A method for the modal analysis of continuous gyroscopic systems with nonlinear constraints is developed, which assumes that the nonlinear constraints can be expressed with piecewise-linear force-deflection profiles. Using this assumption, the mode shapes and natural frequencies are found for each state, and a mapping method based on the inner product of the mode shapes is developed to map the displacement of the system between states. To illustrate this method, a model for the vibration of a traveling string in contact with a piecewise-linear constraint is developed as an analog of the interaction between magnetic tape and a guide in data storage systems. Several design parameters of the guide are considered: flange clearance, stiffness, symmetry, and the guide’s position. Critical bifurcation thresholds exist, below which the system exhibits no chaotic behavior and is dominated by period one, symmetric behavior, and above which the system contains asymmetric, higher periodic motion with windows of chaotic behavior. These bifurcation thresholds are particularly pronounced for the transport speed, flange clearance, symmetry of the force deflection profile, and guide position.

This paper presents a novel 3-DOF planar parallel mechanism with 360-degree rotational capability, which can be used as a positioning device. A high rotational capability is necessary to reduce process time and to apply the mechanism to various fields such as micro machining and PCB depaneling. The proposed mechanism has the advantage of a continuous rotational capability over existing planar parallel mechanisms with limited rotation. The position and velocity kinematics are derived, and the singularities are analyzed based on the Jacobian matrices. The workspace can be determined not to have a singularity inside, and the kinematic variables for enlarging the singularity-free workspace are determined.

This paper deals with transverse vibrations of axisymmetrical annular plates of concave parabolic thickness. A closed-form solution of the partial differential equation of motion is reported. An approach in which both method of multiple scales and method of factorization have been employed is presented. The method of multiple scales is used to reduce the partial differential equation of motion to two simpler partial differential equations that can be analytically solved. The solutions of the two differential equations are two levels of approximation of the exact solution of the problem. Using the factorization method for solving the first differential equation, which is homogeneous and includes a fourth-order spatial-dependent operator and second-order time-dependent operator, the general solution is obtained in terms of hypergeometric functions. The first diferential equation and the second differential equation (nonhomogeneous) along with the given boundary conditions give so-called zero-order and first-order approximations, respectively, of the natural frequencies and mode shapes. Any boundary conditions could be considered. The influence of Poisson’s ratio on the natural frequencies and mode shapes could be further studied using the first-order approximations reported here. This approach can be extended to nonlinear, and/or forced vibrations.

In this paper an analytical method and a PDE-based solution to control temperature distribution in FGM plates is introduced. For the rectangular FGM plate under consideration, it is assumed that the material properties such as thermal conductivity, density, and specific heat capacity, vary in the width direction (y); and the governing heat conduction equation of the plate is a second-order partial differential equation. Since there has been little control synthesis work for PDE-based systems as compared to the abundance of control design techniques available for ordinary differential equations (ODEs), most of the proposed control approaches for continuous domain rely on discretizing the PDE model into a set of ODEs. Using Lyapunov’s theorem, we will show that with applying controlled heat flux through the boundary of the domain, the temperature distribution of the plate will approach to the desired distribution of T d ( x , y ). Finally, numerical methods are used to analyze transient heat transfer as distributed temperature T ( x , y , t ) converge to desired one of T d ( x , y ).

During the everyday usage of an automobile, only 10–16% of the fuel energy is used to drive the car — to overcome the resistance from road friction and air drag. One important loss is the dissipation of vibration energy by shock absorbers in the vehicle suspension under the excitation of road irregularity and vehicle acceleration or deceleration. In this paper we design, characterize, and test a retrofit regenerative shock absorber which can efficiently recover the vibration energy in a compact space. Rare-earth permanent magnets and high permeable magnetic loop are used to configure a four-phase linear generator with increased efficiency and reduced weight. Finite element method is used to analyze the magnetic field and guide the design optimization. A theoretical model is created to analyze the waveforms and regenerated energy of the harvester at various vibration amplitudes, frequencies, equilibrium positions, and design parameters. Experimental studies of a 1:2-scale prototype are conducted and the results agree very well with the theoretical predictions.

