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The lack of methods for rigorous dynamic analysis of foundations and structures for vibrating machines has resulted in below optimum performance and in some cases reduction of life of machines, structures and foundations. The costs and complexities of these machines make it necessary to conduct proper geotechnical site investigations. and dynamic analyses to obtain the response of the soil, foundation and structure as a system to excitation. In order to highlight the use of dynamic analyses, the response of the foundations and structures were compared to the "rule of thumb" which is based on mass ratio. Furthermore sensitivity analyses were carried out comprising the following variables: • Shear modulus of soil, G • Poisson's ratio of soil,Y • Type of structure (ie raft, table top and multi-storey) • Stiffness of structure • Stiffness of foundation The fundamentals of structural dynamics have not been dealt with in this dissertation. The dynamic analyses were carried out using a finite element analysis program called Strand 7. The results were typical of a finite element analysis, giving stresses, strains, deflections, amplitudes, frequencies and velocities of vibration. The traditional "elastic halfspace model" is deficient as it does not account for soil comprising various layers. The theory has been based on an isolated circular footing. Most foundations are located in soils with layered mediums, are rectangular and in some cases are affected by the interaction of foundations in close proximity. Furthermore there is a need to account for the non-linear effects and properties of soil. It is therefore becoming more attractive to adopt mathematical models of soils using finite elements, where the visco-elastoplastic properties of soils can be realized and modeled. Furthermore the finite element method overcomes limitations such as layering and shapes or foot-prints of foundations. The "rule of thumb" or mass ratio method of design procedure is as follows:- • firstly the requirements of stresses and serviceability must be satisfied. This is usual in a statically loaded system. the ratio of the machine mass to that of the foundation together with the structure should be greater than 3 in the case of a revolving machine and 5 in the case of a reciprocating machine. • in order to obtain uniform settlement of the foundation the distance of the combined centre of gravity of the machine and foundation from the centre of area in contact with the soil is limited to 5% of the corresponding dimension of the foundation. It is evident that the mass ratio lacks accuracy in that there are several parameters that are required to describe the satisfactory performance of a system such as amplitude, frequency and velocity of vibration. The finite element method allows for calibration of the model to account for the real behaviour of the system. Calibration is generally conducted using sensitive transducers called accelerometers. The accelerometers produce power spectral density (PSD) graphs from which deflections and stresses can be back calculated. The deflections and stresses are compared with calculated deflections and stresses. Descriptions of the methods of analysis followed by presentation of results, discussions and interpretations have been included. To motivate the use of dynamic analyses case histories have been presented and discussed. Finally the dissertation concludes with findings of the study together with recommendations for the way forward in terms of research. / Thesis (M.Sc.)-University of Natal, Durban, 2002.

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Real-time substructure is a novel hybrid method for the dynamic testing of structures. During an experiment, the structure of interest is divided into two entities. The crucial parts for the project undertaken are physically replicated and loaded dynamically through powerful actuators while the rest is numerically modelled and solved via real-time software. The dynamics of both substructures must be accurately reproduced, as well as their mutual interaction. The applications are multiple but that of earthquake engineering is primarily considered in this research. Beyond the accurate modelling of both substructures, three main issues are crucial to the validity of a real-time hybrid simulation. Firstly, the loading equipment must be capable of imposing large loads and accurate displacements on the laboratory specimen. The behaviour of this loading system must be consistent and predictable over a wide range of frequencies and velocities. Secondly, the computational solver employed to emulate the numerical model dynamics requires stability, computational efficiency and accuracy. It must be able to deal with non-linear multi-degree of freedom systems. Thirdly, the interaction between the two substructures must be reliably emulated by a set of communication devices. The reciprocal boundary conditions must be imposed on the interface of each substructure. This notably implies quasi-instantaneous measurement and application of physical forces and displacements. The two substructures have to be solved simultaneously and in real-time. The three areas mentioned above have been investigated in this research. Initially, the laboratory installations of the hardware and software were focussed on. The servo-controlled hydraulic actuation system was optimised and a development rig was designed and constructed. It was found that hardware settings could greatly improve the general actuator performance, even though some particular situations could compromise it. This work was then complemented by an extensive study of the necessary actuation compensation. Numerous algorithms – either previously published or developed in the course of this research – were implemented and formally compared through a set of real-time experiments. Particularly, some challenging multi-axis experiments with a high level of actuator coupling were conducted. Direct extrapolation coupled with adaptive delay estimation was found to be the most effective approach to ensure synchronisation of the substructures. Attention was then given to the integration algorithms used to solve the numerical substructure problem and output the actuator demand on a real-time basis. Both explicit and implicit schemes were considered, even though an explicit formulation is required for this hybrid application. Computationally simple schemes are more suitable and several were shown to satisfy the necessary accuracy and stability requirements. Successful realtime hybrid tests were carried out with fifty degrees of freedom in the numerical substructure, including non-linear force/displacement relationships and using integration time-steps proving unconditional stability of the algorithms used. Finally, a realistic earthquake engineering application of the real-time substructure method was conducted. A steel column was tested physically as part of 20-storey building structure subject to the 1940 El Centro earthquake. To further display the usefulness of the method, an energy dissipative device was also integrated in the numerical model and its effect on the building response was shown.

