Improvements in autonomous systems technology and a growing demand within military operations are spurring a revolution in Human-Robot Interaction (HRI). These mixed-initiative human-robot teams are enabled by Multi-Modal Communication (MMC), which supports redundancy and levels of communication that are more robust than single mode interaction. (Bischoff & Graefe, 2002; Partan & Marler, 1999). Tactile communication via vibrotactile displays is an emerging technology, potentially beneficial to advancing HRI. Incorporation of tactile displays within MMC requires developing messages equivalent in communication power to speech and visual signals used in the military. Toward that end, two experiments were performed to investigate the feasibility of a tactile language using a lexicon of standardized tactons (tactile icons) within a sentence structure for communication of messages for robot to human communication. Experiment one evaluated tactons from the literature with standardized parameters grouped into categories (directional, dynamic, and static) based on the nature and meaning of the patterns to inform design of a tactile syntax. Findings of this experiment revealed directional tactons showed better performance than non-directional tactons, therefore syntax for experiment two composed of a non-directional and a directional tacton was more likely to show performance better than chance. Experiment two tested the syntax structure of equally performing tactons identified from experiment one, revealing participants’ ability to interpret tactile sentences better than chance with or without the presence of an independent work imperative task. This finding advanced the state of the art in tactile displays from one to two word phrases facilitating inclusion of the tactile modality within MMC for HRI

The purpose of this study is to develop an analytical solution for modal analysis of actively damped orthotropic composite plates in bending and to verify it with experimental analysis. The analytical modal analysis solution for composite plate dynamics is derived using Euler theory. This analysis applies to structures with orthotropic lamina of uniform material properties at any lamination angle. The bending-extensional coupling can be neglected for plates that are symmetric or approximately symmetric, which allows an exact solution for natural frequency and mode shape to be obtained. An exact solution can be found for natural vibration and in general. The active control is modeled analytically by combining the Lagrange equation with the Ritz Assumed Mode method. This analysis produces a generalized coordinate vector that correlates the assumed mode to the particular amplitude of a particular case. The kinetic energy dissipated by the piezoelectric actuator from the system over one oscillation can be calculated from the generalized coordinate vector and the assumed mode. The equivalent damping ratio of the active control system is calculated as the ratio between the kinetic energy absorbed by the piezoelectric actuator from the system in one oscillation and the maximum strain energy of the system during that oscillation. A point mass on the plate, such as an accelerometer mass, can also be modeled as a single layer of uniform mass, that is an isotropic layer, by equating the potential energy of the point mass with the potential energy of the uniform mass layer. It is important to note that the mass of the isotropic layer is frequency dependent, and it has no effect on the plate stiffness. The analytical model is validated by comparison to experimental work. The samples studied were aluminum and composite plates of various lengths. The active control predictions were also validated using previous experimental work completed at California Polytechnic State University in San Luis Obispo. These cases included active control of an aluminum beam with a patch of piezoelectric material and an aluminum sailplane with a patch of piezoelectric material. Results indicate that while the analytical mode solutions are in good agreement with the experimental results, they are also systematically higher than the experimental results. The analytical active control solutions match previous work when the piezoelectric effects are linear. The main result of adding an active control system is approximately a 5-10% increase in modal frequencies and a 200-800% increase of damping ratio.

