Compressive sensing (CS) theory states that, if certain conditions are met, a signal can be retrieved at a sampling rate that is lower than what Nyquist theorem requires. Among these conditions are the sparsity of the signal and the incoherence of the sensing matrix, which is constructed based on how the sensing system is designed. One effective method to render the sensing matrix incoherent is to use random processes in its construction. Diverse approaches have been proposed to randomize the sensing matrix including transmission at random transmitter positions and spectral coding with the use of a physical structure that responds very differently at disparate frequencies. In this work, a holey cavity with various frequency modes is used to spectrally code the ultrasound wave fields. Then, with the use of CS theory and simulations, it is shown that the sensing system that is equipped with such a cavity performs meaningfully better than a regular system in terms of sensing capacity, beam focusing, and imaging. What is more, the validity of Born approximation is investigated in this work to show its extent of applicability in imaging relatively small targets. Due to computational limitations, the simulation domain has been selected to be comparatively small; yet, the achieved results evidently show the concept and warrant further studies on holey cavities in ultrasound imaging, including their fabrication and experimental corroboration. The decrease in the number of measurements necessary for correct image reconstruction can make ultrasound sensing systems more efficient in size and scan time in a variety of applications including medical diagnosis, non-destructive testing, and monitoring.

Cycloidal rotors have the inherent ability to provide vectorized thrust with fast reaction times. However, their present efficiency levels restricts their routinely use as propulsion elements for air-vehicles. Efforts have been made to improve the performance of cycloidal rotors through the optimal combination of its geometric parameters. In the present work the performance improvement of cycloidal rotors is demonstrated using a different approach, namely by imposing an unsteady change on the dynamics and structure of the vortices developed around the blades. This required change on the flow field, around the blades, was applied by adding an harmonic vibration to the traditional cycloidal movement of the blades, thus causing the blades to vibrate as they describe their oscillating pitch movement. This research on the effect of harmonic vibration, on lift and drag coefficients, was done first for a single blade profile, and later for a full cycloidal rotor, and is based on the Takens reconstruction theorem and Poincaré map. Therefore, diverse test cases and conditions were considered: a single static airfoil, an oscillating blade profile, and a complete cycloidal rotor. We concluded that the optimal combination of harmonic vibration parameters, specifically; amplitude, phase angle and vibration frequency, under adequately tuned design conditions, can have a beneficial effect on cycloidal rotor performance.

Norway has an opportunity to harvest ocean wave energy through gyroscopic precession as an alternative source of renewable energy, within practical limitations. This research assesses the energy extracted by gyroscopic wave energy generators and their use to provide supplementary power to fish farms and lighting on oilrigs. This project implements the Moving Frame Method (MFM) in dynamics to model the extracted power from a gyroscopic wave energy generator. The MFM leverages Lie Group Theory, Cartan’s moving frames and a new notation from the discipline of geometrical physics. Continuing, the Principle of Virtual Work extracts the equations of motion from the structure of the Special Orthogonal Group. However, the MFM supplements its analysis with a novel application of the restriction on the variations of the angular velocities. This research extends previous work as follows: it accounts for motor torques, it opens a placeholder for buoyancy, and it solves the full 3D set of equations (without assuming negligible yaw). After showing how to obtain the suite of descriptive equations of motion, this project integrates them, however with a relatively simple integration scheme. To complete each step in the analysis, the rotation matrix is updated using the Cayley Hamilton Theorem and the Rodriguez formula. Finally, the results are displayed using the Web Graphics Library such that the actual numerical analysis and display happens on cell phones.

