Stefan Berczyński

Vibration of Steel–Concrete Composite Beams Using the Timoshenko Beam Model

In this paper we present a solution of the problem of free vibrations of steel–concrete composite beams. Three analytical models describing the dynamic behavior of this type of constructions have been formulated: two of these are based on Euler beam theory, and one on Timoshenko beam theory. All three models have been used to analyze the steel–concrete composite beam researched by others. We also give a comparison of the results obtained from the models with the results determined experimentally. The model based on Timoshenko beam theory describes in the best way the dynamic behavior of this type of construction. The results obtained on the basis of the Timoshenko beam theory model achieve the highest conformity with the experimental results, both for higher and lower modes of flexural vibrations of the beam. Because the frequencies of higher modes of flexural vibrations prove to be highly sensitive to damage occurring in the constructions, this model may be used to detect any damage taking place in such constructions.

Experimental Verification of Natural Vibration Models of Steel-concrete Composite Beams

The article presents the results of experimental dynamic investigations of three steel-concrete composite beams. The beams differed in the stiffness of their shear connection. Steel stud connectors were used in B1 and B2 beams, whereas in B3 beam a perforated steel slat was used. The main goal of the study was to determine basic dynamic characteristics of the beams. Impulse excitation was used in the investigations. The obtained results made it possible to validate two numerical models: (i) a continuous one which was developed using the Timoshenko beam theory; (ii) a discrete one which was developed according to the rigid finite element (RFE) method. After validation of the parameters of both models it turned out that both models provide results consistent with experimental results.

Identi cation of the Dynamic Models of Machine Tool Supporting Systems. Part I: An Algorithm of the Method

In this paper we present an original algorithm for the identification of dynamic models of machine tool supporting systems on the basis of limited information about an object contained in the experimentally determined frequency response characteristics obtained for a given excitation. We have described the way of creating models that are later to be identified. The models have been built in the convention of the rigid finite element method, which is complemented by the added option that allows us to model slideway joints. Any stiffness and damping coefficients of any spring–damping elements of a given model can be estimated by means of the elaborated method. In order to select decision variables, we have used a sensitivity analysis of the frequency response characteristics on changes in the values of a models parameters. The Fishers model of uncertainty has been adopted for the algorithm. The minimization of the identification criterion has been carried out using gradient methods. In order to assess the uniqueness of the obtained solutions the Cramer– Rao information inequality has been used. On the basis of the presented algorithm a computer program IDENT has been elaborated. It enables an effective estimation of parameters of machine tool supporting systems. The numerical tests have confirmed both the reliability of the algorithm and the high effectiveness of the IDENT program. In this paper we present both the results and the commentary of one such test.

Nonlinear evolution of two fast-particle-driven modes near the linear stability threshold

A system of two coupled integro-differential equations is derived and solved for the non-linear evolution of two waves excited by the resonant interaction with fast ions just above the linear instability threshold. The effects of a resonant particle source and classical relaxation processes represented by the Krook, diffusion, and dynamical friction collision operators are included in the model, which exhibits different nonlinear evolution regimes, mainly depending on the type of relaxation process that restores the unstable distribution function of fast ions. When the Krook collisions or diffusion dominate, the wave amplitude evolution is characterized by modulation and saturation. However, when the dynamical friction dominates, the wave amplitude is in the explosive regime. In addition, it is found that the finite separation in the phase velocities of the two modes weakens the interaction strength between the modes.

Identification of the Dynamic Models of Machine Tool Supporting Systems. Part II: An Example of Application of the Method

In this paper we present the results of the parameter identification of the spring–damping elements of the model of a real machine tool supporting system. The identification was carried out on the basis of the experimentally determined frequency response characteristics of the tested FWD-32J milling machine. We describe the experiments that were conducted in order to determine these characteristics and we give an example of how the identified model of this machine can be applied in simulation tests with a view to minimizing the relative vibrations between the tool and the workpiece. The model of the tested machine was created in the convention of the rigid finite element method complemented by the added option that allows us to model slideway joints. The frequency response characteristics that were used to identify, verify, and validate the model were determined by means of noise excitation. An originally elaborated computer program IDENT was used in the computations, and this has been described in detail in Part I of this paper. Very good consistency between the model and the object was achieved. The simulation tests that have been carried out made it possible to locate the weak points in the supporting system of the investigated machine tool.

