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This work focuses on the broadband attenuation of structural vibration and, in the process, employs a new perspective of vibrational energy harvesting devices. The first part of the research studies and develops a continuously distributed vibration control device which combines the benefits of point mass-spring-dampers at low frequencies as well as the resistive or dissipative influence of constraining treatments at high frequencies. This embodiment provides broadband passive vibration attenuation for a minimal cost in added mass, spanning the present divide between the ability to attenuate a single low frequency and the need to attenuate all frequencies. The second part adopts a vibration control perspective to energy harvesting analysis and considers the harvesting devices to be electromechanically stiffened and/or damped vibration absorbers. Rigorous analysis and experiments are carried out which show that vibration control and energy harvesting appear to be mutually beneficial given that maximum harvested energy from structural vibrations is achieved when the harvesters exert a finite dynamic influence on the host system. This suggests that vibration control concerns presently alleviated using tuned-mass-dampers are ideal energy harvesting applications. A generalized analytical model is derived which is applicable to both portions of the work. Continuously distributed vibration control devices are studied in depth and a superposition method is presented which allows for convenient implementation of a realistic device design into the numerical model. Tests carried out with the distributed device validate the model as well as show the device's competitive benefits compared with traditional, and much heavier, vibration control treatments. The inclusion of electromechanical coupling effects into the modeling is straightforward and numerous analyses are carried out to observe how electromagnetic and piezoelectric energy harvesting devices affect the dynamics of the host vibrating structure while the harvesters themselves convert the 'absorbed' energy into electrical power. Altering the device created in the first portion of the research to use a piezoelectric material as the distributed spring yields one such embodiment capable of both surface vibration control and energy harvesting. Tests carried out with the device additionally serve as model validation but also indicate that, for a given harvester, the attenuation of and energy harvesting from structural vibrations are nearly simultaneously maximized as modeling predicted. / Ph. D.

This dissertation is concerned with the evaluation of a new statistically sound reconstruction methodology for continuous 3-D dynamic response fields of harmonically excited structures in steady-state vibration. This results in an experimental process which reconstructs the response field from a set of 3-D projections based on Laser-Doppler-Vibrometer (LDV) localized instantaneous velocity measurements. Included along with an estimate of the 3-D velocity field, are its statistical characteristics and the inferential tools required to test the quality of the estimation. This dissertation documents in detail the development and evaluation of the proposed reconstruction methodology and its relevant subprocesses which inc1ude the formulation of a deterministic laser-structure kinematic model, and regression models that afford statistical inference for the time-domain and spatial-domain structural dynamics, as well as for the projection recombination process. / Ph. D.

A criterion using rigid-body modes to verify the conservation of mass inertias is presented. Conservation of rod element mass guarantees convergence to the exact eigensolutions of a rod. Conservation of beam element mass guarantees convergence to the exact eigensolutions of a Bernoulli-Euler beam without rotatory inertia. Conservation of element mass and rotatory inertia guarantees convergence to the exact solutions of a Bernoulli-Euler beam with rotatory inertia. Conservation of mass moment of inertia is not a requirement for convergence, but is important for a beam mass matrix with respect to their accuracy and consistency with various boundary conditions. Based on this criterion, a concept for the formulation of a non-consistent mass matrix is presented. The concept unifies the formulation of various kinds of rod and beam mass matrices, and facilitates the generation of new mass matrices for optimization. To gain more physical insight into the formulation, the shape functions for the non-consistent mass matrices are also introduced. Four examples are considered. The first two examples are used to find the optimized mass matrices for rods and beams and to study their eigensolution errors. The optimized mass matrices minimize the root mean square errors of natural frequencies over a specified range of modes. The results of using a rod optimized mass matrix show that the root mean square error of natural frequencies for the first half of total extractable modes is reduced from 5%, obtained from using the consistent-mass and the lumped-mass matrices, to 1%. The results also show that if equally spaced elements are used for a rod, all the eigenvectors are exact. However, if unequal-length elements are used, both the frequency errors and eigenvector errors increase, and the upper half of total extractable modes are not reliable. The results of using a beam optimized mass matrix show that the root mean square error of natural frequencies is reduced from 0.16%, obtained from using a consistent-mass matrix, to 0.10%. The upper half of the total modes are not reliable. The remaining two examples are used to study the performances of all rod and beam mass matrices (consistent-mass, lumped-mass, and higher-order mass matrices) on a portal arch. According to the results, the higher-order mass matrix generates the most accurate eigensolutions. The use of the higher-order mass matrix in place of the consistent-mass matrix is recommended. The block-diagonal lumped-mass matrix performs better than the diagonal lumped-mass matrices at free ends of a structure. The eigensolution errors for all the mass matrices start to increase significantly after the first one third of the total modes. Finally, a technique for finding the modal reduction mass matrices is proposed. Fully populated modal reduction mass matrices for a rod are successfully extracted. This type of models generate exact natural frequencies and mode shapes for all the extractable modes of a rod problem. Further investigation of this technique is recommended. / Ph. D.