The undergraduate course, Design of Machine Elements has been offered by the University of Connecticut’s Mechanical Engineering Department for many years. It has been one of the most difficult courses for students to follow and understand, and also for the faculty to teach. A strong basic knowledge of mathematics, theoretical mechanics and the mechanics of materials is required for students to take this mandatory course and to fully follow its contents. To understand entirely the concepts of Design of Machine Elements, students should be acquainted with the history of the strength of materials. Being aware of the importance of such a course the ME faculty has worked to establish outstanding structural engineering teaching and research methods, and to create a departmental nucleus of intensive development of engineering mechanics research and development. The efforts described in this paper have facilitated the teaching and learning of the mechanics of materials and consequently the Design of Machine Elements as well. To accomplish these in both teaching and practical problem solving the instructor must use the unconventional approaches and students must put a great deal of effort into learning the material. It is important for students to have a general knowledge of mathematics and theoretical mechanics, but as this is a foundation of the course, the instructor should review and clarify the specific assumptions of engineering mechanics and strength of materials. One of the pedagogical challenges to be overcome, which is faced by both instructors and students, has always been to connecting the basic theorems and application procedures of engineering mechanics to their practical use in designing machine elements and in calculating static and dynamic stresses and deformations. The concept of avoiding stress concentrations by properly designing the shapes of machine frames and parts should also be emphasized. Transforming plane stresses and deformations into three-dimensional representations and calculations should also be considered. Since machine elements are usually in motion, a dynamic approach to stress and deflection analysis is important as well. After introducing the analysis of dynamic stresses and deformations, the instructor should cover the concept of fatigue, which is the next crucial step. The instructors’ approaches and the unconventional methods they use to familiarize students with such complicated concepts are discussed in this paper. An analysis of representations of stresses and deformations and fatigue analyses of different machine elements are also considered. This paper connects to some approaches previously presented in earlier papers as well as in courses, books and discussions by outstanding engineering mechanics theoreticians, including UConn faculty, especially Dr. Roman Solecki. The paper concludes by recommending effective teaching approaches to complicated machine design concepts and summarizing the lessons learned. This paper is a companion piece to the IMECE 2015 50776 [1].

A new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Timoshenko beam model that incorporates the surface energy, transverse shear and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when the surface energy effect is not considered. It is shown that the band gaps predicted by the current model depend on the surface elastic constants of each constituent material, beam thickness, unit cell size, and volume fraction. The numerical results reveal that the band gap based on the current non-classical model is always larger than that given by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.

In this work, a central difference finite volume lattice Boltzmann method (CDFV-LBM) is developed to compute 2D inviscid compressible flows on triangular meshes. The numerical solution procedure adopted here for solving the lattice Boltzmann equation is nearly the same as the procedure used by Jameson et al. for the solution of the Euler equations. The integral form of the lattice Boltzmann equation using the Gauss divergence theorem is applied on a triangular cell and the numerical fluxes on each edge of the cell are set to the average of their values at the two adjacent cells. Appropriate numerical dissipation terms are added to the discretized lattice Boltzmann equation to have a stable solution. The Boltzmann equation is discretized in time using the fourth-order Runge-Kutta scheme. The computations are performed for three problems, namely, the isentropic vortex and the supersonic flow around a NACA0012 airfoil and over a circular-arc bump. The effect of changing the grid resolution and the dissipation coefficients on the accuracy of the results is also studied. Results obtained by applying the CDFV-LBM are compared with the available numerical results which show good agreement.

At this moment all the methods which had been proposed have extremely limited application to only several specific constructions of kinematically indeterminate linkages, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem due to lack of enough four-bar loop information in their constructions. Planar single degree of freedom linkages up to ten-bar include two different types of mechanisms, i.e. pure bar linkages, such as four-, six-, eight-, and ten-bar; and geared-bar linkages, i.e. geared-five, seven, and nine-bar. The huge varieties of different types and constructions can serve as great testbeds for these methods. This research systematically investigates and modifies the graphical approach, i.e. virtual cam method, whose employment will show it to be an almost-universal method which can be compliantly applied on very wide range of kinematically indeterminate linkages. The procedures and criteria of the methodology are proposed and examined thoroughly to help locate key instant centers of all planar single degree of freedom kinematically indeterminate linkages up to ten-bar so that their complete sets of instant centers can be located successfully. We call this modified and improved technique as Virtual Cam – Hexagon Method. The results are verified carefully against traditional Kennedy Theorem approach and CAD modeling.

