Bingen Yang

Transfer Functions of One-Dimensional Distributed Parameter Systems

Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.

Modal expansion of structural systems with time delays

Conventional modal analyses are not applicable to structural systems with time delays because time delays destroy any possible orthogonality among system eigenvectors. A new series solution method is proposed for transient response analysis of a class of delayed linear structural systems. In this method, inverse Laplace transform is combined with a root locus sensitivity analysis, leading to a relation between the transfer function residues and eigensolutions of the delayed system. With this relation, closed-form time-domain response can be accurately and efficiently estimated in series of eigenvectors, without involving transfer function singularities and s-domain integration, which are usually encountered in inverse Laplace transform. The proposed method is illustrated on a gyroscopic dynamic system under delayed feedback control.

Noncolocated Control of a Damped String Using Time Delay

Recent research studies noncolocated control of flexible mechanical systems using time delay. The developments are limited to undamped flexible systems; damped flexible systems have not been considered. This paper investigates noncolocated vibration control of a viscously damped string using time delay. The control system is formulated in the Laplace transform domain. Based on the understanding of the system eigenstructure, a modified Bode plot of the feedback controller is introduced in a design region

Analysis of Ring-Stiffened Cylindrical Shells

A new analytical and numerical method is presented for modeling and analysis of cylindrical shells stiffened by circumferential rings. This method treats the shell and ring stiffeners as individual structural components, and considers the ring eccentricity with respect to the shell middle surface. Through use of the distributed transfer functions of the structural components, various static and dynamic problems of stiffened shells are systematically formulated. With this transfer function formulation, the static and dynamic response, natural frequencies and mode shapes, and buckling loads of general stiffened cylindrical shells under arbitrary external excitations and boundary conditions can be determined in exact and closed form. The proposed method is illustrated on a Donnell-Mushtari shell, and compared with finite element method and two other modeling techniques.

Eigenvalue Inclusion Principles for Distributed Gyroscopic Systems

Several inclusion principles have been presented for distributed gyroscopic systems under pointwise, non dissipative constraints. When a distributed gyroscopic system is modified with an added spring (or a lumped mass), its natural frequencies will increase (or decrease), and alternate with those of the unmodified system.

Nonlinear Deployable Mesh Reflectors

A reflector is a structural device that receives and reflects electromagnetic signals. A reflector normally has a dish shape as working surface and is supported by another structure (commonly a truss) behind. Unlike reflectors on the ground, when a reflector is installed onto a satellite or a space shuttle and used in space, many crucial requirements must be considered, one of which requires that the reflector has to be deployable. Because the size of a space reflector is usually much larger than the spacecraft that carries it, the reflector must be first folded into a small volume on the ground that can be stored inside the spacecraft, and then be deployed into the space after the spacecraft has been launched onto the designated orbit. After the deployment is completed, the reflector will produce and automatically maintain a working surface (aperture) with tolerant surface errors. Due to this particular feature, such structural devices are called deployable reflectors. As one of many types of deployable reflectors, deployable mesh reflectors have broad space applications, and have brought continuously interest in academia and industry in the past. Deployable mesh reflectors have been used in several renowned projects, such as ETS VIII for satellite communication, MBSAT for global broadcasting, “NEXRAD in Space (NIS)” mission for remote sensing and climate forecasting and GEO-mobile satellites by Boeing for mobile communications (Thomson 2002; Natori et al. 1993; Meguro et al. 1999; Im et al. 2003). Deployable mesh reflectors are also envisioned for many other applications such as high data rate deep space communications, Earth and planetary radars, and RF astronomy observations. Figure 8.1 illustrates a structure design for deployable mesh reflectors that has been considered by NASA engineers and studied in our research. The reflector is supported by the flat truss on the boundary and the working surface is constructed by the mesh and the front net. The nodes of the front net and rear net are connected by tension ties, where the actuators are installed. Those actuators properly adjust the length of the tension ties, so as to generate and maintain the desired working surface during the deployment and the in-space mission. According to the structural configuration in Fig. 8.1, the mesh reflector can be modeled as a nonlinear truss structure (shown in Fig. 8.2), whose elements can only sustain axial tension stress. The structure is fixed on the boundary and the working surface is formed by the truss elements. The tension ties are connected to the nodes, which provide the vertical external loads because of the symmetry between the front net and the rear net in the configuration under the concern. There are two crucial factors in performance assessment of deployable mesh reflectors: the aperture size of the reflector (mostly in term of the diameter) and the root-mean-square (RMS) value of the surface error. According to the antenna theory, larger-sized reflectors are capable of transmitting greater amount of data with higher resolution, and the smaller surface RMS error implies broader frequency bandwidth of the transmitted signals. The characteristic ratio, which is defined as the ratio of the reflector diameter to surface RMS error, is one of the key parameters to evaluate the performance of the mesh surface. Obviously, to increase the characteristic ratio, we can either increase the diameter of the reflector or decrease the surface RMS error; both of which, however, will enlarge the number of mesh cells, and increase the complexity and difficulty in design and manufacturing of this kind of reflectors. Therefore, development of large-sized deployable reflectors with small surface RMS errors, although in urgent demand due to the stringent requirements on surface performance to serve signal with high accuracy, has been a challenge for years.Previous investigations (Hedgepeth 1982a,b) have shown the performance limitation due to thermoelastic strain and manufacturing errors of materials in passive structure. It has been suggested that active surface (shape) control becomes necessary to improve the surface performance of deployable space reflectors for space missions and other applications. In this chapter, we present the results from our research project on developing the active surface control (ASC) architecture by using nonlinear modeling and analysis techniques.The remaining of the chapter is arranged as follows: Sect. 8.1 specifically states the objectives of the research. Section 8.2 presents the theoretical formulation of problem modeling and analysis. Then the numerical results and discussions will be provided on a sampled deployable mesh reflector in Sect. 8.3. Finally, Sect. 8.4 addresses some remarks on the progress of development of ASC architecture and the future research direction, and then concludes the chapter. Open image in new window Fig. 8.1 Configuration of a deployable mesh reflector Open image in new window Fig. 8.2 3D truss model of mesh reflectors

