Conventional modal analysis is performed using FFT Analyzers with modal analysis software developed by one of many test/analysis software vendors. The analysis is performed in the frequency domain using frequency response functions. A recent advancement in modal analysis involves analyzing the measured free response of a structure in the time domain. The Ibrahim Time Domain (ITD) Algorithm is such a method which has been used and verified at government environmental test facilities. The ITD is an accurate numeric solution. Minimal operator interaction is required for proper performance of the algorithm. The results of the ITD Algorithm are far superior to those of conventional frequency response methods when the test structure has closely spaced or heavily damped modes of vibration. Currently, the ITD exists only on mainframe computers. The purpose of this research is to adapt the numeric routine to a mini-computer (DEC PDP-11/34). In this way, the ITD Algorithm could be incorporated in any environmental test facility with access to a mini-computer.

For oblique and normal water waves at various frequencies, the use of moored cylinders as breakwaters is considered numerically using linear three-dimensional analysis. The breakwater can be used by itself for protection of small structures or as a series of cylinders to protect a harbor, shoreline, or moored vessel from the destructive energy associated with incident water waves. The breakwater is completely submerged below the free surface and is attached to the ocean floor with six symmetrically configured mooring lines. The cylinder is filled with air and the mooring lines remain taut during the structure's motion. Six degrees of freedom describe the motion of the breakwater and additional degrees of freedom are introduced as the cables are modeled with the use of lumped masses connected with springs. The fluid is assumed to be inviscid and incompressible, so that the velocity field can be written as the gradient of the velocity potential. A boundary integral method is used to solve the integral equations that define the external fluid flow. Free vibrations of the cylinder in both air and water are considered and "dry " and "wet" natural frequencies are computed. Motions caused by water waves are studied to establish the effect of certain parameters on the effectiveness of the breakwater. The transmission coefficient is shown to be somewhat misleading when compared to plots that show the spatial variation of the wave amplitude. / Master of Science

A finite generalized integral transform was applied to three general classes of problems in the vibrations of continuous media. For its kernel the eigenfunction of an associated eigenvalue problem was used and the result was denoted the eigentransform. The eigentransform was applied to (1) continuous media with both non-uniform stiffness and mass distributions; (2) continuous media with uniform stiffness but non-uniform mass distribution; and (3) to problems with time-dependent boundary conditions. A general method was presented for treating vibrations of continuous media with non-uniform stiffness and mass distributions. The eigentransform was applied to the governing partial differential equation and subsequently the transformed displacement was found to satisfy an infinite set of coupled ordinary differential equations similar to those encountered in the vibrations of discrete masses. These equations led to a matrix eigenvalue problem from which approximate eigenvalues and eigenvectors were obtained. The differential equations were uncoupled using a transformation matrix of the eigenvectors and then were solved for the generalized time function. Finally, the inversion series for the transform was used to obtain the solution for the dynamic response. To illustrate the method, the first four frequencies and mode shapes were determined for the longitudinal vibration of a tapered rod. The eigentransform was used to develop a general procedure for treating continuous media with uniform stiffness but non-uniform mass distribution. These results, similar to those for the general non-uniform problem, reduced this problem to a matrix eigenvalue problem. The mode shapes were determined by summation using the eigenvectors and mode shapes for the uniform continuous media. Several problems for beams and plates with concentrated masses were solved as examples. This approach demonstrated definite computational advantages for plates over past treatments where frequency equations were determined as infinite series. Vibrations of continuous media with time-dependent boundary conditions were then treated using the eigentransform. One dimensional media were considered first and next isotropic and orthotropic plates. One-dimensional continuous media were treated in a general way by specifying a differential operator of even order in the spatial derivatives. Applications to rods and beams were presented. The vibration of isotropic plates for an arbitrary shape was treated by expressing the equations in normal and tangential coordinates. The eigentransform of the governing equation was performed using an identity and theorem of vector analysis. The time-dependent boundary conditions were allowed to have an arbitrary variation along the boundary. Detailed applications were then made to rectangular and circular isotropic plates. The eigentransform of the orthotropic plate equation was performed by integration by parts. Again the boundary conditions were permitted to vary arbitrarily around the boundary. The response of a simply supported plate with an arbitrary edge displacement was determined as an illustration. This investigation demonstrated that the eigentransform is a logical generalization of other finite integral transforms. The concept of a generalized finite integral transform extends the advantages of integral transforms to a much broader class of boundary value problems. / Ph. D.