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The convenience of Operational Modal Analysis (OMA), over conventional Experimental Modal Analysis (EMA), has seen to its increasing popularity over the last decade for the purpose of evaluating dynamic properties of structures. OMA features an advantage of requiring only output information, which is in tandem with its main drawback of lacking scaled modeshape information. While correctly scaled modeshapes can be assumed under a restrictive assumption of spectrally white inputs, in reality, input spectra are at best broadband in nature. In this thesis, an OMA method for Multiple-Input Multiple-Output (MIMO) applications in mechanical structures is developed. The aim is to separate MIMO responses into a collection of Single-Input Single-Output (SISO) processes (matrix FRF) using cepstral-based methods, under less restrictive and hence more realistic coloured broadband excitation. Existing cepstral curve-fitting techniques can be subsequently applied to give regenerated FRFs with correct relative scaling. This cepstral-based method is based on the matrix Mean Differential Cepstrum (MDC) and operates in the frequency domain. Application of the matrix MDC onto MIMO responses leads to a matrix differential equation which together with the use of finite differences, directly solves or identifies the matrix FRF in a propagative manner. An alternative approach based on whitened MIMO responses can be similarly formulated for the indirect solution of the matrix FRF. Both the direct and indirect approaches can be modified with a Taylor series approximation to give a total of four propagative solution sequences. The method is developed using relatively simple simulated and experimental systems, involving both impulsive and burst random excitations. Detailed analysis of the results is performed using more complicated Single-Input Multiple-Output (SIMO) and MIMO systems, involving both driving and non-driving point measurements. The use of the matrix MDC method together with existing cepstral curve-fitting technique to give correct relative scaling is demonstrated on a simulated MIMO system with coloured inputs. Accurate representation of the actual FRFs is achieved by the matrix MDC technique for SIMO set-ups. In MIMO scenarios, excellent identification was obtained for the case of simulated impulsive input while the experimental and burst random input cases were less favourable. The results show that the matrix MDC technique works in MIMO scenarios, but possible noise-related issues need to be addressed in both experimental and burst random input cases for a more satisfactory identification outcome.

This thesis represents the work that has been done by the author during his Master of Engineering Science candidature in the area of vibration control of flexible structures at the School of Mechanical Engineering, The University of Adelaide, between March 2003 and June 2004. The aim of this research is to further extend the application of the Spatial Control Approach for two-dimensional flexible structures for attenuating global structural vibration with the possible implication of reduction in noise radiation. The research was concentrated on a simply supported thin flexible plate, using piezoelectric ceramic materials as actuators and sensors. In this work, active controllers were designed for the purpose of controlling only the first five vibration modes (0-500Hz) of the plate. A spatial controller was designed to minimize the total energy of the spatially distributed signal, which is reflected by the spatial H2 norm of the transfer function from the disturbance signal to the vibration output at every point over the plate. This approach ensures the vibration contributed by all the in bandwidth (0-500 Hz) vibration modes is minimized, and hence is capable of minimizing vibration throughout the entire plate. Within the control framework, two cases were considered here; the case when the prior knowledge of the incoming disturbance in terms of reference signal is vailable and the case when it is not available. For the case when the reference signal is available, spatial feedforward controller was designed; whereas for the case when the reference signal is not available, spatial feedback controller was designed to attenuate the global disturbance. The effectiveness of spatial controllers was then compared with that of the standard point-wise controllers numerically and experimentally. The experimental results were found to reflect the numerical results, and the results demonstrated that spatial controllers are able to reduce the energy transfer from the disturbance to the structural output across the plate in a more uniform way than the point-wise controllers. The research work has demonstrated that spatial controller managed to minimize the global plate vibrations and noise radiation that were due to the first five modes. / Thesis (M.Eng.Sc.)--School of Mechanical Engineering, 2005.

Thesis (Ph.D.)--Tufts University, 2005. / Adviser: Robert Greif. Submitted to the Dept. of Mechanical Engineering. Includes bibliographical references (leaves 231-237). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.) -- McMaster University, 1998. / Includes bibliographical references (p. 215-222). Also available via World Wide Web.