The synthesis of coupled systems including linear propagation media and nonlinear lumped subsystems is investigated. The resulting coupled system is expected to exhibit improved dynamic behavior. Such improvements are sought after by designing exclusively the lumped nonlinear subsystem and not by modifying the propagation medium. The lumped subsystem can be static or dynamic as well as passive or active. The design method is based on the Volterra-Wiener theory of nonlinear systems combined with the Linear Fractional Transformation employed for the analysis of uncertain linear systems. Although the techniques are applicable to a variety of practical engineering and physical systems, this work addresses acoustic source localization. Indeed, a moving acoustic source can be considered to nonlinearly modify the characteristics of a carrier acoustic wave. Such an acoustic carrier might be a monochromatic or polychromatic tone as well as other broadband signals such as band-limited white or colored noise. The sound source position signal is propagated through a nonlinear operator and then, under noise-free environment assumptions, determines the sound pressure level at the receiver location. In this paper, the proposed method is applied to the simplified case of a one-dimensional acoustic cavity defined by totally reflective barriers. Furthermore, the lossless wave equation is assumed to govern the sound pressure level in the homogeneous domain of interest. However, even in this simple scenario, only the additional assumptions of negligible source velocity and acceleration allow the derivation of an expression for the sound pressure level containing exclusively source displacement. In this context, simulation data series or analytical solutions, approximate or exact, are post-processed in order to determine the Volterra kernels, which effectively are a convenient extension of the impulse response concept in the nonlinear case, of the operator connecting source displacement to sound pressure level at the receiver. The outcome is Linear Time Invariant models depicting the dominant sound propagation dynamics. Then the synthesis stage is based on the properties of interconnected nonlinear systems that are described in the Volterra-Wiener framework. By using such properties, the signal processing algorithm for the estimation of the acoustic source position based on the received sound pressure level is finally developed.

Plant community and ground surface form a partially continuous ecosystem in conveying surface runoff and its erosion energy. It is one of the mechanisms for maintaining the stable development of a partially continuous ecosystem that the plant community and ground surface dissipate the erosion energy produced by surface runoff so as to control the soil erosion process of the ecosystem. Based on the energy fundamentals of hydraulics and by idealizing the structure of plant community, we obtain an ecological hydraulic model in this paper through a series of mathematical deductions, which includes three equations: (1) the equation on approaching energy balance of surface runoff moving across plant community and ground surface; (2) the equation on the process of dissipating energy of surface runoff by plant community and ground surface in an ecosystem; (3) the equation on the relationship among the pattern of plant community, ground surface and energy dissipation of surface runoff. Theoretically, the ecological hydraulic model can be used to calculate the dynamical process of energy dissipation of surface runoff by plant community and ground surface in a partially continuous ecosystem and to discuss the optimization of plant community pattern in a given section of the ecosystem.

Chatter is caused by two main mechanisms: the regenerative waviness and the mode coupling. Both of these two chatter mechanisms always exist simultaneously, but most studies only discuss the regenerative chatter behavior. The purpose of this paper is to investigate the mode coupling behavior in end milling process. A mechanical model considering both of the regenerative and mode coupling effects is then constructed to simulate the milling dynamics. It is shown that the stability of milling is dominated by the eigenvalues of the process matrix and the structure vibration trajectories are affected by the eigenvectors of the process matrix. The rotation direction of chatter vibration is an important feature to determine whether mode coupling chatter occurs or not. By analyzing vibration trajectories, this paper then shows that chatter vibration will rotate in the direction which periodically accumulates the vibration energy. Finally, some methods for adjusting the cutting conditions to avoid the mode coupling chatter are proposed.

In Kyoto bow fabrication, in order to bond each material, the glue which is made from the skin of the deer (Nibe) has been traditionally used. Recently, the synthetic adhesive is used instead of Nibe. The purpose of this study is to clarify the effects of the type of adhesive on the performance for the archer to draw Kyoto bow (Nibe bow and Synthetic bow). The measurement of motion was performed using MAC 3D system, and in order to clarify the relationships between the deformation and the load required to draw of the Kyoto bow, the motion analysis of the archer during the drawing motion of the Kyoto bows was performed by attaching markers and load cell onto the bows. In addition, the velocity of the arrow was calculated by the image processing. The loads and the maximum velocities of arrow with both bows were similar, however the arrow of Nibe bow drastically accelerates rather than that of Synthetic bow at the some point. Additionally, the time required to draw the bow of Nibe bow was significant shorter than that of Synthetic bow.

