Modern Practice in Stress and Vibration Analysis VI

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Authors: O.V. Menshykov, I.A. Guz
Abstract: This paper concerns fracture dynamic problems for elastic cracked solids with allowance for crack faces contact interaction. The contact problem for a penny-shaped crack with an initial opening under normally incident tension-compression wave is solved by the method of boundary integral equations. The solution is compared with those obtained without allowance for crack faces contact interaction for various values of the initial opening.
Authors: M.R.M. Aliha, R. Ashtari, Majid R. Ayatollahi
Abstract: A series of fracture toughness tests have been conducted on a type of coarse grain marble. The tests were carried out either in pure mode I or in pure mode II conditions by using the cracked chevron notched Brazilian disc (CCNBD) specimen. A total number of 44 CCNBD specimens were tested, half in pure mode I and the rest in pure mode II, to obtain reliable values for mode I and mode II fracture toughness (KIc and KIIc) of the tested marble. The average value of KIc for this marble was approximately about 1.12 MPa m showing a good agreement with those reported for similar coarse grain marbles. The mode II fracture toughness was found to be 2.25 MPa m in average which is approximately twice the mode I fracture toughness. However, the conventional fracture criteria suggest that the mode I fracture toughness should be higher than the mode II fracture toughness, (KIc>KIIc). According to these criteria, the ratio of KIIc / KIc is a figure typically between 0.63 and 0.96. It is shown in this paper that enhanced mode II fracture toughness of CCNBD specimen could be due to the effects of highly negative T-stress when the specimen is subjected to mode II. It is also shown that an improved prediction for the ratio KIIc / KIc can be achieved when the effect of T-stress is taken into account.
Authors: R. Hashemi, Majid R. Ayatollahi
Abstract: The mechanical properties of composite laminates play a key role in the success of composite reinforcement method, but various investigations suggest that the stiffness of epoxybased composites is sensitive to the variation of moisture ratio and temperature of the working environment. The aim in this research is to characterize the effect of hygrothermal aged composite patch on the strength of repaired cracks, under mixed mode I/II conditions. For this purpose a reinforced sheet, i.e. a crack fastener hole specimen is examined by using a finite element simulation. The crack tip parameters and fracture characteristics of repaired cracks are determined as a function of the total amount of moisture inside the composite patch. The results of this study show that the performance of composite reinforcement technique depends on the amount of water absorption within the bonded patches.
Authors: Giulio Fanti, R. Basso, V. Montauti
Abstract: The ISO 6267 standard defines a damping measuring method in terms of the half-time of the vibration of clamped alpine skis that is mainly related to the first vibration mode only. By means of the experimental test done in laboratory, it is shown that this method is not able to completely characterize the damping of the skis that depends on the vibration mode considered. For example in the case a ski sample, damping ratio varies from 0.45%±0.05% of the first mode to 2.1%±0.1% of the fourth one. The experimental test done on ski tracks by means of piezo-accelerometers placed on the skis running at speed of 12.5 m/s showed that the skis vibrate according to a combination of at least the first 4 vibration modes and that the snow better excites frequencies greater than the first one. As the excitation frequencies on the skis during the descent are much higher than the first natural frequency of the ski, it appears not correct to hypothesize that only the damping coefficient relative to the first natural frequency is representative of the ski vibrations. To improve the UNI ISO 6267 standard, a new method based on the Fourier Transform filtering to separate the time history into the vibration components is proposed for the characterization of the ski damping that is variable with its natural modes.
Authors: S. Nachum, E. Altus
Abstract: In this study the natural frequencies and mode shapes of the kth order of nonhomogeneous (deterministic and stochastic) rods are found. The solution is based on the functional perturbation method (FPM). The natural frequency and mode shape of the kth order is found analytically to any desired degree of accuracy. In the deterministic it is shown that the FPM accuracy range for the frequency ω and the mode shape is less then 1%. The stochastic case demonstrates the power of this method. The material and geometrical properties will be considered as statistically homogeneous random field with exponential two-point correlation. It is shown that the accuracy depends on the stochastic information used, the correlation distance (roughly the “grain size”), and whether we are interested in the properties of ω or ω2.
Authors: Rodanthi Salamaliki-Simpson, Stefan Kaczmarczyk, Phil Picton, Scott Turner
Abstract: This paper focuses on the investigation of the autoparametric coupling effects and modal interactions in a suspension rope system with a time varying length. Equations of motion of a multi-degree-of-freedom discrete, non-stationary and non-linear model are presented and are used to analyze the dynamic response of an elevator suspension rope system under resonance conditions. The equations of motion involve quadratic and cubic non-linear terms which are responsible for the modal interaction between the lateral and longitudinal oscillations of the rope and the car motions. The model takes into account the periodic excitations caused by motion of the host structure. The results confirm that adverse responses may arise and internal autoparametric resonance phenomena may occur.
Authors: C. Li, S. Hu, J. Li
Abstract: This paper presents the application of modal analysis and parameter identification using data of random vibration test to a cylinder structure. It is deduced that the impulse response function can be substituted by the cross-correlation function computed directly from the response-only data based on the white noise excitation or broadband input. So the modal parameter identification can be done by the least squares complex exponential (LSCE) method. And the modal parameters are obtained from the random vibration test data by the complex exponential method. Compared with the results of traditional modal test, the results of random vibration test are proved to be correct, and also the feasibility of this idea is proved well.
Authors: David J. Rodrigues, Alan R. Champneys, Michael I. Friswell, R.E. Wilson
Authors: Piotr Koziol, Cristinel Mares, Ibrahim Esat
Abstract: This paper deals with the mathematical model of dynamic behaviour of a beam resting on viscoelastic random foundation for which the modulus of subgrade reaction is assumed to be a homogeneous random function of the space variable. An approximate analytical solution for the fourth-order differential equation with random parameters is obtained in the case of a ∞ C -class correlation function. This higher order regularity of correlation function implies the regularity of associated stochastic function [1] in the sense of the mean-square analysis [2]. The numerical results for the average displacement have been obtained by using Bourret’s approximation method. A special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in the numerical examples.
Authors: Irina Trendafilova, Emil Manoach, Matthew P. Cartmell, Marek Krawczuk, Wiesław M. Ostachowicz, Magdalena Palacz
Abstract: This work was motivated by the recent NATO funded research on preventing disasters from collapse and improving the safety of aircraft structures. It considers the problem for vibrationbased damage detection in aircraft panels modelled as isotropic plates. The explored method does not use any assumptions of model or linearity, it is simply based on pure signal analysis of the vibration response of plates. FE modelling is used to model the plate’s dynamic response in its intact and in its damaged state. The signals obtained are analysed using multivariate analysis applied in the measured frequency domain. This reduces the data dimensionality and is expected to have a clustering effect. At this stage the measured data is transformed into features – new variables- which have smaller dimension than the initial ones and make the categories more distinguishable. Then a very simple pattern recognition (PR) method is applied to discriminate between the two categories of data -data coming from the undamaged plate and data coming from the damaged plate. This is the second stage when the obtained features are used for the actual recognition between the defined categories. The paper suggests the use of the Karhunen-Loeve transform in order to extract features from the measured frequency response functions of the plate. When the data dimensionality is brought down to two the response of the plate can be visualised. The clustering effect on the features coming from undamaged plate and those from the damaged is obvious.

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