Influence of imperfect interfaces on bending and vibration of laminated composite shells

This paper is devoted to modeling elastic behavior of laminated composite shells, with special emphasis on incorporating interfacial imperfection. The conditions of imposing traction continuity and displacement jump across each interface are used to model imperfect interfaces. Vanishing transverse shear stresses on two free surfaces of a shell eliminate the need for shear correction factors. A linear theory underlying elastostatics and kinetics of laminated composite shells in a general configuration is presented from Hamilton's principle. In the special case of vanishing interfacial parameters, this theory reduces to the conventional third-order zigzag theory for perfectly bonded laminated shells. Numerical results for bending and vibration problems of laminated circular cylindrical panels are tabulated and plotted to indicate the influence of the interfacial imperfection. (C) 2000 Elsevier Science Ltd. All rights reserved.

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.

Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.

Updating finite element models using measured vibration data

The modelling of mechanical structures using finite element analysis has become an indispensable stage in the design of new components and products. Once the theoretical design has been optimised a prototype may be constructed and tested. What can the engineer do if the measured and theoretically predicted vibration characteristics of the structure are significantly different? This thesis considers the problems of changing the parameters of the finite element model to improve the correlation between a physical structure and its mathematical model. Two new methods are introduced to perform the systematic parameter updating. The first uses the measured modal model to derive the parameter values with the minimum variance. The user must provide estimates for the variance of the theoretical parameter values and the measured data. Previous authors using similar methods have assumed that the estimated parameters and measured modal properties are statistically independent. This will generally be the case during the first iteration but will not be the case subsequently. The second method updates the parameters directly from the frequency response functions. The order of the finite element model of the structure is reduced as a function of the unknown parameters. A method related to a weighted equation error algorithm is used to update the parameters. After each iteration the weighting changes so that on convergence the output error is minimised. The suggested methods are extensively tested using simulated data. An H frame is then used to demonstrate the algorithms on a physical structure.

The prediction of vibration in large electric machines

This thesis reports the development of a reliable method for the prediction of response to electromagnetically induced vibration in large electric machines. The machines of primary interest are DC ship-propulsion motors but much of the work reported has broader significance. The investigation has involved work in five principal areas. (1) The development and use of dynamic substructuring methods. (2) The development of special elements to represent individual machine components. (3) Laboratory scale investigations to establish empirical values for properties which affect machine vibration levels. (4) Experiments on machines on the factory test-bed to provide data for correlation with prediction. (5) Reasoning with regard to the effect of various design features. The limiting factor in producing good models for machines in vibration is the time required for an analysis to take place. Dynamic substructuring methods were adopted early in the project to maximise the efficiency of the analysis. A review of existing substructure- representation and composite-structure assembly methods includes comments on which are most suitable for this application. In three appendices to the main volume methods are presented which were developed by the author to accelerate analyses. Despite significant advances in this area, the limiting factor in machine analyses is still time. The representation of individual machine components was addressed as another means by which the time required for an analysis could be reduced. This has resulted in the development of special elements which are more efficient than their finite-element counterparts. The laboratory scale experiments reported were undertaken to establish empirical values for the properties of three distinct features - lamination stacks, bolted-flange joints in rings and cylinders and the shimmed pole-yoke joint. These are central to the preparation of an accurate machine model. The theoretical methods are tested numerically and correlated with tests on two machines (running and static). A system has been devised with which the general electromagnetic forcing may be split into its most fundamental components. This is used to draw some conclusions about the probable effects of various design features.

Mechanical vibration characteristics of bell-type pump maintings

This thesis describes an analytical and experimental study to determine the mechanical characteristics of the pump mounting, bell housing type. For numerical purposes, the mount was modelled as a thin circular cylindrical shell with cutouts, stiffened with rings and stringers; the boundary conditions were considered to be either clamped-free or clamped-supporting rigid heavy mass. The theoretical study was concerned with both the static response and the free vibration characteristics of the mount. The approach was based on the Rayleigh-Ritz approximation technique using beam characteristic (axial) and trigonometric (Circumferential) functions in the displacement series, in association with the Love - Timoshenko thin shell theory. Studies were carried out to determine the effect of the supported heavy mass on the static response, frequencies and mode shapes; in addition, the effects of stringers, rings and cutouts on vibration characteristics were investigated. The static and dynamic formulations were both implemented on the Hewlett Packard 9845 computer. The experimental study was conducted to evaluate the results of the natural frequencies and mode shapes, predicted numerically. In the experimental part, a digital computer was used as an experiment controller, which allowed accurate and quick results. The following observations were made: 1. Good agreements were obtained with the results of other investigators. 2. Satisfactory agreement was achieved between the theoretical and experimental results. 3. Rings coupled the axial modal functions of the plain cylinder and tended to increase frequencies, except for the torsion modes where frequencies were reduced. Stringers coupled the circumferential modal functions and tended to decrease frequencies. The effect of rings was stronger than that of stringers. 4. Cutouts tended to reduce frequencies; in general, but this depends on the location of the cutouts; if they are near the free edge then an increase in frequencies is obtained. Cutouts coupled both axial and circumferential modal functions. 5. The supported heavy mass had similar effects to those of the rings, but in an exaggerated manner, particularly in the reduction of torsion frequencies. 6. The method of analysis was found to be a convenient analytical tool for estimating the overall behaviour of the shell with cutouts.