The multi-pulse orbits and chaotic dynamics of the simply supported laminated composite piezoelectric rectangular plates under combined parametric excitation and transverse loads are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motions for the laminated composite piezoelectric rectangular plates are derived from von Karman-type equation and third-order shear deformation laminate theory of Reddy. The four-dimensional averaged equation under the case of primary parametric resonance and 1:2 internal resonances is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plates. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plates. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plates are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plates.

In this paper an analytical method and a PDE-based solution to control temperature distribution in FGM thick plates is introduced. For the rectangular FGM thick plate under consideration, it is assumed that material properties such as thermal conductivity, density, and specific heat capacity are constant in length and width (x, y direction) but they vary in thickness direction of the plate; and the governing heat conduction equation of the thick plate is a second-order partial differential equation. Since there has been little control synthesis work for PDE-based systems as compared to the abundance of control design techniques available for ordinary differential equations (ODEs), most of the proposed control approaches for continuous domain rely on discretizing the PDE model into a set of ODEs. Using Lyapunov’s theorem, it will be shown how to obtain boundary heat flux required for producing a desired distribution of T d (x, y, z) .

The robots that can move on rough terrains are very important especially in Rescue operation, exploration, etc. In this research, a mechanism is introduced for a ring-like robot with a flexible body. This robot is moved by arms which are placed radially and have Reciprocating motion in this direction. By controlling the contraction and the extension of the arms which contact the ground, the robot will be forced to move which is called rolling-creeping motion. The robot is stable in stationary state; also the maximum angle which it can be stable is determined. Considering the speed of contracted arm is the input parameter, the speed of the extended arm for locomotion of the robot has been obtained from that. Not only the speed of mass center is accounted, but also the variation of the input parameter is computed for constant speed of the robot. So, dynamic analysis is illustrated by quasi-static stability assumption. Finally, the results of the motion simulation are shown to confirm equations.

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

In the classic cable theory, vibration of cables is usually analysed by writing the equations of motion in the nearness of the initial equilibrium configuration. Thus, a fundamental difference exists between out-of-plane motion, which substantially corresponds to the linear behaviour of a taut string, and in-plane motion, where self weight determines a sagged initial profile. This work defines a continuous approach in order to establish the initial shape when the cable is subjected to wind or fluid flow arbitrarily directed and a finite element approach in order to investigate the dynamic around the initial equilibrium shape of the cable. In particular, the equations of motion for a three dimensional case are written fully accounting for initial shape. This means that in the additional deformation also in the out-of-plane and along cable directions there is a term linked with the initial position. Stochastic solutions in the frequency domain are derived for a wind-exposed cable after linearization of the problem and by applying the Proper Orthogonal Decomposition Technique (POD) with the aim of reducing computational effort. Differences are shown with respect to the case in which out-of-plane initial displacement is neglected. In addition, a POD based approach to simulate modal wind forces is proposed and applied to the fully nonlinear equations of motion.

Hummingbirds and some insects exhibit “Figure-8” flapping motion that allows them to go through a variety of maneuvers including hovering. Understanding the flight characteristics of Figure-8 flapping motion can potentially yield the foundation of flapping wing UAVs that can experience similar maneuverability. In this paper, a mathematical model of the dynamic and aerodynamic forces associated with Figure-8 motion generated by a spherical four bar mechanism is developed. For validation, a FWMAV prototype with the wing attached to a coupler point and driven by a DC servo motor is created for experimental testing. Wind tunnel testing is conducted to determine the coefficients of flight and the effects of dynamic stall. The wing is driven at speeds up to 12.25 Hz with results compared to that of the model. The results indicate good correlation between mathematical model and experimental prototype.

