Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 73-77). Also available on the World Wide Web.

Thesis (M.S.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 78-82). Also available on the World Wide Web.

Thesis (M.S.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 86-88). Also available on the World Wide Web.

Thesis--University of California, Berkeley. / Includes bibliographical references (p. 57). 23

Thesis (M.S.)--Oregon State University, 2008. / Printout. Includes bibliographical references. Also available on the World Wide Web.

The use of piezoelectric materials for actuation, and vibration suppression of thin beams, is the subject of study in this doctoral thesis. The initial focus is set on reducing beam vibrations with resistively shunted piezoelectric patches, where the converted electrical energy is dissipated by the resistor to give an additional damping. The amount of additional damping achieved depends on the value of shunted resistor, the dimensions of the piezoelectric, and its location on the substructure. Hence, the resistively shunted piezoelectric-beam was modelled to determine the optimal values, and to examine its dynamics. A multi-modal model was derived based on the Euler-Bernoulli beam theory, and a reduced non-dimensionalized transfer function was obtained from the multi-modal model. The presented model was derived from assumptions which aptly describe the dynamics of the resistively shunted piezoelectric-beam. The aptness of the presented model in representing the system, over the existing models, was evident from the comparison of the analytical predictions with the existing experimental data. With the model derived, the second part of the work deals with determining the value of resistance which would yield maximum amplitude attenuation (referred as the optimal resistance value). A method for obtaining the optimal resistance value from the analytical model, based on the presence of a fixed-point in the amplitude response, exists in the literature. But, this method cannot be used on the presented analytical model, as it includes the base-damping of the structure. Hence, a different approach was adopted to determine the optimal resistance from the analytical model. Analytical results were also validated with experimental results from a cantilever piezoelectric-beam. The amplitude plots of the first, second, and third modes of the piezoelectric-beam exhibited a softening e ect, indicating a non-linear behaviour of the piezoelectric patches. Hence, a non-linear constitutive equation was required to describe the behaviour of the piezoelectric patches. In the third part of the work, a two-step experimental procedure was devised to construct the non-linear constitutive equation of the piezoelectric actuators. In the first step, the piezoelectric patches were short circuited and a family of displacement curves were obtained for the first, second and third modes of the piezoelectric-beam by base excitation. The pro le of backbone curves from these plots were used to identify the type of non-linear terms required to describe the mechanical domain. In the second step, voltage excitation was used to obtain a similar set of displacement curves. A comparison of the profile of the backbone curves, of the displacement frequency response plot, from the voltage excited data with those from the base excited data, lead to the identification of the non-linear electromechanical coupling term. The constitutive equation, which accounts for the non-linear nature, of the piezoelectric actuator contains (apart from the linear terms) a quadratic strain term, a cubic strain term, and a term with the product of cubic strain and electric field.

>Magister Scientiae - MSc / This dissertation consists of two main sections. The first section focuses on generating zero order Bessel beams using axicons. An axicon with an opening angle y = 5⁰ was illuminated with a Gaussian beam of width ω₀ = 1.67 mm from a cw fiber laser with central wavelength λ = 1064 nm to generate zero order Bessel beams with a central spot radius r₀ = 8.3 ± 0.3 μm and propagation distance ½zmax = 20.1 ± 0.5 mm. The central spot size of a Bessel beam changes slightly along the propagation distance. The central spot radius r₀ can be varied by changing the opening angle of the axicon, y, and the wavelength of the beam. The second section focuses on applications of the generated Bessel beams in laser microdrilling. A Ti:Sapphire pulsed femtosecond laser (λ = 775 nm, ω₀ = 2.5 mm, repetition rate kHz, pulse energy mJ, and pulse duration fs) was used to generate the Bessel beams for drilling stainless steel thin sheets of thickness 50 μm and 100 μm and microscopic glass slides 1 mm thick. The central spot radius was r₀ = 15.9 ± 0.3 μm and ½zmax = 65.0 ± 0.5 mm. The effect of the Bessel beam shape on the quality of the holes was analysed and the results were discussed. It was observed that Bessel beams drill holes of better quality on transparent microscopic glass slides than on stainless steel sheet. The holes drilled on stainless steel sheets deviated from being circular on both the top and bottom surface for both thicknesses. However the holes maintained the same shape on both sides of each sample, indicating that the walls are close to being parallel. The holes drilled on the glass slides were circular and their diameters could be measured. The measured diameter (15.4±0.3 μm) of the hole is smaller than the diameter of the central spot (28.2 ± 0.1 μm) of the Bessel beam. Increasing the pulse energy increased the diameter of the drilled hole to a value close to the measured diameter of the central spot.

No description available.

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The objective of this research project was to create a Finite Element Routine for the Linear Analysis of Post-Tensioned beams using the program CALFEM® [20] developed at the division of Structural Mechanics in Lund University, Sweden. The program CALFEM and our own made files were written in MATLAB, an easy to learn and user-friendly computer language. The approach used in this thesis for analyzing the composite beam consists in embedding the steel tendons at the exact location where they intersect the concrete parent elements, without moving the concrete parent element nodes. The steel tendons are represented as one dimensional bar elements inserted into the concrete parent elements, which at the same time are represented as 8 node Iso-parametric plane elements. The theory presented in Ref. [4] served as basis for the modeling of the post-tensioned beams; however it only explained the procedure for modeling simple reinforced concrete beams, due to this we needed to make the appropriate adjustments so we could model post-tensioned beams. Assembly of the tendon stiffness into the concrete elements will depend on the bond interface between the steel and concrete, this bonding effect will be modeled using link elements; the stiffness of this link element used in the concrete-tendon interface will be the change in cohesion (between the grout or duct and the steel tendon) at the interface due to the relative slip between the concrete and the steel elements nodes. Loads (Distributed, Concentrated or Post-Tensioning) are applied directly into the concrete parent elements, and then from their resultant displacement the displacements and forces of all the steel tendon elements are obtained, this is done consecutively for all the post-tensioned tendons at every load increment. Four examples from different references and software programs are solved and compared with our results: (1) A simply reinforced cantilever plate. (2) A reinforced concrete beam, under the effect of a vertical concentrated load at mid-span. For this problem the force distribution along the steel reinforcement is obtained for two conditions, perfectly bonded and perfectly un-bonded, our results are compared with the ones obtained with the program SEGNID. (3) Consists of a continuous un-bonded post-tensioned beam with two spans, without stress losses on the tendon. The reactions at the supports and the concrete stress distribution at the location of the mid-support are obtained after the post-tensioning force is applied at both ends. (4) Consist on a un-bonded post-tensioned beam with stress losses on the tendons due to friction, wobbling and anchorage loss, under gradual loading and consecutive post-tensioning of two tendons, the results are compared with the ones reported using the program BEFE [5] developed at the University of Technology Graz, Austria. The results obtained using our program are very similar to the ones obtained with the other programs, including the more powerful curved embedded approach used by BEFE [5].