The purpose of the work is dynamic analysis of passive dampers used in structural systems to reduce excessive vibrations caused by wind or earthquakes. Special systems are considered that contain inerter, i.e. device using rotational inertia, in combination with a viscoelastic damper. The so-called fractional models of viscoelastic dampers describe their dynamic behavior in a wide frequency range using a small number of model parameters. To describe material behavior over a wider frequency range, the time-temperature superposition principle is used. The shifting factor is calculated from the well-known William-Landel-Ferry formula. This allows for determination of damper parameters at any temperature based on the parameters obtained at the reference temperature. Laplace transformation of the derived equations of motion leads to the non-linear eigenproblem, which could be solved using the continuation method. The influence of temperature on the dynamic characteristics of the system is examined.
In the present paper the numerical approach for the modeling of the flow past rotating geometries is presented. Practical methods for two cases are described: the one where whole domain is moving with uniform angular velocity, where the rotation might be included in the governing equations only (in the terms related to Coriolis and centrifugal forces), and the one where part of the domain is rotating, whereas another one is stationary. The second case is illustrated by examples describing the steady and transient flow around a rotating propeller and by a centrifugal pump. Simulations are performed using OpenFOAM CFD solver, with the models covering flow rotation: MRF (multiple reference frame) and AMI (arbitrary mesh interface).
This paper presents the development of a mathematical model of a bio-mechanical system: human ‒ power tool, on the example of an impact drill. The physical model of the operator's upper limb with 5 degrees of freedom, in accordance with ISO 10068 standard was used. The paper presents the results of theoretical analysis regarding elementary and net displacements for individual directions. Moreover mathematical relationships describing them were determined. The result of the synthesis of these relations and the adopted (in accordance with the standard) physical model of the upper limb is the general matrix form of differential equations of motion of the analysed bio-mechanical system, built using the Lagrange’s equations of the second kind.
The objective of this work is to demonstrate the use of multiscale curvature tensor analysis to characterize deformations of piezoelectric bimorph actuator and to study the relation between loaded electric charge and the resulting deformed surface curvature. In particular, the strength of the correlations between surface shape characterized by curvature parameters (i.e., principal, Gaussian or mean curvature) and charge density is sought. The impact that the scale of the analysis of the curvature can have on the values of the curvature parameters for the deformed surfaces and the correlation with discharge energy is also studied. In this study the deformations of piezoelectric bimorph actuators are studied. In order to achieve quasi-static measurements, a dedicated charge amplifier was built to supply charge to the actuator. The deformations were then measured by Polytec® 3D laser scanning vibrometer PSV-400 by integration of captured motion. The obtained data was used to calculate curvature tensor field at multiple scales by applying the normal-based method. Principal, mean and Gaussian curvature was calculated at multiple scales and were correlated with applied charge. The obtained results contribute to better understanding of piezoelectric behavior under electric field.
External boundaries of acoustic devices can channel sound propagation, and in some cases can create buildup or attenuation of acoustic energy within a confined space. In this paper, it is proposed an efficient practical numerical method (based on FEM) of calculation of attenuation of sound power transmission through ducts. The method shows its viability by presenting the reasonably consistent anticipation of the experimental result. One can observe the mechanical behaviour of the duct’s medium for lower frequencies (high transmission loss) and wave behaviour for higher frequencies (small or zero attenuation). The authors proved that mechanical vibrations of medium reduce the possibility of acoustic energy transmission in duct systems. The radiation impedance for the duct is calculated as well.
The subject of the paper is a circular plate with clamped edge supported on elastic foundation. Mechanical properties of the plate symmetrically vary in its thickness direction. Free axisymmetric flexural vibration problem of the plate with consideration of the shear effect is analytically studied. Two partial differential equations of motion based on the Hamilton principle are obtained. The system of equations is analytically solved and the fundamental natural frequency of axisymmetric vibration for example plates is derived.
Vibration mills used in the industry are an alternative to conventional gravity mills. Compared to gravity mills they have much lower demand for energy of the milling process, significantly lower mass and several times lower cost of raw materials milling. In addition, they have much greater technological possibilities, which justifies their use in many cases. Apart from a number of advantages, vibration mills have disadvantages. The dynamics of work causes a significant transfer of vibrations to the ground and a major load on the vibrator bearings. As a result, they require temperature monitoring and the use of complex cooling systems. It is possible to reduce these negative effects by using new construction solutions.
Medical robots with an instant center of rotation mechanism in a trocar are used for operating a human body or servicing artificial organs. The result of the work is the development of a multicriteria optimization model of a discussed medical robot, considering safety factor, first eigenfrequency and buckling coefficient as a criteria. The article also analyzes two issues of mechanics, the natural frequency and linear buckling. A discrete mesh model of a novel robot design with ten degrees of freedom and ended with a scalpel was developed based on finite element method. For the given loads and supports, a multi-criteria optimization model was evolved, which was solved by using the response surface method and the multi-objective genetic algorithm. The results section shows the Pareto fronts for the criteria and geometrical dimensions of the kinematic chain. The courses of resonant vibrations and buckling strains were also characterized. The solved optimization model gives correct values for the adopted criteria. The values of resonance were defined, which makes it possible to select mechatronic drive systems in terms of the input they generate. Variability of the resonant vibrations phenomena, as well as shapes and directions of buckling, provide information about the displacements taking place in the medical robot system.
This paper concerns a substitute model of the metal-elastomer vibroinsulator that can find use in the mathematical description of vibration machine suspensions. In the case of a plane system, the flexibility matrix of the vibroinsulator was derived and two typical configurations of machine suspensions: symmetrical and asymmetrical, were analysed. For the case of a spatial motion, the elastic matrix of the vibroinsulator and the method of determining its elements was specified. Due to the non-linear character of the vibroinsulator's work, which is caused by large deformations of elastomeric elements under static loads, the analysis was limited to the surroundings of the work point and linear model. The results of theoretical analyses were confirmed by experimental tests.