In this paper, a path-generating motion control scheme is proposed for a unicycle-type wheeled mobile robot navigating through multiple obstacles. The proposed motion control scheme computes the driving force and rotational torque of the robot in real time that drive the robot to a given goal position while avoiding multiple obstacles. The nonholonomic constraints as well as the dynamic equations of the mobile robot are used in the design of the motion control scheme, where a repulsive potential function is used for obstacle avoidance. In the control design, the Lyapunov stability theorem is used as a mathematical design tool. Under certain conditions, the proposed control guarantees asymptotic stability while keeping all internal signals bounded. The effectiveness of the proposed control method has been shown with realistic computer simulations.

Kinematic parameters have significant influences on the motion stability of parallel manipulators at singular configureations. Taking the plane 3-RPR parallel manipulator as an example, the motion stability at different types of singular configurations corresponding to the angular speed and velocity of the movable platform are investigated. At first, the second order of uncoupled dynamics equation for the 3-RPR parallel manipulator is established with the aid of the second class Lagrange approach. According to the Lyapunov first approximate stability criterion, the approximate conditions for the 3-RPR parallel manipulator with a stabile motion at singular configurations are determined based on the Gerschgorin circle theorem. Next, the exact Hurwitz criterion is utilized to study the motion stability and the load capability of the manipulator corresponding to the angular speed and velocity of the movable platform, as well as the directions of the external forces at two kinds of singular configurations: with a gained rotation-type DOF, and with a gained translation-type DOF, respectively. The results show that increasing both the angular speed and the velocity of the mass center of the movable platform can efficiently improve the motion stability of the 3-RPR parallel manipulator at singular configurations.

A decline in oil-related revenues challenges Norway to focus on new types of offshore installations and their maintenance. Often, ship-mounted crane systems transfer cargo or crew onto marine structures such as floating windmills. This project analyzes the motion of a ship induced by an onboard crane in operation. It analyzes the motion of a crane mounted on a ship using The Moving Frame Method (MFM). The MFM draws upon Lie group theory and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. This work extends a previous project that assumed many simplifications. It accounts for the masses and geometry of all components. This current approach also accounts interactive motor couples and prepares for buoyancy forces and added mass. The previous work used a symbolic manipulator, resulting in unwieldy equations. In this current phase, this research solves the equations numerically using a relatively simple numerical integration scheme. Then, the Cayley-Hamilton theorem and Rodriguez’s formula reconstructs the rotation matrix for the ship. Furthermore, this work displays the rotating ship in 3D, viewable on mobile devices. WebGL is a JavaScript API for rendering interactive 3D and 2D graphics within any compatible web browser without the use of plug-ins. This paper presents the results qualitatively as a 3D simulation. This research proves that the MFM is suitable for the analysis of “smart ships,” as the next step in this work.

The present paper proposes the application of the Reissners Mixed Variational Theorem (RMVT) for the accurate stress analysis of general multi-layered beam problems. Laminated materials usually differ from homogeneous materials in that they exhibit much higher transverse shear and transverse normal deformabilities. These characteristics, and others such as the Transverse Anisotropy (TA) and the Interlaminar Continuity of transverse stresses (IC), make Classical Laminated Theories (CLT) inappropriate for the analysis of multi-layered structures. The Carrera Unified Formulation (CUF) sets a framework in which classical-to-refined beam models can be generated by expanding the unknown variables over the cross-sectional domain by means of arbitrary functions. A LW expansion is adopted for both displacements and transverse stresses over the cross-section section domain. In this manner, the ZZ condition is automatically satisfied through the use of independent kinematics for each layer in a LW sense, with no need of introducing ad-hoc ZZ functions.

This paper proposes a path-planning control scheme for a mobile robot navigating through multiple obstacles. The proposed control consists of a trajectory generation scheme and a motion control scheme. The trajectory generation scheme computes the translational and rotational reference velocities in real time that drive the robot to a given goal position while avoiding multiple obstacles. The trajectory generation scheme is insensitive to high-frequency measurement noises. The motion control scheme computes the driving force and rotational torque required for the robot to track the reference velocities. The nonholonomic constraints of the mobile robot are used in the design of the kinematic trajectory generation scheme, where a repulsive potential function is used for obstacle avoidance. The dynamic model of the robot is used in the design of the motion control scheme. In the control design, the Lyapunov stability theorem is used as a mathematical design tool. Under certain conditions, the proposed control guarantees asymptotic stability while keeping all internal signals bounded. The effectiveness of the proposed control method has been shown with realistic computer simulations.