Damage location in structures by monitoring vibration characteristics

The aim of this work was to investigate the feasibility of detecting and locating damage in large frame structures where visual inspection would be difficult or impossible. This method is based on a vibration technique for non-destructively assessing the integrity of structures by using measurements of changes in the natural frequencies. Such measurements can be made at a single point in the structure. The method requires that initially a comprehensive theoretical vibration analysis of the structure is undertaken and from it predictions are made of changes in dynamic characteristics that will occur if each member of the structure is damaged in turn. The natural frequencies of the undamaged structure are measured, and then routinely remeasured at intervals . If a change in the natural frequencies is detected a statistical method. is used to make the best match between the measured changes in frequency and the family of theoretical predictions. This predicts the most likely damage site. The theoretical analysis was based on the finite element method. Many structures were extensively studied and a computer model was used to simulate the effect of the extent and location of the damage on natural frequencies. Only one such analysis is required for each structure to be investigated. The experimental study was conducted on small structures In the laboratory. Frequency changes were found from inertance measurements on various plane and space frames. The computational requirements of the location analysis are small and a desk-top micro computer was used. Results of this work showed that the method was successful in detecting and locating damage in the test structures.

Investigations into vibration and sound transmission characteristics of cylindrical shells

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On waveform analysis, the adaptive task technique, and the effect of vibration on manual control skill

A re-examination of fundamental concepts and a formal structuring of the waveform analysis problem is presented in Part I. eg. the nature of frequency is examined and a novel alternative to the classical methods of detection proposed and implemented which has the advantage of speed and independence from amplitude. Waveform analysis provides the link between Parts I and II. Part II is devoted to Human Factors and the Adaptive Task Technique. The Historical, Technical and Intellectual development of the technique is traced in a review which examines the evidence of its advantages relative to non-adaptive fixed task methods of training, skill assessment and man-machine optimisation. A second review examines research evidence on the effect of vibration on manual control ability. Findings are presented in terms of percentage increment or decrement in performance relative to performance without vibration in the range 0-0.6Rms'g'. Primary task performance was found to vary by as much as 90% between tasks at the same Rms'g'. Differences in task difficulty accounted for this difference. Within tasks vibration-added-difficulty accounted for the effects of vibration intensity. Secondary tasks were found to be largely insensitive to vibration except secondaries which involved fine manual adjustment of minor controls. Three experiments are reported next in which an adaptive technique was used to measure the % task difficulty added by vertical random and sinusoidal vibration to a 'Critical Compensatory Tracking task. At vibration intensities between 0 - 0.09 Rms 'g' it was found that random vibration added (24.5 x Rms'g')/7.4 x 100% to the difficulty of the control task. An equivalence relationship between Random and Sinusoidal vibration effects was established based upon added task difficulty. Waveform Analyses which were applied to the experimental data served to validate Phase Plane analysis and uncovered the development of a control and possibly a vibration isolation strategy. The submission ends with an appraisal of subjects mentioned in the thesis title.

Vibration in electromagnetically heated steel

When a ferromagnetic steel billet was heated by induction a large increase in the amplitude of longitudinal vibration frequently occurred as a result of resonance. This happened when a natural frequency of the bar coincided with twice the heating frequency or multiples thereof. The temperature at which resonance occurred depended on a number of factors including billet length and heating power. Resonance was most often observed when the surface temperature of the billet reached the Curie point. It is well established that magnetostrictive vibrations occur in a ferromagnetic material subjected to an alternating electromagnetic field, but existing data suggests that linear magnetostriction decreases towards the Curie point. Linear magnetostriction was measured in a sample of mild steel up to 800ºC using a high temperature strain gauge. The magnetostriction constant 100 was calculated assuming an average grain orientation in mild steel. The data was found to be comparable to that published for single crystals of iron. It was discovered that linear magnetostriction was responsible for resonance below 600ºC but not for temperatures near the Curie point. Other possible causes of resonance such as forces produced by the interaction between eddy currents and the alternating electromagnetic field, the alpha to gamma phase transformation and the existence of a thin ferromagnetic layer were investigated. None were found to account for resonance in bars of mild steel heated by induction. Experimental work relating to the induction heating of steel is compared to previous work on the subject of electromagnetic generation of ultrasound where a similar increase of the amplitude of longitudinal waves in steel is reported at the Curie point. It is concluded that the two phenomena are related as they show strong similarities.