The objective of this work is to study the local and global nonlinear vibrations of isotropic single-layered and multi-layered cross-ply doubly curved shallow shells with simply supported boundary conditions. The study is based-on the full nonlinear partial-differential equations of motion for shells. These equations of motion are based-on the von K\'rm\'{a}n-type geometric nonlinear theory and the first-order shear-deformation theory, they are developed by using a variational approach. Many approximate shell theories are presented. We used two approaches to study the responses of shells to a primary resonance: a $direct$ approach and a $discretization$ approach. In the discretization approach, the nonlinear partial-differential equations are discretized using the Galerkin procedure to reduce them to an infinite system of nonlinearly coupled second-order ordinary-differential equations. An approximate solution of this set is then obtained by using the method of multiple scales for the case of primary resonance. The resulting equations describing the modulations of the amplitude and phase of the excited mode are used to generate frequency- and force-response curves. The effect of the number of modes retained in the approximation on the predicted responses is discussed and the shortcomings of using low-order discretization models are demonstrated. In the direct approach, the method of multiple scales is applied directly to the nonlinear partial-differential equations of motion and associated boundary conditions for the same cases treated using the discretization approach. The results obtained from these two approaches are compared. For the global analysis, a finite number of equations are integrated numerically to calculate the limit cycles and their stability, and hence their bifurcations, using Floquet theory. The use of this theory requires integrating $2n+(2n)^2$ nonlinear first-order ordinary-differential equations simultaneously, where $n$ is the number of modes retained in the discretization. A convergence study is conducted to determine the number of modes needed to obtain robust results. The discretized system of equation are used to study the nonlinear vibrations of shells to subharmonic resonances of order one-half. The effect of the number of modes retained in the approximation is presented. Also, the effect of the number of layers on the shell parameters is shown. Modal interaction between the first and second modes in the case of a two-to-one internal resonance is investigated. We use the method of multiple scales to determine the modulation equations that govern the slow dynamics of the response. A pseudo-arclength scheme is used to determine the fixed points of the modulation equations and the stability of these fixed points is investigated. In some cases, the fixed points undergo Hopf bifurcations, which result in dynamic solutions. A combination of a long-time integration and Floquet theory is used to determine the detailed solution branches and chaotic solutions and their stability. The limit cycles may undergo symmetry-breaking, saddle node, and period-doubling bifurcations. / Ph. D.

Hamilton's principle and a third-order shear-deformation theory are used to derive a set of five coupled partial-differential equations governing the nonlinear response of composite plates. The reduction of these equations by using classical plate theory is discussed and the corresponding partial-differential equations governing both rectangular and circular plates are derived. Generalized Levy-type solutions are obtained for the problem of linear free vibrations and linear stability of shear-deformable cross-ply laminated plates. The governing equations are transformed into a set of first-order linear ordinary-differential equations with constant coefficients. The general solution of these equations is obtained by using the state-space concept. Then, the application of the boundary conditions yields equations for the natural frequencies and critical loads. However, a straightforward application of the state-space concept yields numerically ill-conditioned problems as the plate thickness is reduced. Various methods for overcoming this problem are discussed. An initial-value method with orthonormalization is selected. It is shown that this method not only yields results that are in excellent agreement with the results in the literature, but it also converges fast and gives all the frequencies and buckling loads regardless of the plate thickness. Further It is shown that the application of classical plate theory to thick plates yields inaccurate results. The influence of modal interactions on the response of harmonically excited plates is investigated in detail. The case of a two-to-one autoparametric resonance in shear-deformable composite laminated plates is considered. Four first-order ordinary-differential equations describing the modulation of the amplitudes and phases of the internally resonant modes are derived using the averaged Lagrangian when the higher mode is excited by a primary resonance. The fixed-point solutions are determined using a homotopy algorithm and their stability is analyzed. It is shown that besides the single-mode solution, two-mode solutions exist for a certain range of parameters. It is further shown that in the multi-mode case the lower mode, which is indirectly excited through the internal resonance may dominate the response. For a certain range of parameters, the fixed points lose stability via a Hopf bifurcation, thereby giving rise to limit cycle solutions. It is shown that these limit-cycles undergo a series of period-doubling bifurcations, culminating in chaos. Finally, the case of a combination resonance involving the first three modes of axisymmetric circular plates is studied. The method of multiple scales is used to determine a set of ordinary-differential equations governing the modulation of phases of the modes involved and that the excited mode is not necessarily the dominant one. Furthermore, it is shown that for a choice of parameters the multi-mode response loses stability through a Hopf bifurcation, resulting in periodically or chaotically modulated motions of the plate. / Ph. D.

