SNL 100-00 wind turbine tip. Thermal response of the panel subjected to pulsed and continuing lightning currents at three different lightning protection levels, LPL I, LPL II, and LPL III, is studied. Temperature-dependent anisotropic thermal properties of the composite panel are included in the analysis. The FEA results include temperature distributions and ablation zone profiles. The results show the Umeshmotion + ALE method is sufficient for the pulsed lightning current at all three LPL levels since the moving phase boundary, i.e. the ablation front, is found to be confined within the top layer of the laminate. For the continuing lightning currents at all three LPL levels, the Umeshmotion + ALE method is not applicable since the moving phase boundary comes to rest at depths exceeding the thickness of the top layer of the composite laminate.     

The closed form solutions for axisymmetric modeling of thermal stress due to repetitive pulse laser heating

Repetitive pulse laser heating is increasingly being used in the laser processing industry such as laser welding, laser cutting and laser drilling due to its energy accumulation effect. Modeling of thermo-mechanical coupling effect of repetitive pulse laser heating can enhance the understanding of its thermo physical process. In this paper, an axisymmetric modeling of thermal stress for repetitive pulse laser heating solid materials is introduced, and its closed form solutions are obtained based on a semi-analytical method. The accuracy and efficiency of the closed form solutions are verified by comparison with the existing numerical modeling software based on the finite element method. Distributions of thermal stress for different radial locations, axial locations and duty cycles are calculated, and effects of these parameters on temporal profile of the thermal stress distributions are analyzed. In the region of laser irradiation, three components of thermal stress are all shown as compressive stress. And outside the region of laser irradiation, the hoop component is shown as tensile stress. On the material surface, the change of thermal stresses is very sharp as a result of direct absorption of incident laser energy. With the increasing of the depth, the rises and decreases of thermal stresses become smooth gradually. The duty cycle has a significant effect on the profiles of thermal stresses. In the same conditions, the maximum value of thermal stresses gets higher as the duty cycle decreases. Results of this study can provide some theoretical basis for parameter inversion and optimization of repetitive pulse laser heating, as well as some corresponding experimental research.     

Analysis of free damped vibrations of laminated composite cylindrical shells

Damped free vibrations of multilayered composite cylindrical shells are investigated. Vibration and damping analysis of cylindrical shells is performed by using the first-order shear deformation theory (FOSDT). Based on other researchers' works, two damping models are developed, i.e., the energy method (EM), and the method of complex eigenvalues (MCE). Several numerical examples of the damped free vibration problem of laminated composite cylindrical shells have been solved and comparison has been made with the results of other authors.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 646–659, September–October, 1995.