No description available.

The purpose of this research is to analyze a new type of vibration isolator consisting of two pre-bent struts which are clamped at both ends and intermediately bonded with a viscoelastic filler. The proposed isolation device has the ability to support a relatively large static load with little deflection and offers a low axial resistance under dynamic excitation, making it ideal for isolating vertical vibrations. In this research, four of these vibration isolators are used to support a rigid, square plate. The symmetric case is analyzed first. Then the plate has a center of mass which is located at some distance from the geometric center of the plate. When the system is subjected to vertical harmonic base excitations, this eccentric weight introduces rotational as well as vertical motions of the plate. This research will investigate the effects of various eccentricities on the efficiency of the vibration isolators in the configuration described. The displacement transmissibility will be the measure of the isolators' effectiveness at mitigating vibrations transmitted from the base to the rigid plate. For each case, the nonlinear equilibrium equations and the governing equations of motion for small vibrations about equilibrium are numerically solved, and the transmissibility is calculated and plotted over a wide range of frequencies. These plots are used to recognize ranges of frequencies for which isolation is achieved and frequencies at which resonance occurs in the system. At the resonant frequencies, the physical behavior of the system is analyzed to determine the types of vibration modes which occur in the system. A free vibration analysis is also performed to obtain a better understanding of resonances in the system. / Master of Science

Linear theory is useful in determining small static and dynamic deflections. However, to characterize large static and dynamic deflections, it is no longer useful or accurate, and more sophisticated analysis methods are necessary. In the case of beam deflections, linear beam theory makes use of an approximate curvature expression. Here, the exact curvature expression is used to derive the governing partial differential equations that describe the in-plane equilibrium and dynamics of a long, thin, inextensible beam, where the self-weight of the beam is included in the analysis. These beam equations are expressed in terms of arclength, and the resulting equilibrium shape is called the elastica. The analysis gives solutions that are accurate for any deflection size, and the method can be used to characterize the behavior of many structural systems. Numerical and analytical methods are used to solve or to approximate solutions to the governing equations. Both a shooting method and a finite difference, time-stepping algorithm are developed and implemented to find numerical solutions and these solutions are compared with some analytical approximation method results. The elastica equations are first used to determine both linear and nonlinear equilibrium configurations for a number of boundary conditions and loading types. In the case of a beam with a significant self-weight, the system can exhibit nonlinear static behavior even in the absence of external loading, and the elastica equations are used to determine the weight corresponding to the onset of instability (or self-weight buckling). The equations are also used to characterize linear and nonlinear vibrations of some structural systems, and experimental tests are conducted to verify the numerical results. The linear vibration analysis is applied to a vibration isolator system, where a postbuckled clamped-clamped beam or otherwise highly-deformed structure is used (in place of a conventional spring) to reduce system motion. The method is also used to characterize nonlinear dynamic behavior, and the resulting frequency-response curves are compared with those in the literature. Finally, the method is used to investigate the dynamics of subsea risers, where the effects of gravity, buoyancy, and the current velocity are considered. / Dissertation

Vibrations resulting from earthquakes, machinery, or unanticipated shocks may be very damaging and costly to structures. To avoid such damage, designers need a structural system that can dissipate the energy caused by these vibrations. Using elastically buckled struts may be a viable means to reduce the harmful effects of unexpected vibrations. Post-buckled struts can support high axial loads and also act as springs in a passive vibration isolation system by absorbing or dissipating the energy caused by external excitation. When a base excitation is applied, the buckled strut may act to reduce the dynamic force transmitted to the system, thus reducing the structural damage to the system. Several models of buckled and pre-bent struts are examined with different combinations of parameters and end conditions. The models include pinned or fixed columns supporting loads above their buckling load, and columns with an initial curvature supporting various loads. The varying parameters include external damping, internal damping, and stiffness. The columns will be subjected to simple harmonic motion applied at the base or to a multi-frequency base excitation. The response of each model is measured by the deflection transmissibility of the supported load over a large range of frequencies. Effective models reduce the motion of the supported load over a large range of frequencies. / Master of Science

Hole deviation is one of the most significant problems in drilling applications. Deviated holes result in inefficient blasting and have severe economic impacts due to increased equipment consumption. Conversely, straighter holes help in increasing production scales and reduce operational costs. The reason for hole deviations could range from anisotropic behavior of the rocks being drilled to the behavior of the drill string under the action of imposed forces. Deviations caused due to rock anisotropy are complex in nature and non-controllable to some extent but deviations due to mechanics of drill strings can be controlled as they lie in the operator’s area of influence. In this thesis, a 2D mathematical model is constructed which predicts the bending behavior of the drill rod and the model is further extended to predict the buckled profile of the entire drill string. Two bit state parameters are defined which help in better characterization of hole deviation and understanding of deflected state of the drill bit. Epiroc’s drilling data is inserted in the model developed and the buckled profile of the drill string is studied. The developed model is used to further understand the effect of various drilling parameters like bit thrust, angle of inclination, hole length, etc. on hole deviation. Through the results it was concluded that the bending stiffness of the drill rods is the most critical parameter influencing hole deviation for Epiroc’s drilling data and drill string setup. Finally, potential improvements and techniques to validate results obtained from the mathematical model are proposed. / Hålavvikelse är ett av de mest avgörande problemen i borrapplikationer. Hålavvikelse resulterar i ineffektiv sprängning och får allvarliga ekonomiska konsekvenser på grund av ökad utrustningskonsumtion. Omvänt hjälper rakare hål att öka produktionsskalorna och minska driftskostnaderna. Anledningen till hålavvikelser variera från anisotropi hos bergformationerna som borras till borrsträngens beteende under påverkan av pålagda krafter. Avvikelser orsakade på grund av berganisotropi är komplexa till sin natur och kan inte kontrolleras till viss del, men avvikelser på grund av mekanik i borrsträngar kan kontrolleras eftersom de ligger i operatörens inflytandeområde. I denna avhandling konstrueras en matematisk 2D-modell som förutsäger borrstångens böjningsbeteende och modellen utökas ytterligare för att förutsäga den böjda profilen för hela borrsträngen. Två olika borrkroneparametrar definieras för att bättre karakterisera hålavvikelsen och förstå borrkronans böjning. Epirocs borrsträngsdata används i den utvecklade modellen och borrsträngens böjda profil studeras. Den utvecklade modellen används för att ytterligare förstå effekten av hålavvikelse för olika borrparametrar som kraften på borrkronan, lutningsvinkel, hållängd etc. Utifrån resultaten drogs slutsatsen att borrsträngens böjstyvhet är den mest kritiska parametern som påverkar hålavvikelsen för Epirocs borrdata och borrsträngsinstallation. Slutligen föreslås potentiella förbättringar och tekniker för att validera resultat som erhållits från den matematiska modellen.