This work investigates the modal properties of general cyclically symmetric systems and the multi-stage systems with cyclically symmetric stages. The work generalizes the modal properties of engineering applications, such as planetary gears, centrifugal pendulum vibration absorber (CPVA) systems, multi-stage planetary gears, etc., and provides methods to improve the computational efficiency to numerically solve the system modes when cyclically symmetric structures exist. Modal properties of cyclically symmetric systems with vibrating central components as three-dimensional rigid bodies are studied without any assumptions on the system matrix symmetries: asymmetric inertia matrix, damping, gyroscopic, and circulatory terms can be present. In the equation of motion of such a cyclically symmetric system, the matrix operators are proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode type is characterized by specific central component modal deflections and substructure phase relations. Instead of solving the full eigenvalue problem,all vibration modes and natural frequencies can be obtained by solving smaller eigenvalue problems associated with each mode type. This computational advantage is dramatic for systems with many substructures or many degrees of freedom per substructure. Group theory is applied to further generalize the modal properties of cyclically symmetric systems when both rigid-body and compliant central components exist, such as planetary gears with an elastic continuum ring gear. The group theory for symmetry groups is introduced, and the group-theory-based modal analysis does not rely on any knowledge of the properties of system matrices in system equations of motion. The three types of modes (substructure modes, translational-tilting modes, and rotational-axial modes) are characterized by specific rigid-body central component modal defections, substructure phase relations, and nodal diameter components of compliant central components. The general formulation of reduced eigenvalue problems for each mode type is obtained through group-theory-based method, and it applies to discrete, continuous, or hybrid discrete-continuous cyclically symmetric systems. The group-theory-based modal analysis also applies to systems with other symmetry types. The group-theory-based modal analysis is generalized to analyze the multi-stage systems that are composed of symmetric stages coupled through the motions of rigid-body central components. The proposed group-theory-based modal analysis applies to multi-stage systems with cyclically symmetric stages, such as multi-stage planetary gears and CPVA systems with multiple groups of absorbers. The method also applies to multi-stage systems with component stages that have different types of symmetry. For a multi-stage system with symmetric stages, a unitary transformation matrix can be built through an algorithmic and computationally inexpensive procedure. The obtained unitary transformation matrix provides the foundation to analyze the modal properties based on the principles of group-theory-based modal analysis. For general multi-stage systems with symmetric component stages, the vibration modes are classified into two general types, single-stage substructure modes and overall modes, according to the non-zero modal deflections in each component stage. Reduced eigenvalue problems for each mode type are formulated to reduce the computational cost for eigensolutions. Finite element models of multi-stage bladed disk assemblies consist of multiple cyclically symmetric bladed disks that are coupled through the boundary nodes at the inter-stage interface. To improve the computational efficiency of calculating the full system modes, a numerical method is proposed by combination of the multi-stage cyclic symmetry reduction method and the subspace iteration method. Compared to the multi-stage cyclic symmetry reduction method, the proposed method improves the accuracy of obtained eigensolutions through an iterative process that is derived from the subspace iteration method. Based on the cyclic symmetry in each component stage of bladed disk, the proposed iterative method that can be performed using single stage sector models only, instead of using matrix operators for the full multi-stage bladed disks. Parallel computations can be performed in the proposed iterative method, and the computational speed for eigensolutions can be increased significantly. / Doctor of Philosophy / Cyclically symmetric structures exist in many engineering applications such as bladed disks, circular plates, planetary gears, centrifugal pendulum vibration absorbers (CPVA), etc. During steady operation, these cyclically symmetric systems are subjected to traveling wave dynamic loading. Component vibrations result in undesirable effects, including high cycle fatigue (HCF) failure, noise, performance reduction, etc. Knowledge of the modal properties of cyclically symmetric systems is helpful to analyze the system forced response and understand experimental modal testing. In this work, single stage cyclically symmetric systems are proved to have highly structured modes. The single stage systems considered in this work can have both rigid bodies and elastic continua as components. Group theory is used to study the modal properties, including the system mode types and the characteristics of different mode types. All the vibration modes of single stage cyclically symmetric systems can be solved from reduced eigenvalue problems. The methodology also applies to systems with other types of symmetry. For multi-stage systems with cyclically symmetric substructures, such as multi-stage planetary gears, a group-theory-based method is developed to analyze the modal properties. For industrial applications, such as multi-stage bladed disk assemblies, this work develops an iterative method to facilitate the calculations of system modes. The modal properties and methods for solving system modes apply to mechanical systems, including CPVA systems, the single/multi-stage planetary gears in power transmission systems, bladed disk assemblies in turbines, circular plates, elastic rings, etc.

