Vibration analysis of a printed circuit board

The reliability of the printed circuit board assembly under dynamic environments, such as those found onboard airplanes, ships and land vehicles is receiving more attention. This research analyses the dynamic characteristics of the printed circuit board (PCB) supported by edge retainers and plug-in connectors. By modelling the wedge retainer and connector as providing simply supported boundary condition with appropriate rotational spring stiffnesses along their respective edges with the aid of finite element codes, accurate natural frequencies for the board against experimental natural frequencies are obtained. For a PCB supported by two opposite wedge retainers and a plug-in connector and with its remaining edge free of any restraint, it is found that these real supports behave somewhere between the simply supported and clamped boundary conditions and provide a percentage fixity of 39.5% more than the classical simply supported case. By using an eigensensitivity method, the rotational stiffnesses representing the boundary supports of the PCB can be updated effectively and is capable of representing the dynamics of the PCB accurately. The result shows that the percentage error in the fundamental frequency of the PCB finite element model is substantially reduced from 22.3% to 1.3%. The procedure demonstrated the effectiveness of using only the vibration test frequencies as reference data when the mode shapes of the original untuned model are almost identical to the referenced modes/experimental data. When using only modal frequencies in model improvement, the analysis is very much simplified. Furthermore, the time taken to obtain the experimental data will be substantially reduced as the experimental mode shapes are not required.In addition, this thesis advocates a relatively simple method in determining the support locations for maximising the fundamental frequency of vibrating structures. The technique is simple and does not require any optimisation or sequential search algorithm in the analysis. The key to the procedure is to position the necessary supports at positions so as to eliminate the lower modes from the original configuration. This is accomplished by introducing point supports along the nodal lines of the highest possible mode from the original configuration, so that all the other lower modes are eliminated by the introduction of the new or extra supports to the structure. It also proposes inspecting the average driving point residues along the nodal lines of vibrating plates to find the optimal locations of the supports. Numerical examples are provided to demonstrate its validity. By applying to the PCB supported on its three sides by two wedge retainers and a connector, it is found that a single point constraint that would yield maximum fundamental frequency is located at the mid-point of the nodal line, namely, node 39. This point support has the effect of increasing the structure's fundamental frequency from 68.4 Hz to 146.9 Hz, or 115% higher.

Vibration analysis of submerged rectangular microplates with distributed mass loading

This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropic plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibration induced by an acoustic field or by the attached mass loading. This paper investigates the issue of involving these two types of loading simultaneously. Based on Lamb's assumption of the fluid-loaded structure and the Rayleigh–Ritz energy method, this paper presents an analytical solution for the natural frequencies and mode shapes of the coupling system. Numerical results for microplates with different types of boundary conditions have also been obtained and compared with experimental and numerical results from previous literature. The theoretical model and novel analytical solution are of particular interest in the design of microplate-based biosensing devices.

Stress and vibration analysis:contributions to the development of techniques and methodologies

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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.

An investigation of the mechanics of wire drawing with the superposition of an oscillatory drawing stress

A number of investigators have studied the application of oscillatory energy to a metal undergoing plastic deformation. Their results have shown that oscillatory stresses reduce both the stress required to initiate plastic deformation and the friction forces between the tool and workpiece. The first two sections in this thesis discuss historically and technically the devolopment of the use of oscillatory energy techniques to aid metal forming with particular reference to wire drawing. The remainder of the thesis discusses the research undertaken to study the effect of applying longitudinal oscillations to wire drawing. Oscillations were supplied from an electric hydraulic vibrator at frequencies in the range 25 to 500 c/s., and drawing tests were performed at drawing speeds up to 50 ft/m. on a 2000 lbf. bull-block. Equipment was designed to measure the drawing force, drawing torque, amplitude of die and drum oscillation and drawing speed. Reasons are given for selecting mild steel, pure and hard aluminium, stainless steel and hard copper as the materials to be drawn, and the experimental procedure and calibration of measuring equipment arc described. Results show that when oscillatory stresses are applied at frequencies within the range investigated : (a) There is no reduction in the maximum drawing load. (b) Using sodium stearate lubricant there is a negligible reduction in the coefficient of friction between the die and wire. (c) Pure aluminium does not absorb sufficient oscillatory energy to ease the movement of dislocations. (d) Hard aluminium is not softened by oscillatory energy accelerating the diffusion process. (e) Hard copper is not cyclically softened. A vibration analysis of the bull-block and wire showed that oscillatory drawiing in this frequency range, is a mechanical process of straining; and unstraining the drawn wire, and is dependent upon the stiffness of the material being drawn and the drawing machine. Directions which further work should take are suggested.

Rolling bearing vibrations: the effects of varying compliance, manufacturing tolerances and wear

In this study some common types of Rolling Bearing vibrations are analysed in depth both theoretically and experimentally. The study is restricted to vibrations in the radial direction of bearings having pure radial load and a positive radial clearance. The general vibrational behaviour of such bearings has been investigated with respect to the effects of varying compliance, manufacturing tolerances and the interaction between the bearing and the machine structure into which it is fitted. The equations of motion for a rotor supported by a bearing in which the stiffness varies with cage position has been set up and examples of solutions,obtained by digital simulation. is given. A method to calculate amplitudes and frequencies of vibration components due to out of roundness of the inner ring and varying roller diameters has been developed. The results from these investigations have been combined with a theory for bearing/machine frame interaction using mechanical impedance technique, thereby facilitating prediction of the vibrational behaviour of the whole set up. Finally. the effects of bearing fatigue and wear have been studied with particular emphasis on the use of vibration analysis for condition monitoring purposes. A number of monitoring methods have been tried and their effectiveness discussed. The experimental investigation was carried out using two purpose built rigs. For the purpose of analysis of the experimental measurements a digital mini computer was adapted for signal processing and a suite of programs was written. The program package performs several of the commonly used signal analysis processes and :include all necessary input and output functions.