Pattern formation in buckled membranes was studied along with the morphology of flowers formed at the tip of silicon nanowires and ripples formed in suspended graphene sheets. Nash's perturbation method was tested for a simple case where initial and final metrics embed smoothly and there is a smooth path from one surface to another and was found to work successfully. The method was tested in more realistic conditions where a smooth path was not known and the method failed. Cylindrical flower-like membranes with a metric of negative Gaussian curvature were simulated in three and four dimensions. These four dimensional flowers had 2 orders of magnitude less energy than their three dimensional counterparts. Simulations were used to show that the addition of a fourth spatial dimension did not relieve all bending energy from the cylindrical membranes. Patterns formed at the tip of silicon nanowires were studied and found to be of the Dense Branching Morphology type. The rate of branching is dependent on the curvature of the gold bubble on which they are grown. Graphene was simulated using the modified embedded atom method potential and buckles were found to form if the carbon bonds were stretched. An energy functional was found for the energy of a sheet with a metric different from that of flat space. / text

We investigate theoretically and experimentally the nonlinear responses of a clamped-clamped buckled beam to a variety of external harmonic excitations and internal resonances. We assume that the beam geometry is uniform and its material is homogeneous. We initially buckle the beam by an axial force beyond the critical load of the first buckling mode, and then we apply a transverse harmonic excitation that is uniform over its span. The beam is modeled according to the Euler-Bernoulli beam theory and small strains and moderate rotation approximations are assumed. We derive the equation of motion governing the nonlinear transverse planar vibrations and associated boundary conditions using the extended Hamilton's principle. The governing equation is a nonlinear integral-partial-differential equation in space and time that possesses quadratic and cubic nonlinearities. A closed-form solution for such equations is not available and hence we seek approximate solutions. We use perturbation methods to investigate the slow dynamics in the neighborhood of an equilibrium configuration. A Galerkin approximation is used to discretize the nonlinear partial-differential equation governing the beam's response and obtain a set of nonlinearly coupled ordinary-differential equations governing the time evolution of the response. We based our theory on a multi-mode Galerkin discretization. To investigate the large-amplitude dynamics, we use a shooting method to numerically integrate the discretized equations and obtain periodic orbits. The stability and bifurcations of these periodic orbits are investigated using Floquet theory. We solve the nonlinear buckling problem to determine the buckled configurations as a function of the applied axial load. We compare the static buckled configurations obtained from the discretized equations with the exact ones. We find out that the number of modes retained in the discretization has a significant effect on these static configurations. We consider three cases: primary resonance, subharmonic resonance of order one-half of the first vibration mode, and one-to-one internal resonance between the first and second modes. We obtain interesting dynamics, such as phase-locked and quasiperiodic motions, resulting from a Hopf bifurcation, snapthrough motions, and a sequence of period-doubling bifurcations leading to chaos. To validate our theoretical results, we ran an experiment, which is a modified version of the experiment designed by Kreider and Nayfeh. We find that the obtained theoretical results are in good qualitative agreement with the experimental results. In the case of one-to-one internal resonance, we report, theoretically and experimentally, energy transfer between the first mode, which is externally excited, and the second mode. / Ph. D.

No description available.

The purpose of this research is to study a new type of vibration isolator, utilizing the post-buckled stiffness of elastic struts (or columns). The advantage of the post-buckled state is that ideally it can support more static load with a relatively small static deflection than traditional vibration isolators such as springs or rubber mounts, but can also exhibit a low axial stiffness when dynamic excitation is introduced. Three models consisting of buckled or pre-bent struts serving as vibration isolators which support a rigid bar are examined in this research. The three cases studied are 1) two buckled struts supporting a symmetric rigid bar, 2) two buckled struts supporting an asymmetric rigid bar, and 3) two pairs of buckled struts with a bonded filler supporting a symmetric rigid bar. The models are subjected to a harmonic excitation at the base, and external damping is included. The struts in all cases are modeled as an elastica, and the boundary conditions are clamped/clamped for all cases. Because the purpose of the struts is to reduce unwanted vibrations, determining the displacement transmissibility of the system is the main goal of this research. Transmissibility versus frequency plots are generated for all cases, with varying parameters such as stiffness, damping, and location of center of mass, to determine how they affect the behavior of the struts. Models that produce a large range of frequencies at which the transmissibility is well below unity are the most effective. Vibration shapes are also determined for certain frequencies so that the physical behavior of the system can be studied. / Master of Science