# Browsing by Subject "Vibration"

###### Results Per Page

###### Sort Options

Item Open Access A Study in Laterally Restrained Buckled Beams for the use in a Vertical Isolation System(2021) McManus, Michael AllenLinear vibration isolation systems, used to reduce the transmissibility of vertical vibration, requires a vertical static displacement that increases with the square of the natural period of the isolation system. The static displacement of a vertical isolation system with a one second natural period is 0.25 m. The nonlinear stiffness of buckled beams loaded in the transverse direction can be designed to reduce the vertical static displacement requirement of vertical systems. This study presents an analysis of large displacement mechanics of slender beams that buckle against a constraint, and extracts the transverse constraint force via the Lagrange multiplier enforcing the constraint. The constraint prescribes a maximum allowable lateral displacement along the length of the beam and a specified longitudinal displacement at the mid span of the beam. No small curvature assumption is involved. Lateral and longitudinal displacements are parameterized in terms of Fourier coefficients. Coefficient values for constrained equilibria are found by minimizing the bending strain energy such that lateral and longitudinal constraints are satisfied. Because the full expression for curvature is used, this is a nonlinear constrained optimization problem.

Edge and mid-point horizontal constraint positions are varied to gain a better understanding of the constraint forces at each position. This modeling approach is then used to design a system of post-buckled leaf springs in order to meet vibration isolation requirements without over-stressing the springs. This process is discussed in detail along with the process and challenges associated with the physical model. Theoretical predictions are compared to laboratory scale measurements. Experimental results from the physical model are compared to the theoretical and numerical simulation results. The potential for rocking responses of the vertical isolation system are quantified via the modeling of the nonlinear dynamics of a platform supported by a system of springs and carrying a mass concentrated above the platform.

Item Open Access Aeroelastic Modeling of Blade Vibration and its Effect on the Trim and Optimal Performance of Helicopter Rotors using a Harmonic Balance Approach(2020) Tedesco, MatthewThis dissertation concerns the optimization of the aeroelastic performance of conventional

helicopter rotors, considering various design variables such cyclic and higher

harmonic controls. A nite element model is introduced to model the structural

eects of the blade, and a coupled induced velocity/projected force model is used

to couple this structural model to the aerodynamic model constructed in previous

works. The system is then optimized using two separate objective functions: minimum

power and minimum vibrational loading at the hub. The model is validated

against several theoretical and experimental models, and good agreement is demonstrated

in each case. Results of the rotor in forward

ight demonstrate for realistic

advance ratios the original lifting surface model is sucient for modeling normalized

induced power. Through use of the dynamics model the vibrational loading minimization

is shown to be extremely signicant, especially when using more higher

harmonic control. However, this decrease comes at an extreme cost to performance

in the form of the normalized induced power nearly doubling. More realistic scenarios

can be created using multi-objective optimization, where it is shown that vibrational

loading can be decreased around 60% for a 5% increase in power.

Item Open Access Analysis of the Elastica with Applications to Vibration Isolation(2007-05-02T17:38:28Z) Santillan, Sophia TeresaLinear 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.Item Open Access Control of Vibratory Energy Harvesters in the Presence of Nonlinearities and Power-Flow Constraints(2012) Cassidy, Ian LernerOver the past decade, a significant amount of research activity has been devoted to developing electromechanical systems that can convert ambient mechanical vibrations into usable electric power. Such systems, referred to as vibratory energy harvesters, have a number of useful of applications, ranging in scale from self-powered wireless sensors for structural health monitoring in bridges and buildings to energy harvesting from ocean waves. One of the most challenging aspects of this technology concerns the efficient extraction and transmission of power from transducer to storage. Maximizing the rate of power extraction from vibratory energy harvesters is further complicated by the stochastic nature of the disturbance. The primary purpose of this dissertation is to develop feedback control algorithms which optimize the average power generated from stochastically-excited vibratory energy harvesters.

