Bounding the Polynomial Approximation Errors of Frequency Response Functions

Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the character- ization of a linear dynamic behavior. The major problems to be faced are leakage and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. The kernel idea of the LPM is a local polynomial approx- imation of the FRF and the leakage errors in a small-frequency band around the frequency where the FRF is estimated. Polyno- mial approximation of FRFs is also present in other measurement and design problems. For that reason, it is important to have a good understanding of the factors that influence the polynomial approximation errors. This article presents a full analysis of this problem and delivers a rule of thumb that can be easily applied in practice to deliver an upper bound on the approximation error of FRFs. It is shown that the approximation error for lowly damped systems is bounded by (B_{LPM}/B_{3dB})^{R+2} with B_{LPM} the local bandwidth of the LPM, R the degree of the local polynomial that is selected to be even (user choices), and B_{3dB} the 3 dB bandwidth of the resonance, which is a system property

The application of vibration analysis techniques to the development of an ultrasonically assisted die forming process

One of the requirements for significant cost savings in the manufacture of tinplate cans in the packaging industry, is to achieve a die formed diameter reduction (or neck) on the can, inexpensively and reliably. A novel technique for the formation of a neck on metal canisters, uses the ability of ultrasonic vibration to reduce the apparent friction (and hence forming force) between the die work surface and the material being formed. Ultrasonic forming, although known to be a viable technique, has not been fully exploited due to a lack of understanding of the process. This has resulted in a lack of tool design knowledge and process reliability problems. The aim of the research reported in this thesis, is to investigate the vibration characteristics of ultrasonically excited forming tools with reference to the metal forming process and particularly, from a tool design viewpoint. [Continues.

Predicting material damping in composite blades - a novel low order approach and experimental validation

Fibre-reinforced polymer (FRP) composites are being used increasingly in turbomachinery components, due to their light weight and high specifi c strength. Bladed components are sensitive to vibrations, which are driven by the magnitude of excitation and their damping. Vibrations cause high-cycle-fatigue and eventual failure, so care must be taken to minimise vibration amplitude, through engineered damping if possible. Modelling material damping in composites is challenging due to their anisotropy but tailoring the layup of a laminate could potentially positively influence the material damping. This work presents a low-order modelling approach and experimental measurement technique, producing computationally efficient and simple damping predictions for composite components with arbitrary geometry and layup. This "smeared" approach, whilst similar to existing approaches, uses a strain energy computation to determine the material damping, but homogenises the effective properties of entire layups, rather than lamina properties, as typically used for macro-scale modelling. Initial experimental validation of the approach showed it to predict damping well for abstract single-layup specimens. Improved input damping parameters were produced through the development of a novel test rig, consisting of heavy tip masses attached to rectangular coupon specimens. This reduces extraneous damping contributions signifi cantly. The test rig facilitated further investigation into the scalability of smeared predictions, showing that the smeared elastic moduli and damping parameters can be used to represent the behaviour of thicker laminates effectively if out-of-plane stress and strain contributions are accounted for during modal loss factor computation. This investigation, coupled with input parameters gathered using the test rig, provided the con fidence to apply the smeared technique to geometrically complex, multilaminates. The technique predicted modal damping effectively, proven with full experimental validation. Throughout the work, the smeared approach is shown to produce equivalent, and sometimes superior, accuracy to the existing layered approach, with a signifi cant reduction in computational cost.Open Acces

Structural dynamics analysis in the presence of unmeasured excitations

Methods for comprehensive structural dynamic analysis generally employ input-output modal analysis with a mathematical model of structural vibration using excitation and response data. Recently operational modal analysis methods using only vibration response data have been developed. In this thesis, both input-output and operational modal analysis, in the presence of significant unmeasured excitations, is considered. This situation arises when a test structure cannot be effectively isolated from ambient excitations or where the operating environment imposes dynamically-important boundary conditions. The limitations of existing deterministic frequency-domain methods are assessed. A novel time-domain estimation algorithm, based on the estimation of a discrete-time autoregressive moving average with exogenous excitation (ARMAX) model, is proposed. It includes a stochastic component to explicitly account for unmeasured excitations and measurement noise. A criterion, based on the sign of modal damping, is incorporated to distinguish vibration modes from spurious modes due to unmeasured excitations and measurement noise, and to identify the most complete set of modal parameters from a group of estimated models. Numerical tests demonstrate that the proposed algorithm effectively identifies vibration modes even with significant unmeasured random and periodic excitations. Random noise is superimposed on response measurements in all tests. Simulated systems with low modal damping, closely spaced modes and high modal damping are considered independently. The accuracy of estimated modal parameters is good except for degreesof- freedom with a low response level but this could be overcome by appropriate placement of excitation and response measurement points. These observations are reflected in experimental tests that include unmeasured periodic excitations over 200% the level of measured excitations, unmeasured random excitations at 90% the level of measured excitations, and the superposition of periodic and random unmeasured excitations. Results indicate advantages of the proposed algorithm over a deterministic frequency domain algorithm. Piezoceramic plates are used for structural excitation in one experimental case and the limitations of distributed excitation for broadband analysis are observed and characterised in terms of actuator geometry and modal deformation. The ARMAX algorithm is extended for use with response measurements exclusively. Numerical and experimental tests demonstrate its performance using time series data and correlation functions calculated from response measurements

THE TECHNIQUE OF DETERMINATION OF STRUCTURAL PARAMETERS FROM FORCED VIBRATION TESTING

This thesis details the results of an investigation into a technique for determination of "useful" structural parameters from forced vibration testing. The implementation of this technique to full scale civil engineering structures was achieved by several developments in the experimental and computational fronts: a vibration generator and a computer-aided-testing system for the former and two computational algorithms for the latter. The experimental developments are instrumental to exciting large structures and acquisition of large quantities of useful data in digital format. These data serve as inputs to the computational algorithms whose outputs are structural parameters. These parameters are in either modal or spatial forms which cannot be measured directly but have to be extracted from the raw data. The modal-parameter-extraction method is based on direct Least-Square fitting technique and is simple to implement. The technique can yield good accuracy if the residual effects from out-of-range modes are removed from the raw data before fitting. The spatial-parameter- extraction method distinguishes itself from other conventional methods in the way that the orthogonality property is not explicitly used. This method is applicable to situations where conventional methods are not; i.e. in cases if modal matrices are not square. Some success was achieved in cases in which computer synthesized or good quality laboratory test data were used. Full scale field tests of a tall office block and a slender tower were carried out and their modal models obtained. Attempts to obtain spatial models of these structures were not carried out, however, as this task can be a separate research topic in its own right. Further research in such application is still required

Identifying Position-Dependent Mechanical Systems: A Modal Approach Applied to a Flexible Wafer Stage

Increasingly stringent performance requirements for motion control necessitate the use of increasingly detailed models of the system behavior. Motion systems inherently move, therefore, spatio-temporal models of the flexible dynamics are essential. In this paper, a two-step approach for the identification of the spatio-temporal behavior of mechanical systems is developed and applied to a lightweight prototype industrial wafer stage. The proposed approach exploits a modal modeling framework and combines recently developed powerful linear time invariant (LTI) identification tools with a spline-based mode-shape interpolation approach to estimate the spatial system behavior. The experimental results for the wafer stage application confirm the suitability of the proposed approach for the identification of complex position-dependent mechanical systems, and its potential for motion control performance improvements