This work examines the application of sensor arrays to structures. The wave equation solution of Euler-Bernoulli beam theory provides the structural model for this study. A review of basic array theories for the enhancement of signal-to-noise ratio (SNR) and determination of angle of arrival (AOA) leading to source localization is given. Array techniques are considered with applications to dispersive flexural waves where the propagation velocity is not constant but dependent on frequency. The theory is validated through experiments with harmonic and broad band applications. The test apparatus consisted of a long thin beam with anechoic terminations to emulate an infinite beam for frequencies above 300 Hz and a finite beam below 200 Hz. The beam was excited by a shaker (with a force transducer) mounted on one end of the beam. Measurements were taken with accelerometers and a laser velicometer at the other end of the beam. The infinite beam case was used to isolate the travelling wave response to single harmonic excitation. The finite case was used to consider transient response of the beam to an impulse. The harmonic response experiments on the infinite beam is used to demonstrate two things. First they show that the SNR increases by the square root of the number of sensors. Secondly they show that AOA can be determined explicitly from the phase between sensors for single frequency applications. The measured values of AOA were within ±3 degrees for these experiments. This technique applies to harmonic signals in a highly damped medium. The technique developed for transient applications uses the magnitude and the variance of the correlation coefficient of a densely populated array to determine AOA. This technique is based on correlation between measurements along a wave front. It does not assume a phase relationship between sensors but instead exploits the spread of the signal as it travels. The spread is characteristic of a dispersive medium. This resolution of this technique is directly linked to the population of the array and the angular relationship between elements. The experiments verified that this technique measures the AOA for within the resolution of the array. For arrays from 3x4 to 7x10 resolution of ± 6 to 9 degrees was possible. This work has developed array theory for application to dispersive waves in structures. It highlights the differences in the phase relationship between elements for dispersive versus non dispersive media. It shows improvement of SNR using structural arrays. The potential for AOA determination on highly damped structures using harmonic signals was demonstrated. AOA determination was also shown for finite structures using impact excitation. / Ph. D.

This paper presents a detailed discussion of the development of the matrix equations used in the vibration analysis of a lumped-mass approximation of a multi-anchor piping system or foundation structure. The investigation is presented in two main sections, the first of which presents a formulation of the matrix eigenvalue problem for small oscillations. The development of the stiffness matrix is presented in the second section. The coefficients derived by the M. W. Kellogg Co. for the solution of pipe stress problems are utilized here, as well as the matrix transformation methods developed by J. E. Brock in “A Matrix Method For Flexibility Analysis of Piping Systems”. A sample four-anchor foundation was analyzed and the results were in close agreement with measured results published by V. H. Neubert and W. H. Ezell in “Dynamic Behavior of a Foundation-Like Structure”. The procedures presented in this paper will theoretically apply to any piping system of ai;ty degree of complexity, but practical limitations are imposed by the size of presently available digital computers. / Master of Science

