To visualize vibrations in mechanical systems, e.g., machine tools, their movements are measured by means of suitable sensors. The signals from these sensors are processed and displayed as animated pictures on a computer screen. Accelerometers have been chosen as the most suitable sensors for this purpose. Their main advantages include small size, wide sensitivity range and frequency bandwidth. In addition, accelerometers measure signals with reference to the Earth, so they do not require stable fixtures such as used with cameras or lasers. The visualization methodology involves nine accelerometers attached to a mechanical component, e.g., a dynamometer's platform. Vibration signals were acquired using a data acquisition (DAQ) system which is controlled by a LabVIEW��-based program. These signals are processed to suppress errors and convert acceleration into generalized coordinate that describes motion of the visualized component as a rigid plate's movement in 3-D space. The animation is accomplished by displaying a time series of pictures representing instantaneous position of the plate. The animation program employs homogenous coordinate transformation to draw 3-D 'wireframe' pictures. Since various errors distort the measured signals, the animated movement may be inaccurate. The knowledge of a mathematical model of the system whose vibrations are animated allows detection and suppression of distortions. For this purpose, the signals measured from the actual dynamic system are compared with the signals simulated by the system's model subjected to the same excitation as the actual system. Discrepancies between the actual and simulated signals are detected. They are analyzed to identify possible sources and forms of distorting signals. As the next step, the measured (actual) signals are corrected by removing estimated distortions. A methodology and software package capable of performing all functions necessary to implement the visualization of vibration have been developed in this research using LabVIEW�� programming environment. As compared with commercial software for experimental modal analysis, the most distinctive feature of the developed package is improved accuracy achieved by applying concepts utilized in control theory, such as modeling of multi-input-multi-output (MIMO) systems and on-line system identification for the model development and correction of signals. / Graduation date: 1998

The objective of this research is the computer simulation of the vibrations of the suspension system of a two-cylinder reciprocating compressor. A theoretical model is developed to describe the various steps undertaken to calculate the response of this six-degree-of-freedom rigid system. The response, which is in the form of a displacement vector, serves as the input to a computer animation of the motion of the orbit of the compressor with respect to the four suspension system springs. The theoretical model is developed by calculating (1) the System Mass and Inertial Matrix, (2) the Gyroscopic Matrix, (3) the Total Assembly Stiffness Matrix, and (4) the Shaking Forces and Moments Matrix. Experimental and finite element methods used to evaluate the parameters required to calculate these matrices are also discussed. An eigenanalysis is performed to calculate the eigenvalue frequencies and eigenvectors for the system. The force analysis is performed to calculate the forcing function in the time domain for the first 40 harmonics. The Fast Fourier Transform method is used to transform the forcing function from the time domain to the frequency domain. The validity of the results are checked by simultaneously developing another model using IMP (Integrated Mechanisms Program). The response is then calculated in original coordinates, after performing a modal transformation. Finally, the response, which is a displacement vector, is utilized by an animation program in PHIGS (Programmer's Hierarchical Interactive Graphics Standard) to animate the motion of the orbit of the compressor. / Master of Science

The effect of the shape of piezoceramic actuators on the vibration response of a simply supported beam is investigated. An equation is derived to convert between the shape of the piezoceramic actuator and the resulting moment distribution caused on the structure. A beam simulation program is then created to model the vibrations caused by various shaped moment distributions exciting a simply supported beam. The length of the moment distribution is iterated from the length of the beam to zero length, within the program, to show the trends in modal amplitudes. The amplitude of each mode is then plotted for each length of the moment distribution. An equation is then derived to explain the resulting minimums and maximums of the modal amplitudes. The equation is shown to be a useful tool in designing shapes to meet specific control criteria. An example is given showing how the shape of the actuator can be designed to give superior performance for specific control criteria than a traditional rectangular shape. Two possible actuator shapes are shown for the situation. One shape is optimized for the given control criteria by causing the maximum response for the critical mode. The results from the beam simulation for both shapes are shown. The shape of the actuator may now be used as a variable in the cost function for control optimization. / Master of Science