In this paper, dynamic characteristics of a beam with breathing crack is considered. Breathing crack is modeled as a bilinear oscillator. The stiffness of the cracked beam is estimated by using influence coefficients based on castigliano’s theorem and strain energy release rate (SERR). The equation of motion of breathing cracked beam is formulated using finite element method using Hamilton’s principle. The equation of motion of breathing cracked beam is converted into Mathieu-Hill type equation to obtain the regions of dynamic instability of beam using Harmonic balance method and it is further solved for Eigen frequency of the cracked beam. The increase in breathing crack depth increases the instability region and it is found that the effect of the crack location near to the fixed end is more for the cantilever beam, and this also increases the instability region. It is found that increase in dynamic instability index increases the instability regions of the cracked structure. In addition to that, the effect of static and dynamic loads are also investigated and discussed. The study has been conducted for the first two instability boundaries of the cracked structure only. It is hence seen that assuming the crack to remain open underestimates the stability boundaries of the system. Permitting the crack to open and close (breath) yields a stability boundaries in between the open and uncracked beam.

This paper presents a new method in dynamics — The Moving Frame Method (MFM) — and applies it to analyze the roll, yaw and pitch of a ship at sea, as induced by an onboard moving crane. The MFM, founded on Lie Group Theory, Cartan’s Moving Frames and a compact notation from geometrical physics, enables this expedited extraction of the equations of motion. Next, the method deploys the power of the special Euclidean Group SE(3) and a restricted variation to be used in Hamilton’s Principle, to extract the equations of motion. The mathematical model is then simplified to get a clearer picture of the parameters that impact the motion of the crane. The equations of interest are numerically solved by using fourth order Runge-Kutta method to obtain the specific data for the motion induced by the crane. Then, The Cayley-Hamilton theorem is used to reconstruct the rotation matrix. To supplement the paper, a webpage is coded with a model of the crane and ship, to graphically visualize the motion in 3D. It is imperative to note that while there are many approaches to dynamics, the MFM presents a consistent method, from 2D to 3D, and across sub-disciplines. The simplification is what has enabled undergraduate students to undertake this project.

Planar ten-bar single degree of freedom linkages have 230 valid isomers, 53 of them are kinematically indeterminate, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem. This paper investigates a graphical approach, i.e. virtual cam method, to help locate the key instant centers of these kinematically indeterminate linkages, after that all the instant centers can be located by Kennedy Theorem accordingly. The criteria of application are proposed and examined carefully, the results are verified against traditional Kennedy Theorem approach and CAD modeling.

The main purpose of this initial paper is to demonstrate the application of order statistics in the estimation of form error from a CMM measurement. Nowadays, modern industry sets high standards for geometrical precision, surface texture and material properties. There are many parameters that can characterize mechanical part, out of which flatness error plays important in the assembly process and performance. Recently, due to the greater availability and price reduction, Coordinate Measurement Techniques have increased their popularity in the industry for on-line and off-line measurements as they allow automated measurements at relatively low uncertainty level. Data obtained from CMM measurements have to be processed and analyzed in order to evaluate component compliance with the required technical specification. The article presents an analysis of a minimal sample selection for the evaluation of flatness error by means of coordinate measurement. In the paper, a statistical approach was presented, assuming that, in the repetitive manufacturing process, the distribution of deviations between surface points and the reference plane is stable. Based on the known, statistical distribution, order statistics theorem was implemented to determine maximal and minimal point deviation statistics, as it played a dominant role in flatness error estimation. A brief analysis of normally distributed deviations was described in the paper. Moreover, the case study was presented for the set of the machined parts which were components of a machine tool mechanical structure. Empirical distributions were derived and minimal sample sizes were estimated for the given confidence levels using the proposed theorem. The estimation errors of flatness values for the derived sample sizes were analyzed and discussed in the paper.