A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ_s + λ_t <u>~</u>2Ï _q, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w_r<u>~</u>3w_q on the resonance λ_s + λ_t <u>~</u>2Ï _q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ_s + λ_t. / Master of Science

The scanning Laser Doppler Vibrometer (LDV) has developed into a useful tool for rapidly acquiring spatially dense structural dynamic response information in a noncontacting manner. The research presented in this paper is part of a larger project at the Structural Imaging and Modal Analysis Laboratory in the Department of Mechanical Engineering at Virginia Polytechnic Institute and State University, Blacksburg, VA, to develop a six-degree-of-freedom (6-DOF) structural response model based on experimental data. This paper represents a portion of the research for the 6-DOF structural imaging project. A method for creating a functionalized description of a discreetly sampled 2-D data field containing response measurements evenly spaced in laser scan angie coordinates is presented. A filtering process involving a median and edge-median filter algorithm followed by a Discrete Fourier Transform/low-pass spatial frequency domain filter/Inverse Discrete Fourier Transform algorithm is used to reduce the effect of errant data recorded by the LDV data acquisition system. A means of evaluating the performance of this process is developed. Finally, an experiment to determine the relationship between structural response stability and ambient temperature and relative humidity is presented. The response of a lightly damped structure was studied over a twenty-six hour period. A direct relationship between temperature and the dynamic response of the structure was found. This study is important to the overall 6-DOF project since structural stability is assumed in merging the various scans of the structure to obtain 6-DOF information. Recommendations are given for further research of topics discussed in this thesis. / Master of Science

Active control of noise and vibration has been previously demonstrated in finite and infinite systems undergoing single and multiple-frequency excitations. Control of broadband noise and vibration has also been reported, but it tends to be limited to infinite and semi-infinite systems. Here, four new adaptive feedforward control algorithms were developed for attenuating the response generated by finite structural systems. The algorithms are based on the filtered-X Least Mean Square (LMS) adaptive algorithm. A system identification of the plant control loop is required to implement this algorithm. An autoregressive moving-average (ARMA) model was used for the system identification since it provides the most computationally-efficient means of representing the frequency response function (FRF) of a lightly-damped structure. In the first control system, an adaptive finite impulse response (FIR) or nonrecursive filter was used as the compensator. A second control approach was realized by employing a recursive compensator. These two algorithms were modified using an equation error minimization technique to form two additional control systems, which eliminate certain stability requirements of the ARMA system identification. Each algorithm was simulated and then demonstrated experimentally. Lastly, an analysis of control system causality was developed to determine the importance of this topic with regard to controlling finite structural systems. An exemplary parametric study of one of the four control systems presented, will demonstrate the analytical tool by examining the effects of system damping, compensator order, and a time delay in the control path, which is responsible for acausal control solutions. It was determined that control is always achievable, despite a delay in the control path, and also that control system performance can be improved by increasing the order of the control compensator. Both of these results were verified experimentally. / Master of Science

Proper mathematical models of structures are beneficial for designers and analysts. The accuracy of the results is essential. Therefore, verification and/or correction of the models is vital. This can be done by utilizing experimental results or other analytical solutions. There are different methods of generating the accurate mathematical models. These methods range from completely analytically derived models, completely experimentally derived models, to a combination of the two. These model generation procedures are called System Identification. Today a popular method is to create an analytical model as accurately as possible and then improve this model using experimental results. This thesis provides a review of System Identification methods as applied to vibrating structures. One simple method and three more complex methods, chosen from current engineering literature, are implemented on the computer. These methods offer the capability to correct a discrete (for example, finite element based) model through the use of experimental measurements. The validity of the methods is checked on a two degree of freedom problem, an eight degree of freedom example frequently used in the literature, and with experimentally derived vibration results of a free-free beam. / Master of Science