Data-glove-based fuzzy control of piezoelectric forceps actuator

This paper discusses a novel concept idea of utilizing smart structure in biomedical, minimum invasive surgery (MIS), MEMS manufacturing assembly line and also as a miniature robotic gripper system. The proposed prototype of a miniature piezoelectric forceps actuator (PFA) is composed of two symmetric slightly curved composite beams which each bonded with piezoelectric ceramic layer. The PFA is an innovative forceps actuator that comes with a data glove. The data glove is simply a custom-made glove with two embedded resistance-bending sensors located on thumb and index fingers. Any users can control opening and closing of the PFA by just wearing the data glove. A thin curved beam theory bonded with piezoelectric ceramic will be derived based on Hamiltons principle and its deflection behavior will be simulated based on distributed transfer function method (DTFM). A feasibility study of simulation open loop data glove-based fuzzy logic controller allows the user to open and close the PFA remotely. The bending movement of the thumb and index finger will be formulated in a table of rules based to produce the necessary output controller gain to control the PFA.

Modal controllability and observability of general mechanical systems

Controllability and observability are studied for general mechanical systems with combined effects ofdamping, gyroscopic and circulatory forces. A new modal analysis is proposed to represent the system transfer functions by the nonorthogonal eigenvectors that are associated with the original equations of motion. Investigation of linear independence of the rows and columns of the transfer functions yields the modal controllability and observability conditions. Because of their explicit relationships with the vibration modes, the controllability and observability tests require less computation than the conventional criteria, avoid trial and error in selection and positioning of actuators and sensors, and can be applied to systems with unidentified parameters. Moreover, the closed-loop root locus sensitivity coefficients are examined to give insights into modal controllability and observability, and to provide useful guidance for active controller design.

Genetic algorithm based optimization design of miniature piezoelectric forceps

This paper studies about a simulation of a derived model for the steady-state force-deflection behavior of a miniature piezoelectric forceps actuator (PFA) based on complementary strain energy. Utilizing a genetic algorithm (GA) based as a design tool to simulate and optimize the physical design parameters of the PFA to get the optimum grasping force-deflection end tip of the PFA within desired physical constraints. Simulation studies of the optimized PFA parameters based on GA are presented. The piezoelectric forceps is remotely controlled miniature gripper and potentially to be used in tele-surgery, minimally invasive surgery, MEMS industrial assembly line, pick and place hazardous materials in tight and small space.

Static Deflection Behavior of a Piezoelectric Forceps

A model is described for predicting quasi-static behavior of a piezoelectric forceps actuator (PFA), which consists of two slightly curved composite beams with bonded piezoelectric layers. The PFA is an innovative medical device that is potentially useful for minimum invasive surgery. The PFA model is compared to the deflection measurements made by a curvature sensor in experiments. This model, with a slight modification, can also be applied to other types of piezoelectric actuators with curved structural components.Copyright