A study of the nonlinear vibrations of metallic cantilever beams and plates subjected to transverse harmonic excitations is presented. Both experimental and theoretical results are presented. The primary focus is however on the transfer of energy between widely spaced modes via modulation. This phenomenon is studied both in the presence and absence of a one-to-one internal resonance. Reduced-order models using Galerkin discretization are also developed to predict experimentally observed motions. A good qualitative agreement is obtained between the experimental and numerical results. Experimentally the energy transfer between widely spaced modes is found to be a function of the closeness of the modulation frequency to the natural frequency of the first mode. The modulation frequency, which depends on various parameters like the amplitude and frequency of excitation, damping factors, etc., has to be near the natural frequency of the low-frequency mode for significant transfer of energy from the directly excited high-frequency mode to the low-frequency mode. An experimental parametric identification technique is developed for estimating the linear and nonlinear damping coefficients and effective nonlinearity of a metallic cantilever beam. This method is applicable to any single-degree-of-freedom nonlinear system with weak cubic geometric and inertia nonlinearities. In addition, two methods, based on the elimination theory of polynomials, are proposed for determining both the critical forcing amplitude as well as the jump frequencies in the case of single-degree-of-freedom nonlinear systems. An experimental study of the response of a rectangular, aluminum cantilever plate to transverse harmonic excitations is also conducted. Various nonlinear dynamic phenomena, like two-to-one and three-to-one internal resonances, external combination resonance, energy transfer between widely spaced modes via modulation, period-doubled motions, and chaos, are demonstrated using a single plate. It is again shown that the closeness of the modulation frequency to the natural frequency of the first mode dictates the energy transfer between widely spaced modes. / Ph. D.

A new method for predicting forced vibratory blade response to total pressure distortion has been developed using modal and harmonic analysis. Total pressure distortions occur in gas turbine engines when the incoming airflow is partially blocked or disturbed. Distorted inlet conditions can have varying effects on engine performance and engine life. Short-term effects are often in the form of performance degradation where the distorted airflow causes a loss in pressure rise, and a reduction in mass flow and stall margin. Long-term effects are a result of vibratory blade response that can ultimately lead to high cycle fatigue (HCF), which in turn can quickly cause partial damage to a single blade or complete destruction of an entire compressor blade row, leading to catastrophic failure of the gas turbine engine. A better understanding and prediction of vibratory blade response is critical to extending engine life and reducing HCF-induced engine failures. This work covers the use of finite element modeling coupled with computational fluid dynamics-generated pressure fields to create a generalized forcing function. The first three modes of a low-aspect-ratio, transonic, first stage blade of a two-stage fan were examined. The generalized forcing function was decomposed to the frequency domain to identify the dominant harmonic magnitude present, as well as other contributing harmonics. An attempt to define the relationship between modal force with varying total pressure distortion levels produced a sensitivity factor that describes the relationship in the form of a simple multiplier. A generalized force was applied to the blade and varied harmonically across a frequency range known to contain the first natural frequency. The mean rotor stress variation was recorded and compared to experimental results to validate the accuracy of the model and verify its ability to predict vibratory blade response accurately. / Master of Science