Theoretical modeling and experimental validation of fluid-loaded micro rectangular plates

This paper presents a theoretical model on the vibration analysis of micro scale fluid-loaded rectangular isotropic plates, based on the Lamb's assumption of fluid-structure interaction and the Rayleigh-Ritz energy method. An analytical solution for this model is proposed, which can be applied to most cases of boundary conditions. The dynamical experimental data of a series of microfabricated silicon plates are obtained using a base-excitation dynamic testing facility. The natural frequencies and mode shapes in the experimental results are in good agreement with the theoretical simulations for the lower order modes. The presented theoretical and experimental investigations on the vibration characteristics of the micro scale plates are of particular interest in the design of microplate based biosensing devices. Copyright © 2009 by ASME.

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.

A lumped parameter model for the analysis of the motion of the muscles of the lower limbs under whole-body vibration

Through a lumped parameter modelling approach, a dynamical model, which can reproduce the motion of the muscles of a human body standing in different postures during Whole Body Vibrations (WBVs) treatment, has been developed. The key parameters, associated to the dynamics of the motion of the muscles of the lower limbs, have been identified starting from accelerometer measurements. The developed model can be usefully applied to the optimization of WBVs treatments which can effectively enhance muscle activation. © 2013 IEEE.

Analysis and modelling of muscles motion during whole body vibration

The aim of the study is to characterize the local muscles motion in individuals undergoing whole body mechanical stimulation. In this study we aim also to evaluate how subject positioning modifies vibration dumping, altering local mechanical stimulus. Vibrations were delivered to subjects by the use of a vibrating platform, while stimulation frequency was increased linearly from 15 to 60Hz. Two different subject postures were here analysed. Platform and muscles motion were monitored using tiny MEMS accelerometers; a contra lateral analysis was also presented. Muscle motion analysis revealed typical displacement trajectories: motion components were found not to be purely sinusoidal neither in phase to each other. Results also revealed a mechanical resonant-like behaviour at some muscles, similar to a second-order system response. Resonance frequencies and dumping factors depended on subject and his positioning. Proper mechanical stimulation can maximize muscle spindle solicitation, which may produce a more effective muscle activation. © 2010 M. Cesarelli et al.

Whole body vibration training:analysis and characterization

The aim of this work is to contribute to the analysis and characterization of training with whole body vibration (WBV) and the resultant neuromuscular response. WBV aims to mechanically activate muscle by eliciting stretch reflexes. Generally, surface electromyography is utilized to assess muscular response elicited by vibrations. However, EMG analysis could potentially bring to erroneous conclusions if not accurately filtered. Tiny and lightweight MEMS accelerometers were found helpful in monitoring muscle motion. Displacements were estimated integrating twice the acceleration data after gravity and small postural subject adjustments contribution removal. Results showed the relevant presence of motion artifacts on EMG recordings, the high correlation between muscle motion and EMG activity and how resonance frequencies and dumping factors depended on subject and his positioning onto the vibrating platform. Stimulations at the resonant frequency maximize muscles lengthening and in turn, muscle spindle solicitation , which may produce more muscle activation. Local mechanical stimulus characterization (Le, muscle motion analysis) could be meaningful in discovering proper muscle stimulation and may contribute to suggest appropriate and effective WBV exercise protocols. ©2009 IEEE.

Whole body vibration treatments in postmenopausal women can improve bone mineral density:results of a stimulus focussed meta-analysis

Whole body vibration treatment is a non-pharmacological intervention intended to stimulate muscular response and increase bone mineral density, particularly for postmenopausal women. The literature related to this topic is controversial, heterogeneous, and unclear despite the prospect of a major clinical effect. The aim of this study was to identify and systematically review the literature to assess the effect of whole body vibration treatments on bone mineral density (BMD) in postmenopausal women with a specific focus on the experimental factors that influence the stimulus. Nine studies fulfilled the inclusion criteria, including 527 postmenopausal women and different vibration delivery designs. Cumulative dose, amplitudes and frequency of treatments as well as subject posture during treatment vary widely among studies. Some of the studies included an associated exercise training regime. Both randomized and controlled clinical trials were included. Whole body vibration was shown to produce significant BMD improvements on the hip and spine when compared to no intervention. Conversely, treatment associated with exercise training resulted in negligible outcomes when compared to exercise training or to placebo. Moreover, side-alternating platforms were more effective in improving BMD values than synchronous platforms and mechanical oscillations of magnitude higher than 3 g and/or frequency lower than 25 Hz were also found to be effective. Treatments with a cumulative dose over 1000 minutes in the follow-up period were correlated to positive outcomes. Our conclusion is that whole body vibration treatments in elderly women can reduce BMD decline.However, many factors (e.g. amplitude, frequency and subject posture) affect the capacity of the vibrations to propagate to the target site; the adequate level of stimulation required to produce these effects has not yet been defined. Further biomechanical analyses to predict the propagation of the vibration waves along the body and assess the stimulation levels are required.

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.