This dissertation will illustrate the performance of various controllers using two vibratory energy harvesting systems: an electromagnetic transducer embedded within a flexible structure, and a piezoelectric bimorph cantilever beam. Compared with piezoelectric systems, large-scale electromagnetic systems have received much less attention in the literature despite their ability to generate power at the watt--kilowatt scale. Motivated by this observation, the first part of this dissertation focuses on developing an experimentally validated predictive model of an actively controlled electromagnetic transducer. Following this experimental analysis, linear-quadratic-Gaussian control theory is used to compute unconstrained state feedback controllers for two ideal vibratory energy harvesting systems. This theory is then augmented to account for competing objectives, nonlinearities in the harvester dynamics, and non-quadratic transmission loss models in the electronics.

In many vibratory energy harvesting applications, employing a bi-directional power electronic drive to actively control the harvester is infeasible due to the high levels of parasitic power required to operate the drive. For the case where a single-directional drive is used, a constraint on the directionality of power-flow is imposed on the system, which necessitates the use of nonlinear feedback. As such, a sub-optimal controller for power-flow-constrained vibratory energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance controller. Finally, the last section of this dissertation explores a numerical approach to compute optimal discretized control manifolds for systems with power-flow constraints. Unlike the sub-optimal nonlinear controller, the numerical controller satisfies the necessary conditions for optimality by solving the stochastic Hamilton-Jacobi equation.

Item Open Access Modeling and Control of an Electromagentic Transducer for Vibratory Energy Harvesting Applications(2011) Cassidy, Ian LernerThe primary focus of this thesis is on the modeling and control of an electromechanical transducer to harvest energy from large structures (e.g. buildings and bridges). The transducer consists of a back-driven ballscrew coupled to a permanent-magnet synchronous machine. Developing control algorithms to take full advantage of the unique features of this type of transducer requires a mechanical model that can

adequately characterize the device's intrinsic nonlinear behavior. A new model is proposed that can effectively capture this behavior. Comparison with experimental results verifies that the model is accurate over a wide range of operating conditions and that it can be used to correctly design controllers to maximize power generation.

In most vibratory energy harvesting systems the disturbance is most appropriately modeled as a broadband stochastic process. Optimization of the average power generated from such disturbances is a feedback control problem, and the controller can be determined by solving a nonstandard Riccati equation. In this thesis we show that appropriate tuning of passive parameters in the harvesting system results in a decoupled solution to the Riccati equation and a corresponding controller that only requires half of the states for feedback. However, even when the optimal controller requires all of the states for feedback, it is possible to determine the states that contribute the most to the power generation and optimize those partial-state feedback gains using a gradient descent method.

To demonstrate the energy harvesting capability of the transducer, impedance matching theory is used to optimize power from a small, base-excited single-degree-of-freedom (SDOF) oscillator. For this system, both theoretical and experimental investigations are compared and results are shown to match closely. Finally, statistical linearization is used to determine the optimal full-state controller and the optimal static admittance for the experimental SDOF oscillator when it is excited by a stochastic disturbance.