Results are presented of an experimental and analytical investigation to determine the feasibility of using active control techniques to (1) attenuate the response of a flexible payload to low frequency sinusoidal vibration disturbances, (2) damp the transient response of a flexible payload to step disturbances, and (3) eliminate isolator static deflections under conditions of gradually changing steady acceleration levels. An active vibration isolation system was developed and an experimental working model of the system was built and tested. Digital and analog computer studies were conducted to obtain the transmissibility and transient response characteristics of the isolation system. The analytical and experimental results indicate that the active vibration isolation system is very effective in attenuating the response of a one- and two-degree-of-freedom payload to vibratory disturbances. / Master of Science

Tuned vibration absorbers (TVA) have been discussed in literature since the early twentieth century. These devices are implemented to suppress the system's vibration by transferring energy to the absorber mass. This research examines an electromagnetic tuned vibration absorber that can have its tuned frequency altered by gap and current variation. The advantage of an adjustable TVA is that the system can be tuned to various excitation frequencies to cancel vibration. This research examines a unique embodiment using permanent magnets and an electromagnetic absorber to alter the system dynamics. The focus is to allow changes in tuned frequency to cancel system vibrations. This research develops the electromagnetic theory, presents absorber system simulations, and tests the dynamic absorber's response. The electromagnetic field is investigated to determine the field between a stationary magnet and the absorber electromagnet. This field can be numerically calculated as the superposition of four constituent fields. With the electromagnetic field determined, the force to displacement relation between the stationary magnet and the absorber electromagnet is calculated. The best fit is determined to be an inverse square relationship. Once the spring force relation is determined, the damping mechanisms are discussed and experiments proposed to isolate the different damping mechanisms. In the simulations, it is found that by having an adjustable electromagnetic TVA the natural frequency can be adjusted 2-3% with a +10 amp input and over 50% for a variable gap. The advantage of the variable gap is that it may be adjusted once and then no additional energy is needed, while the advantage of the variable current is that the system may be rapidly altered. The experiments are undertaken to test the constructed absorber for the spring and damping force. The tests confirm the spring force relation and quantify the high damping present in the tested configuration. Then the absorber system transfer functions are recorded. The absorber is then applied to a single degree of freedom system to verify its cancellation results by a gap variation. / Ph. D.

This study evaluates the application of smart damping materials for reducing structural noise and vibrations. The primary purposes of this study are to: 1. Explore the feasibility of smart damping materials, such as piezoelectric materials, for augmenting and improving the noise and vibration benefits of passive damping materials, and 2. Provide a preliminary evaluation of the noise and vibration benefits, and weight savings of smart damping material as compared to conventional damping treatments. To achieve the objectives of the study, a special test rig, designed to measure both vibrations and structure-borne noise of a test plate, was constructed and validated in the early stages of the study. Upon validating the test rig and the instrumentation that was set up for data collection and processing, a series of tests were performed. The tests were intended to establish a baseline for the test rig and compare the performance of smart damping materials with a number of passive interior automotive treatments. Further, in order to evaluate the effect of smart damping materials on the sound transmission loss, a series of tests were conducted according to the SAE J1400 test specifications. The tests evaluate the transmission loss for smart damping materials for an undamped and a damped plate. The passive damping technique used for this study involved attaching piezoelectric patches with resonant electrical shunts. The vibration modes of the plate were determined both analytically and experimentally, using laser measurement techniques, in order to determine effective placement of the piezoceramic materials. Three piezoceramic patches were applied to control four structural resonance frequencies of the plate. The tests show that smart damping materials have substantial performance benefits in terms of providing effective noise and vibration reduction at a frequency range that is often outside the effective range of passive damping materials. Further, judging by the acceleration and noise reduction per added weight, the test results indicate that smart damping materials can decrease the vibration peak of a steel plate at 151 Hz by up to 16.24 dB with an additional weight of only 0.11 lb. The addition of constrained-layer damping (CLD) can decrease that same peak by 18.65 dB, but it weighs 10 times more. This feature of smart damping materials is particularly useful for solving particular noise or vibration problems at specified frequencies, without adding any weight to the vehicle or changing the vehicle structure. / Master of Science

An optical detection technique is developed to detect and measure the resonant vibration of the cellular membrane. Biological membranes are active components of living cells and play a complex and dynamic role in life processes. They are believed to have oscillation modes of frequencies in the range of 1 to 1000 GHz. To measure such a high-frequency vibration, a linear laser cavity is designed to produce a train of femtosecond pulses of adjustable repetition rate. The method is then directly applied to liposomes, "artificial membrane", stained with a liphophilic potential sensitive dye. The spectral behavior of a selection of potential sensitive dyes in the membrane is also studied.