The ability to precisely control the applied force and deformation of a grasped object is the focus of this paper. A simple mechanical end effector system with parallel grippers was developed to study compliance effects in precision grasping. A servo gripper was instrumented with force and position sensors, associated circuitry, hardware, and visual indicators; moreover, the sensors and servo motor were connected to a microcontroller that interfaced with a laptop computer. A closed-loop position control system was embedded within a force control system. Springs of varying, known stiffness were grasped to characterize and calibrate the force control system. Compliance effects of the servo gripper were observed and measured while grasping these springs under several discrete control conditions. Experimental data were compared to reduced order theoretical models for validation. A control scheme was successfully developed to precisely grasp and hold objects of varying size, shape, stiffness, and orientation, using the real-time data to establish correction factors for compliance and sensor drift. It was demonstrated that these effects can be minimized by modifying the motor control signals using the presented force and position feedback scheme.

The first step in the development of an integrated system encompassing Power Take-Off (PTO) with virtual Mass-Damping-Spring (V MCK ) for the VIVACE Converter (Vortex Induced Vibration for Aquatic Clean Energy) is achieved. VIVACE converts hydrokinetic energy of ocean/river currents to mechanical energy using Vortex Induced Vibrations (VIV). Subsequently, its PTO converts the mechanical energy to electricity. The objective integrated system acts as V MCK to support the hydro-mechanical component of VIVACE. The second function of the system is to act as PTO to implement the electro-mechanical component converting the harnessed mechanical energy to electrical energy without suppressing the hydro-mechanical energy harnessing mechanism of VIV. Vortex Induced Vibrations (VIV) are motions induced on long elastic bodies with bluff cross-section placed with their long axis perpendicular to a fluid flow due to periodic irregularities in this fluid-structure interaction phenomenon. In this paper, a single cylinder of VIVACE is considered. Even in this simplest case, the underlying physics of this phenomenon is strongly nonlinear. Special care is needed in designing systems that either support or enhance VIV or harvest the energy of VIV oscillations. In the first physical model of VIVACE, a mass-damper-spring arrangement was employed in the Marine Renewable Energy Laboratory (MRELab) of the University of Michigan to transmit mechanically the power to an electrical generator, which converted it to useful electrical power. A Virtual mass-damping-spring (V MCK ) mechanism is intended to substitute the existing physical elements in the MRELab consisting of an electric motor driven by a power electronic converter allowing for programmable mass, stiffness and damping values. The integrated V MCK system enables improved control of the mechanism originally generating and supporting VIV as well as improved power take-off efficiency and capability. The V MCK system employs advanced switching control of the power transfer process so that VIV for a given damping is not affected. The first step taken in this paper towards development of the integrated system consists of the identification of the V CK system. The mechanical transmission system consists of a belt and two pulleys. The cylinder in VIV is attached to one side of the belt causing it to oscillate and in turn drive the pulleys.

The ambient environment is full of energy of different forms such as sun light, wind, heat, hydraulic energy, and mechanical motion including vibration. People have been seeking ways to convert the ambient energy into useful forms since ancient time. With the global concern of energy and environmental issue, energy harvesting provides one attractive solution and becomes a new research frontier. However, the majority of current research on energy harvesting from mechanical vibration obtains 10μW to 100mW energy, which has only limited applications like self-powered wireless sensors. More than ten review articles appeared in the past five years on vibration energy harvesting, whereas, the majority of which focuses on the applications in microelectronics and wireless sensors. The objective of this review is to survey the research and applications of meso and marco scale energy harvesting from vibration, and discuss the particular challenges and future research directions. Topics include piezoelectric materials and electromagnetic transducers, relevant motion and magnification mechanisms, and power electronics and control, with applications on energy harvesting from human motions, vehicle suspensions and civil structures.

Design of robotic fish based on hydrodynamics is presented and Lighthill’s Large Amplitude Elongated Body Theory (LAEBT) is used for modeling of the robotic fish in linear path. A PID controller for control of speed in linear path is designed and simulations are presented which shows its effectiveness for speed control of the robotic fish. It has been shown that in perspective of used approximate LAEBT model, the used control law maintains kinematic parameters and therefore, the associated efficiency will be maintained.

The nonlinear response of shallow shells subjected to combined acoustic and thermal loads is analyzed using an efficient finite element modal formulation. The acoustic loads have non-white probabilistic characteristics and are simulated by an algorithm capable of reliably converging to a target power spectral density function and marginal probability density function. Factors contributing to the softening, hardening effect and modal contribution are also investigated along with their impact on the root-mean-square responses. Illustrative examples are given for cylindrical and spherical shells subjected to different combinations of acoustic and thermal loads.