A new method in dynamics — the Moving Frame Method (MFM) — is used to conduct the analysis of how a robotic appendage (manipulator) on a Remotely Operated Vehicle (ROV) affects the motion of the ROV. An ROV performs multiple tasks on the seabed in the oil service industry. In most cases, an ROV pilot monitors and adjusts the movement of the vehicle due to induced motion by currents, buoyancy and the manipulators. Simulation data would assist the pilot and improve the stability of the ROV. This paper exploits a new method to analyze the induced movements of the ROV. The method uses the Special Euclidean Group (SE(3)) and the MFM. The method is supplemented with a restricted variation on the angular velocity to extract the equations of motion for the ROV. Then the equations of motion are solved numerically using Runge-Kutta Method and a reconstruction formula (founded upon the Cayley-Hamilton theorem) to secure the 3D rotations of the vehicle. The resulting motion is visualized with selected 2D plots. The 3D animation is displayed on a 3D web page. This paper closes with a summary of the simplifications used in the model and suggestions for advanced work.

This paper concerns with the quasi static linear theory of thermoelasticity for triple porosity materials. The system of governing equations based on the equilibrium equations, conservation of fluid mass, the constitutive equations, Darcy’s law for materials with triple porosity and Fourier’s law of heat conduction. The cross-coupled terms are included in the equations of conservation of mass for the fluids of the three levels of porosity (macro-, meso- and micropores) and in the Darcy’s law for materials with triple porosity. The system of general governing equations is expressed in terms of the displacement vector field, the pressures in the three pore systems and the temperature. The basic internal and external boundary value problems (BVPs) are formulated and on the basis of Green’s identities the uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single-layer and double-layer) and volume potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method and the theory of singular integral equations.

This paper proposes a leader-following formation control for a group of mixed-type mobile robots such as unicycle-type, carlike, and forklift-type robots. These robots are quite different in kinematics and dynamics. The leader follows its desired trajectory while the rest of robots are following the leader in a specified formation. The proposed formation control computes the desired driving force and steering torque of each robot. The proposed control consists of a formation control scheme and a kinematic trajectory generation scheme for the leader of a group. The nonholonomic constraints of each of the mixed-type mobile robots are taken into account in the design of the formation control and trajectory generation schemes, in which the Lyapunov stability theorem and the loop shaping method are used as design tools. Under certain conditions, the proposed formation control guarantees asymptotic stability while keeping all internal signals bounded. The effectiveness of the proposed control has been shown with realistic computer simulations.

Airships are expected to have in future an increasing diffusion in the aeronautic scenario. The use of airships is not necessary expected to be the same proposed in the past. Several new uses will assume a relevant importance in the next 20 years. The resurgence of airships has created a need for dynamics models and simulation capabilities of these lighter-than-air vehicles. A theoretical framework for designing flexible airships has developed deriving the equations for determining the flight behavior of an airship directly form the data of wind tests and CFD simulations. This model has been a fundamental part of the final design activities of the MAAT (Multibody Advanced Airship for Transport) EU FP7 project, which has studied an innovative cruiser feeder airship based transport system. Main results relates to the definition of a specific mathematical model, which allow approximating the behavior of a flexible or low structured semi rigid airship in presence of external oscillations, in pitch or yawing. Different shapes of airships with different shapes, also not conventional, are assumed and aerodynamic behavior has been evaluated when slightly disturbed from steady forward motion or from hovering conditions in presence of an impacting wind. New uses and the exigency of adopting photovoltaic energy for long endurance missions, is producing airship shapes, which are slightly different from traditional Parsifal. The model presents defines effective criteria based on constructal law, which allow designing an airship with an intrinsic stability in pitch and yaw. An approximate condition for a dynamically stable motion, such as unamplifying pitch, has been expressed in familiar aerodynamic quantities. These results allow stating the following theorem, which has been demonstrated: “Stable pitch flight conditions can be ensured if damping moment is in rotational equilibrium with the disturbing moment and if the disturbing force, the damping force, and the inertia force, are in translational balance”. If pitch angle and angular speed are small it can be obtained a relation that must be necessarily satisfied for ensuring a stability condition. An effective flight model based on energetic model of flight is also produced and results have been compared with traditional models giving a good accordance in terms of results.