On the wave amplitude blow-up in the Berk–Breizman model for nonlinear evolution of a plasma wave driven resonantly by fast ions

In this paper the Berk–Breizman (BB) model of plasma wave instability arising on the stability threshold is considered. An interesting although physically unacceptable feature of the model is the explosive behaviour occurring in the regime of small values of the collision frequency parameter. We present an analytical description of the explosive solution, based on a fitting to the numerical solution of the BB equation with the collision parameter equal to zero. We find that the chaotic behaviour taking place for small but non-zero values of the collision parameter is absent in this case; therefore, chaotic behaviour seems to be an independent phenomenon not directly related to the blow-up regime. The time and the velocity dependence of the distribution function are found numerically and plotted to better understand what actually happens in the model. It allows us to obtain a good qualitative understanding of the time evolution of the mode amplitude including the linear growth of the amplitude, reaching its maximum and then decreasing towards the zero value. Nevertheless, we have no satisfactory physical explanation of the amplitude evolution when the amplitude vanishes at some time and then revives but with an opposite phase.

Mechanical analogy of the nonlinear dynamics of a driven unstable mode near marginal stability

The universal integrodifferential model equation derived by Berk et al. [Phys. Rev. Lett. 76, 1256 (1996)] for studying the nonlinear evolution of unstable modes driven by kinetic wave particle resonances near the instability threshold is reduced to a differential equation and next as a further simplification to a nonlinear oscillator equation. This mechanical analogy properly reproduces most of the essential physics of the system and allows an understanding of the qualitative features of the theory of Berk et al.

Model Order Reduction Adapted to Steel Beams Filled with a Composite Material

In presented paper, an analysis of model order reduction (MOR) techniques applied to steel beams filled with a composite material is presented. This research concerns specific construction solutions used in technological machines. The analyzes concern three reduction methods: Guyan reduction also referred as static condensation, Craig-Bampton reduction and Kammer reduction. These techniques are applied to matrix equations describing steel beams filled with a composite material model, established by the finite element method (FEM). The article contains information about preparation of the full model and model parameters identification process. To verify FEM model quality its results are compared to experimental modal analysis results. The analysis compares and contrasts the MOR techniques by considering the nature of the individual algorithms and analyzing results of numerical example. The comparison of reduced models computational time at subsequent stages have also been made.

Modeling of Surface Geometric Structure State After Integratedformed Milling and Finish Burnishing

Abstract The article deals with computer-based modeling of burnishing a surface previously milled with a spherical cutter. This method of milling leaves traces, mainly asperities caused by the cutting crossfeed and cutter diameter. The burnishing process - surface plastic treatment - is accompanied by phenomena that take place right in the burnishing ball-milled surface contact zone. The authors present the method for preparing a finite element model and the methodology of tests for the assessment of height parameters of a surface geometrical structure (SGS). In the physical model the workpieces had a cuboidal shape and these dimensions: (width × height × length) 2×1×4.5 mm. As in the process of burnishing a cuboidal workpiece is affected by plastic deformations, the nonlinearities of the milled item were taken into account. The physical model of the process assumed that the burnishing ball would be rolled perpendicularly to milling cutter linear traces. The model tests included the application of three different burnishing forces: 250 N, 500 N and 1000 N. The process modeling featured the contact and pressing of a ball into the workpiece surface till the desired force was attained, then the burnishing ball was rolled along the surface section of 2 mm, and the burnishing force was gradually reduced till the ball left the contact zone. While rolling, the burnishing ball turned by a 23° angle. The cumulative diagrams depict plastic deformations of the modeled surfaces after milling and burnishing with defined force values. The roughness of idealized milled surface was calculated for the physical model under consideration, i.e. in an elementary section between profile peaks spaced at intervals of crossfeed passes, where the milling feed fwm = 0.5 mm. Also, asperities after burnishing were calculated for the same section. The differences of the obtained values fall below 20% of mean values recorded during empirical experiments. The adopted simplification in after-milling SGS modeling enables substantial acceleration of the computing process. There is a visible reduction of the Ra parameter value for milled and burnished surfaces as the burnishing force rises. The tests determined an optimal burnishing force at a level of 500 N (lowest Ra = 0.24 μm). Further increase in the value of burnishing force turned out not to affect the surface roughness, which is consistent with the results obtained from experimental studies.