In this stud y, we attempt to analyse free nonlinear vibrations of buckling in laminated composite beams. Two new methods are applied to obtain the analytical solution of the nonlinear governing equation of the problem. The effects of different parameters on the ratio of nonlinear to linear natural frequencies of the beams are studied. These methods give us an agreement with numerical results for the whole range of the oscillation amplitude.
Laplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.
People living in buildings may be exposed to dynamic actions. In the diagnosis and design of buildings there is an increasing need of taking into account these activities and verification of compliance of the building requirements for vibration comfort of people residing in buildings. This study presents the results of analysis of such criteria in the following standards: Polish PN-88/B-02171 [1], British BS 6472-1 [2], German DIN 4150 [3], and ISO international standards [4,5]. Basing on the results of this analysis and on the review of selected items of literature, the application of standards recommendations in diagnosis and design of buildings, as well as areas for further research on this subject is indicated. This article is an extended version of the conference paper [6] presented on the conference Urban Transport 2011.
In this paper, the authors consider the influence of axial load on the stability of shells of revolution subjected to external pressure. Shells of different geometry are investigated with emphasis to barrelled shells. The variable quantities are length L and meridional radius of curvature R1 of a shell. The constant parameters are: thickness of the shell h, mass ms and reference radius r0. The material of shells is steel. Numerical calculations were performed in the ABAQUS system. All the shells considered in this paper were subjected to axial compression to determine the force corresponding to the loss of stability in such conditions. A part of this force is then used to preload shell before the buckling analysis in the conditions of external pressure is started. The buckling shapes for shells of different geometry are presented with and without the influence of axial load. The ability of controlling the buckling strength and shape is discussed.
In the paper, the authors describe and solve the problem of optimum control of selected vibration forms in mechanical systems. Two illustrative examples have been used to present the procedure for determination of the optimum controller coefficients.
In the first example, a simplified mechanical system is considered, while in the second one – a rotor with magnetic bearing. In both cases, the integral performance indices have been defined in order to minimize the vibration level at selected points of the structures.
The system with the magnetic bearing is structurally unstable. For this reason, the authors present the way of finding the weight coefficients of integral performance index for unstable, multi-degrees-of-freedom system. In that way, the selected modal forms attain the previously assumed dynamic properties and the performance index takes the minimum value. The results of numerical analysis show that the proposed way is efficient and makes it possible to control selected forms of vibration in the system.
In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range.
The problem of influence of mechanical vibrations on a measurement is well known and analyzed for ground conditions. However, the problem becomes quite essential and difficult to solve in space conditions. The influence of vibrations on accuracy of the measurement was observed on MIPAS – ENVISAT and in PFS Mars Express.
This paper presents an experimental and theoretical investigation on sensitivity to mechanical disturbances of the Fourier-transform infrared spectrometer PFS.
A theoretical analysis has been performed in order to highlight the expected effect of the vibration, then laboratory tests have been designed and carried out for instrument characterization.
The theoretical investigation has been confirmed by experimental tests.
The data were distorted by errors that reflect the influence of vibrations on the instrument and temperature instability of the reference source.
The considerations are a perfect example presenting the scale of vibrations problem and the instability of the reference source in assessing accuracy of the measurement in space.
The article is a continuation of the authors’ elaboration (Dąbrowski, Dziurdź, 2016). The aim of this continuation is to prove that a proposed way of modelling and using the coherent analysis to filter nonlinear disturbances is a useful technique in vibroacoustic diagnostics. The thesis was proved by solving the task of diagnosing the damage of the gear of the car gearbox on the basis of the measurement of mechanical vibrations and the noise in the engine chamber.
A gear system transmits power by means of meshing gear teeth and is conceptually simple and effective in power transmission. Thus typical applications include electric utilities, ships, helicopters, and many other industrial applications. Monitoring the condition of large gearboxes in industries has attracted increasing interest in the recent years owing to the need for decreasing the downtime on production machinery and for reducing the extent of secondary damage caused by failures. This paper addresses the development of a condition monitoring procedure for a gear transmission system using artificial neural networks (ANNs) and support vector machines (SVMs). Seven conditions of the gear were investigated: healthy gear and gear with six stages of depthwise wear simulated on the gear tooth. The features extracted from the measured vibration and sound signals were mean, root mean square (rms), variance, skewness, and kurtosis, which are known to be sensitive to different degrees of faults in rotating machine elements. These characteristics were used as an input features to ANN and SVM. The results show that the multilayer feed forward neural network and multiclass support vector machines can be effectively used in the diagnosis of various gear faults.
In this paper a cross-shaped isolator consisting of cuboidal magnets and a cylindrical isolator are compared by resonance frequency to volume ratio and shape. Both isolators are capable of obtaining a low resonance frequency, i.e. 0.15 Hz and 0.01 Hz for the cross and cylinder, respectively. The volume of both isolators is comparable, only the shape is different, resulting in a tall structure with a small footprint for the cross and a flat with a large diameter cylindrical structure. A sensitivity analysis shows that due to the large amount of magnets, the cross-shaped isolator is less sensitive to manufacturing tolerances.
The present paper addresses the analysis of structural vibration transmission in the presence of structural joints. The problem is tackled from a numerical point of view, analyzing some scenarios by using finite element models. The numerical results obtained making use of this process are then compared with those evaluated using the EN 12354 standard vibration reduction index concept. It is shown that, even for the simplest cases, the behavior of a structural joint is complex and evidences the frequency dependence. Comparison with results obtained by empirical formulas reveals that those of the standards cannot accurately reproduce the expected behavior, and thus indicate that alternative complementary calculation procedures are required. A simple methodology to estimate the difference between numerical and standard predictions is here proposed allowing the calculation of an adaptation term that makes both approaches converge. This term was found to be solution-dependent, and thus should be evaluated for each structure.
A dynamic economy contributes to the increase in the number of workers exposed to mechanical vibration caused by machines and transport equipment. As the means of transport are insufficiently recognised sources of mechanical vibrations, this article presents the results of whole-body and hand-arm vibration tests of 30 most common means of in-house transport. An analysis of vibration signals recorded at each workstation according to PN-EN 14253 and PN-EN ISO 5349 made it possible to determine the weighted values of components of directional vibration acceleration and the values of daily vibration exposure A(8).
In order to assess exposure to whole-body and hand-arm vibration at the tested workstations of in-house transport, indices of vibration hazard related to admissible values, the total evaluation index (developed in a previous study at CIOP-PIB) and a three-degrees scale for assessing exposure to vibrations were used. The assessment showed that the workstations were a major hazard. Vibration hazards at all those workstations were classified as either medium or high.
The reduction of structural vibrations on the example of two pedestrian bridges (in Poznań and Wrocław) with using of tuned mass dampers (TMD) has been presented in the paper. The results of theoretical and experimental studies of pedestrian bridge vibrations has been described and discussed. Basing on the results of calculations and measurements, tuned mass dampers (TMD) has been designed and mounted in the structure of the bridges. The measurements after the assembly of TMD show a high efficiency of vibration damping.
The acoustic properties of the sitar string are studied with the aid of a physical model. The nonlinearity of the string movement caused by the bridge acting as an obstacle to the vibrating string is of special interest. Comparison of the model's audio output to recordings of the instrument shows interesting similarities. The effects dispersion and bridge have on the sound of the instrument are demonstrated in the model.