In recent years civil engineering structures such as floors, footbridges, and staircases, have reported unacceptable vibration when they are dynamically excited by pedestrians. When such structures have a particular combination of high structural flexibility and low inherent damping, there is potential for excessive vibration. Pedestrian-structure interaction (PSI) is especially noticeable when the lowest structural natural frequencies are close to the dominant pedestrian pace frequency or its harmonics. Although most of these structures are designed according to existing standards and guidelines, there are still many uncertainties in the human actions that may lead to unexpected structural behavior, increasing the vibration responses and exceeding serviceability limit states. How a pedestrian excites a structure and how that structure affects a pedestrian's gait is not fully understood. Therefore, a realistic analysis of PSI must be performed to properly incorporate these effects toward more rational structural designs. This study aims to identify, within this class of the walking-induced load problem, the vibration mechanisms, the mathematical models, and methods, to address excessive vibration in pedestrian structures. After conducting an in-depth evaluation of current guidelines and provisions for analysis and design of pedestrian structures, models to enable more realistic design under such uncertainties have been developed. The results establish a body of knowledge regarding human loads and structural responses, yielding the potential for more rational approaches to improve the analysis and design of pedestrian structures.

"The goal of this project was to investigate the dynamic effects of incipient separation of industrial cam-follower systems. Typical industrial cam-follower systems include a force closed cam joint and a follower train containing both substantial mass and stiffness. Providing the cam and follower remain in contact, this is a one degree-of-freedom (DOF) system. It becomes a two-DOF system once the cam and follower separate or jump, creating two new natural frequencies, which bracket the original. The dynamic performance of the system as it passed through the lower of the two post-separation modes while on the verge of jump was investigated. A study was conducted to determine whether imperfections in the cam surface, while the contact force is on the brink of incipient separation, may cause a spontaneous switch to the two-DOF mode and begin vibration at resonance. A force-closed translating cam-follower train was designed for the investigation. The fixture is a physical realization of the two-mass mathematical model. Pro/Engineer was used to design the follower train, Mathcad and TK Solver were used to analyze the linkage and DYNACAM & Mathcad were used to dynamically model the system. The system is designed to be on the cusp of incipient separation when run. Experiments were carried out by bringing the system up to jump speed and then backing off the preload to get the system on the cusp of separation. Data were collected at the prejump, slight jump, and violently jumping stages. The time traces show the acceleration amplitudes grow to large peaks when the system is jumping. The frequency spectrum shows the two new natural frequencies growing in amplitude from non-existant in the prejump stage, to higher values in the violently jumping stage. The peak amplitudes of the phenomenon are small in magnitude compared to the harmonic content of the cam. It is concluded that the contribution of the two-DOF system natural frequencies is not a significant factor from a practical aspect. Although the actual jump phenomenon is of concern in high-speed applications, calculations show that if the follower system is designed sufficiently stiff then the two-DOF situation will not occur."

The primary goal of this thesis is to evaluate vibration control of an all-clamped plate having an unknown disturbance. The vibration control is implemented using a piezoelectric actuator placed at an optimal location. The first part of this thesis considers a robust actuator placement with respect to varying spatial distributions of disturbances. The treatment here, is different from performance-based LQR approaches, since it is based on minimizing the effect of the disturbance distributions. The second part of this thesis addresses a more general case where the plate is under an unknown disturbance. An unknown disturbance is also characterized by the case where the disturbance signal moves randomly over the entire spatial domain. An optimal switching controller algorithm is developed, based on LQR performance, which switches between piezoelectric actuators employed for the vibration control of the plate. A single actuator is selected from the various actuator locations during each time interval, which leads to performance enhancement.