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Combined systems, which are flexible structures carrying moving subsystems, are seen in various applications. Due to structure-subsystem interactions, the structure in a combined system encounters jump discontinuities in its internal forces (such as the bending moment and shear force of a beam). Accurate estimation of such jump discontinuities is important to the performance, safety, and longevity of a combined system. Because of the time-varying nature and complexity of structure-subsystem interactions, conventional series solution methods experience slow convergence, and the Gibbs phenomenon in computation and the improved series expansion methods are limited to certain proportionally damped continua under moving forces and moving oscillators. In this paper, a novel modified series expansion method (MSEM) is proposed to resolve the aforementioned issues with the existing series solution methods. Through the introduction of a jump influence function, the proposed method produces fast-convergent series solutions and accurately predicts the jump discontinuities without the Gibbs phenomenon. The MSEM is applicable to structures with nonproportional damping and subject to arbitrary boundary conditions, and it can easily manage general M-DOF moving subsystems having multiple contact points with a supporting structure. As an important result of this investigation, a mathematical proof of the convergence of the MSEM-based solutions is given for the first time. Additionally, two numerical examples are presented to demonstrate the accuracy, efficiency, and versatility of the proposed MSEM in modeling and analysis of combined systems. [ABSTRACT FROM AUTHOR]

As a new strategy for magnetic levitation envisioned in the 1990s, the Inductrack system with Halbach arrays of permanent magnets has been intensively researched. The previous investigations discovered that an uncontrolled Inductrack system may be unstable even if the vehicle travels well below its operating speed and that instability can be persistent near and beyond the operating speed. It is therefore necessary to stabilize the system for safety and reliability. With strong nonlinearities and complicated electromagneto-mechanical coupling, however, the transient response of such a dynamic system is difficult to predict with fidelity. Because of this, model-based feedback control of Inductrack systems has not been well addressed. In this paper, by taking advantage of a recently available two degrees-of-freedom transient model, a new feedback control method for Inductrack systems is proposed. In the control system development, active Halbach arrays are used as an actuator, and a feedback control law, which combines a properly tuned proportional-integral-derivative controller and a nonlinear force-current mapping function, is created. The proposed control law is validated in numerical examples, where the transient motion of an Inductrack vehicle traveling at constant speeds is considered. As shown in the simulation, the control law efficiently stabilizes the Inductrack system in a wide range of operating speed, and in the meantime, it renders a smooth system output (real-time levitation gap) with fast convergence to any prescribed reference step input (desired levitation gap). [ABSTRACT FROM AUTHOR]

Flexible structures carrying moving subsystems are found in various engineering applications. Periodic passage of subsystems over a supporting structure can induce parametric resonance, causing vibration with ever-increasing amplitude in the structure. Instead of its engineering implications, parametric excitation of a structure with sequentially passing oscillators has not been well addressed. The dynamic stability in such a moving-oscillator problem, due to viscoelastic coupling between the supporting structure and moving oscillators, is different from that in a moving-mass problem. In this paper, parametric resonance of coupled structure-moving oscillator systems is thoroughly examined, and a new stability analysis method is proposed. In the development, a set of sequential state equations is first derived, leading to a model for structures carrying a sequence of moving oscillators. Through the introduction of a mapping matrix, a set of stability criteria on parametric resonance is then established. Being of analytical form, these criteria can accurately and efficiently predict the dynamic stability of a coupled structure-moving oscillator system. In addition, by the spectral radius of the mapping matrix, the global stability of a coupled system can be conveniently investigated in a parameter space. The system model and stability criteria are illustrated and validated in numerical examples. [ABSTRACT FROM AUTHOR]

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed. [ABSTRACT FROM AUTHOR]

A piezoelectric forceps actuator (PFA) is developed for potential use in minimally invasive surgery, biological cell diagnosis and semiconductor industrial applications. This article is concerned with modelling, vibration analysis and boundary feedback control of the actuator. In the development, the PFA is viewed as a slightly-curved beam laminated with piezoelectric layers. By generalised Hamilton's principle, the dynamic governing equations of the actuator are derived. The PFA control system that consists of the piezoelectric composite curved beam, a sensor and control logic is formulated by using distributed transfer functions. With the transfer function formulation, the natural frequencies, mode shapes and frequency response of the actuator are then predicted and a stabilising boundary feedback control law is developed. In addition, a characteristic performance analysis of the PFA is conducted, to relate the system parameters and multimorph configuration to the natural frequencies, damping and piezoelectric moment of the PFA. The theoretical predictions by the actuator model are verified in experiments. [ABSTRACT FROM AUTHOR]

Based on the introduction of a nonnegative adjustable parameter into Poisson's ratio, a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes. Three fundamental issues in this new method are addressed. First, a nonnegative adjustable parameter is introduced into the constitutive law, automatically representing unwrinkled (taut) and wrinkled states of a membrane. Second, a parametric variational principle is developed for the new membrane model. Third, by the variational principle, the original membrane problem is converted to a nonlinear mathematical programming problem. The variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization. Three typical examples are given to show the effectiveness of this method. [ABSTRACT FROM AUTHOR]

Although quaternions are singularity-free in modeling and analysis of rigid bodies in three-dimensional motion, description of torques may lead to unbounded response of a quaternion-based model. This paper gives theorems on the conditions of torque-induced singularity in four coordinate systems: inertial frame, body frame, Euler basis, and dual Euler basis. According to the theorems, torques applied in an inertial frame or a body frame or a Euler basis will never cause unbounded motion; torques applied in a dual Euler basis, however, may lead to unbounded motion. [ABSTRACT FROM AUTHOR]

Large deployable mesh reflectors are found in many space applications. To warrant the performance of this type of space structure, it is desirable to have a methodology for systematic design of deployable mesh reflector surface geometries that can yield high surface accuracy and produce almost uniform distribution of member lengths and triangular facet sizes while maintaining a minimum total member length. The desired design methodology, however, is currently unavailable. This effort aims to fill the aforementioned technical gap in the literature. Presented in this paper is a new optimal geometry mesh design method that automatically determines the nodal coordinates and member connectivity for a given deployable mesh reflector with high surface accuracy and almost uniform member lengths. This design method also guarantees the pseudogeodesic property of the generated surface mesh geometry, which in many cases gives a minimum total member length. The proposed method is applicable to spherical and parabolic surfaces with either a center-feed configuration or offset-feed configuration, and it can meet the operating frequency requirements of large deployable mesh reflectors. [ABSTRACT FROM AUTHOR]

Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a new stability test is established for heat conduction in one-dimensional multilayer composite solids that have internal heat generation at a rate proportional to the interior temperature. In the development, a spatial state formulation in the Laplace transform domain and a root locus analysis yield a stability criterion. This criterion gives an upper bound of heat source for thermal stability and relates the degree of excessive heat production to the number of unstable (positive) eigenvalues. The proposed stability test does not need any information on system eigenvalues, requests minimum computational effort, and is applicable to composites with thermal resistance at layer interfaces and bodies with nonuniformly distributed parameters. The convenience and efficiency of the stability test are demonstrated in three numerical examples. [ABSTRACT FROM AUTHOR]