The current work is devoted to the determination of dispersion curves for elastic wave modes. The studied elastic waves propagate across metal-fiber hybrid composites. In order to solve the problem, special software has been developed with the use of C++. This software works with the MS Windows operating system and the proposed solution is based on the multi-threading mechanism. It makes possible to significantly speed up the calculations. The relatively new approach is used namely the stiffness matrix method. At the very beginning, the dispersion curves are determined for the traditional composite materials of cross-ply configuration, for which the layers are made of glass fiber/epoxy resin and carbon fiber/epoxy resin. The impact of the total number of layers on the dispersion curves is investigated. Next, the influence of the thickness of the layers, which are made of aluminum alloy, on the dispersion characteristic is studied. In the second case, it is assumed that the total thickness of the composite material wall for all cases is identical.
Diagnosing the condition of the machine during its operation by non-invasive methods is most often reduced to measuring the acceleration of vibrations occurring on the housing, as close as possible to the observed element or changes in sound pressure in the immediate vicinity of the machine. For proper inference about the condition of a given machine element, the registered signals should be undisturbed by signals coming from other components and free from external interference. In the case of simple stationary machines, it is quite simple, but in the case of more complex systems, such as a car, which in addition is in motion, things get complicated In the available literature we find examples of the effectiveness of using ordinary coherence function to separate signals from two independent sources[1,2,3]. This work presents attempt to build an algorithm that uses signals from a multi-point measurement system to analyze multiple coherence functions, which allows to separate signals from various sources. It can then get diagnostic information from the signal thus separated. The effectiveness of the algorithm was tested on a model simulating signal mixing, and then using signal coherence function and knowledge of the transmittance function, the signals were separated.
The authors investigate selected solutions, to show how hard it is to find the ones that would simultaneously: dose the feed, work on a centrifugal drive, and could be freely scalable. Moreover, the authors introduce a classification of analysed cases by their amplitude-frequency characteristics. Exemplary characteristics of simplified models allow distinguishing which one of them is suitable to be adopted for dosing conveyor (feeder). The authors come to the conclusion that it is worth to begin the design process exactly by composing a proper mechanical system, in respect of amplitude-frequency characteristics. Furthermore, the paper points out the most important features of vibratory feeders, capable of dosing bulk materials.
The article presents a comparative analysis of determined spectral responses of the airborne sound insulation of single homogeneous baffles using computational and experimental methods. Calculations using theoretical models, such as mass law, the Sharp and Davy models, SoundFlow software and laboratory tests concerned nine plates made of plastic, steel, aluminium and rubber, which are homogeneous materials. These materials are used in the construction of walls in vibroacoustic protection, such as acoustic barriers, machine operating field shields and sound insulating enclosures. Apart from analysing the spectral responses of the sound insulation of the plates, the weighted single-number sound reduction indices Rw, calculated by using prediction methods and laboratory measurements, were compared. Research has shown computational errors of about 6-7 dB for mass law and the Sharp model and about 3 dB for the Davy and Davy-Sharp models and SoundFlow software.
In the paper the influence of machining accuracy of mechanism links on their dynamic response is under investigation. As an example a of planar slider-crank mechanism is studied. The influence of different crosssection area within the assumed tolerance on the dynamic behaviour of mechanism’s connection rod is investigated. For vibration analysis of links the finite element method is used with Bernoulli-Euler beam elements. The calculation were conducted for nominal dimensions of the cross section of the crank and for the two cases for connecting rod: 1) for the maximal stiffness and 2) for the minimal stiffness obtained within the given tolerance. The results of analysis show that the changes in dynamic response for different cross-sectional area of mechanism links, within the assumed tolerance of machining, can be quite significant in the case of high-speed precise mechanisms and manipulators.
This work is devoted to further research and improvement of the vibroacoustic condition monitoring of complex rotation system during operation. The low-frequency vibration and acoustic noise in the range 0-10 kHz is used as diagnostic information. We propose to use Bispectrum (BS) Analysis at the first level of signal processing, and Fractal Analysis of BS contour images at the second level of signal processing for the diagnosis of small imbalance of rotation system. The experimental studies of forced vibrations of the physical model (PM) of the rotation system are carried out under steady-state and non-steady-state rotation excitations. The results of the BS Analysis of vibroacoustical signals, which are emitted by a rotating PM during different excitation modes, are processed in order to determine fractal box-counting dimension (Minkowski dimension). The research shows that a small imbalance can be efficiently detected by the proposed multilevel signal processing in all modes of PM operation.
The main purpose of navigation systems is a position determination different moving objects. For standard inertial navigation systems algorithm, the initial position data are required. Normally these data may be determined by astronomical techniques or satellite and radio navigation systems. However, astronomical techniques depend on climate conditions and satellite and radio systems can be disturbed by electromagnetic countermeasures. It is proposed to use an Inertial Measurement Unit (IMU) and a navigation computer for autonomous determination of an initial position. IMU should be composed of three accelerometers, three gyroscopes and a signal processing circuit. The method proposed the latitude determination uses projections of the Earth’s rate measured by orthogonal IMU gyroscopes and projections of the gravity acceleration measured by orthogonal IMU accelerometers. Experimental tests of the IMU with a ring laser gyros triad and precision pendulum accelerometers confirmed the efficiency of the method on a fixed base. The behavior of the latitude determination under vibration is researched. The latitude determination under vibration was considered analytically by Power Spectral Density theory. It was estimated a variance of the latitude under the broad-band vibration. The method operability under harmonic and random vibration of the base at the real time is considered.