On August 27, 2016, Southwest Airlines flight 3472 from New Orleans to Orlando had to perform an emergency landing when a fan blade separated from the engine hub and destroyed the cowling and punctured the fuselage. Initial findings from the metallurgical examination conducted in the National Transpiration Safety Board Materials Laboratory found that the fracture surface of the missing blade showed curving crack arrest lines consistent with fatigue crack growth. Fatigue is often cause by resonate vibrations. Modal analysis is a method that can model the natural frequencies and bending modes of turbomachinery blades. When performing modal analysis with finite element solvers like Mechanical ANSYS, images are often generated to help an engineer identify mode shapes created by nodal displacements. Manually identifying mode shapes from these generated images is an expensive task. This research proposes an automated process to identify mode shapes from gray-scale images of turbomachinery blades within a jet-engine. This work introduces mode shape identification using principal component analysis (PCA), similar to approaches in facial and other recognition tasks in computer vision. This technique calculates the projected values of potentially linearly correlated values onto P-linearly orthogonal axes, where P is the number of principal axes that define a subset space. Classification was performed using support vector machines (SVM). Using the PCA and SVM algorithm, approximately 5300 training images, representative of 16 different modes, were used to create a classifier. A test set was created with approximately 2000 unknown mode images. The classifier achieved on average 98.4% accuracy on the test set when using the bilinear Eigenface method. The accuracy was 98.6% when using the triangle interpolate Eigenface method. In addition, The results suggest that using digital images to perform mode shape identification can be achieved with better accuracy and computation performance compared to previous work. Potential generalization of this method could be applied to other engineering design and analysis applications.

On August 27, 2016, Southwest Airlines flight 3472 from New Orleans to Orlando had to perform an emergency landing when a fan blade separated from the engine hub and destroyed the cowling and punctured the fuselage. Initial findings from the metallurgical examination conducted in the National Transpiration Safety Board Materials Laboratory found that the fracture surface of the missing blade showed curving crack arrest lines consistent with fatigue crack growth. Fatigue is often cause by resonate vibrations. Modal analysis is a method that can model the natural frequencies and bending modes of turbomachinery blades. When performing modal analysis with finite element solvers like Mechanical ANSYS, images are often generated to help an engineer identify mode shapes created by nodal displacements. Manually identifying mode shapes from these generated images is an expensive task. This research proposes an automated process to identify mode shapes from gray-scale images of turbomachinery blades within a jet-engine. This work introduces mode shape identification using principal component analysis (PCA), similar to approaches in facial and other recognition tasks in computer vision. This technique calculates the projected values of potentially linearly correlated values onto P-linearly orthogonal axes, where P is the number of principal axes that define a subset space. Classification was performed using support vector machines (SVM). Using the PCA and SVM algorithm, approximately 5300 training images, representative of 16 different modes, were used to create a classifier. A test set was created with approximately 2000 unknown mode images. The classifier achieved on average 98.4% accuracy on the test set when using the bilinear Eigenface method. The accuracy was 98.6% when using the triangle interpolate Eigenface method. In addition, The results suggest that using digital images to perform mode shape identification can be achieved with better accuracy and computation performance compared to previous work. Potential generalization of this method could be applied to other engineering design and analysis applications.

This dissertation investigates the turn of the century fascination with synesthesia and efforts by Modernist artists and writers to produce cross-modal works that attempt to defy sensory boundaries. Works of impossible art are artistic and literary experiments with style and form that develop out of the realism and naturalism of the nineteenth century, to be sure; they are also conceived of by their creators as scientific experiments that test what is possible at the limits of perception. Accordingly, while my work is situated within the field of aesthetics, I take a neuroscientific approach to aid in understanding the modes of perception these works are attempting to explore. My project applies the findings of recent neuroscientific studies into clinical synesthesia as a guide for thinking about these Modernist works. The methodology of neuro-aesthetics allows me to develop a theory of sensory mimesis. Sensory mimesis is a holistic approach to explaining phenomenological experience that depends on a sensory semantics, more fundamental and more comprehensive than a linguistic semantics, that I propose filters our access to the world. What we ultimately learn from impossible art is that the range of neurodiversity in humans is broader than we tend acknowledge or appreciate. The notoriously indefinable and uncategorizable character of queer theory is an applicable framework to match the innumerable neurocognitive possibilities that are actually available. To this end, my dissertation suggests that a shift to a neuro-queer-aesthetic paradigm would not only expand human perceptive possibilities, but also enable compassionate engagement within and among our diverse communities. / English