Item Open Access Modulating unimolecular charge transfer by exciting bridge vibrations.(J Am Chem Soc, 2009-12-23) Lin, Zhiwei; Lawrence, Candace M; Xiao, Dequan; Kireev, Victor V; Skourtis, Spiros S; Sessler, Jonathan L; Beratan, David N; Rubtsov, Igor VUltrafast UV-vibrational spectroscopy was used to investigate how vibrational excitation of the bridge changes photoinduced electron transfer between donor (dimethylaniline) and acceptor (anthracene) moieties bridged by a guanosine-cytidine base pair (GC). The charge-separated (CS) state yield is found to be lowered by high-frequency bridge mode excitation. The effect is linked to a dynamic modulation of the donor-acceptor coupling interaction by weakening of H-bonding and/or by disruption of the bridging base-pair planarity.Item Open Access On the Asymptotic Reduction of Classical Modal Analysis for Nonlinear and Coupled Dynamical Systems(2016) Culver, Dean RogersAsymptotic Modal Analysis (AMA) is a computationally efficient and accurate method for studying the response of dynamical systems experiencing banded, random harmonic excitation at high frequencies when the number of responding modes is large. In this work, AMA has been extended to systems of coupled continuous components as well as nonlinear systems. Several prototypical cases are considered to advance the technique from the current state-of-the-art. The nonlinear problem is considered in two steps. First, a method for solving problems involving nonlinear continuous multi-mode components, called Iterative Modal Analysis (IMA), is outlined. Secondly, the behavior of a plate carrying a nonlinear spring-mass system is studied, showing how nonlinear effects on system natural frequencies may be accounted for in AMA. The final chapters of this work consider the coupling of continuous systems. For example, two parallel plates coupled at a point are studied. The principal novel element of the two-plate investigation reduces transfer function sums of the coupled system to an analytic form in the AMA approximation. Secondly, a stack of three parallel plates where adjacent plates are coupled at a point are examined. The three-plate investigation refines the reduction of transfer function sums, studies spatial intensification in greater detail, and offers insight into the diminishing response amplitudes in networks of continuous components excited at one location. These chapters open the door for future work in networks of vibrating components responding to banded, high-frequency, random harmonic excitation in the linear and nonlinear regimes.

Item Open Access Post-Buckled Stability and Modal Behavior of Plates and Shells(2012) Lyman, Theodore ClarenceIn modern engineering there is a considerable interest in predicting the behavior of post-buckled structures. With current lightweight, aerospace, and high performance applications, structural elements frequently operate beyond their buckled load. This is especially true of plates, which are capable of maintaining stability at loads several times their critical buckling load. Additionally, even structures such as cylindrical shells may be pushed into a post-buckled range in these extreme applications.

Because of the nature of these problems, continuation methods are particularly well suited as a solution method. Continuation methods have been extensively applied to a range of problems in mathematics and physics but have been used to a lesser extent in engineering problems. In the present work, continuation methods are used to solve a variety of buckling and stability problems of discrete dynamical systems, plates and cylinders. The continuation methods, when applied to dynamic mechanical systems, also provide very useful information regarding the modal behavior of the structure, including linearized natural frequencies and mode shapes as a by-product of the solution method.

To verify the results of the continuation calculations, the commercial finite element code ANSYS is used as an independent check. To confirm previously unseen stable equilibrium shapes for square plates, a set of experiments on polycarbonate plates is also presented.

Item Open Access Vibration Transmission Reduction Through Multi-Element Multi-Path Structural Design in Thin Beams and Cylindrical Shells(2015) Raudales, DavidUnwarranted vibrations create adverse effects that can compromise structural integrity, precision and stability. This thesis explores an attenuation technique that rethinks the design of simple lightweight flexible structures, providing an alternative to the current methods of active controllers and heavy damping. Through multi-element/multi-path (MEMP) design, a structure is divided up into several constituent substructures with separate, elastically coupled, wave transmission paths that utilize the inherent dynamics of the system to achieve substantial wide-band reductions in the low frequency range while satisfying constraints on static strength and weight. Attenuation is achieved through several processes acting in concert: different subsystem wave speeds, mixed boundary conditions at end points, interaction through elastic couplings, and stop band behavior. The technique is first introduced into thin beams coupled with discrete axial and torsional springs, resulting in wide-band attenuation and agreement between analytical simulations and experimental studies. MEMP design is then implemented into concentric thin cylindrical shells, providing a more three-dimensional study with axially discrete azimuthally-continuous elastic connectors. By employing a modal decomposition of the governing shell equations, simulations reveal more opportunities for attenuation when subjected to various forcing conditions. Future work examines the effect of MEMP shell design on acoustic scattering reduction.