Ji Yao Shen

Identification of dynamic properties of plate-like structures by using a continuum model

Abstract The common approach currently used in the aircraft structural analysis is the finite element method. NASAs research in computational structures technology (CST) is helping to develop the finite element analysis to a new stage, although the significant limitations still exist. The elements used in the finite element method are usually void of dynamics. The consequence is that hundreds and thousands of elements are needed to represent large flexible aircraft structures in order to acquire analytical accuracy. To avoid the large dimensionality the current practice is to reduce the order of the model for structural system identification and control synthesis. This approximation, however, can lead to system instability due to the dynamics which are ignored. In contrast, distributed parameter modeling seems to offer a viable alternative to the finite element approach for modeling large flexible aerospace structures. Distributed parameter models have the advantage of improved accuracy, reduced number of modal parameters, and the avoidance of modal order reduction. Most of the effort on the continuum modeling so far is contributed to the beam-like structures which are composed of beams, tethers and rigid bodies. For the aircraft structural analysis, however, another important type of structural elements is plate. The principle of the monocoque or semi-monocoque type of aircraft construction is fundamentally the use of a thin-walled tube to carry compression, tension, shear, and bending. It is necessary, therefore, to expand the continuum modeling methodology to the plate-like structures to satisfy the requirement in the aircraft structural analysis, especially for the monocoque structures. This paper has developed a continuum modeling algorithm for the identification of dynamic properties of plate-like structures. A closed-form solution of the Timoshenko plate equation consistent with the maximum likelihood estimator has been derived. The closed-form expressions of the gradient functions have thereby been resulted from the solution of the partial differential equation. The proposed distributed parameter model involves far fewer unknown parameters than independent modal characteristics for finite element models. Illustration of this approach is given by a computer simulation which shows that the estimated results by using continuum model are reasonably accurate compared with the theoretical results.

Overview of vibrational-based nondestructive evaluation techniques

Non-destructive damage detection is an important issue in almost all structural areas ranging from aerospace/aeronautical structures, civil infrastructures, and structural materials. The use of vibrational-based nondestructive evaluation techniques to locate structural damage has been attempted to evaluate the integrity of civil infrastructures, composite laminates, continuum structures, and especially aircraft and large space structures. In an attempt to develop a structural health monitoring system for rocket engines, hundreds of technical papers in the vibrational assessment area have been reviewed. This paper provides a comprehensive overview of various vibrational- based nondestructive evaluation techniques, including a brief introduction of the theoretical background of different methods, an analysis of their advantages and drawbacks, and a foresight of the applications of different methods towards different type of structures. To date most research into vibrational-based structural damage detection has been performed by a handful of researchers at a wide variety of sites with little or no coordination in research efforts. Many of these methods have been tested using mass- spring test models or simple planar truss models. Few of standard test problems truly embrace the essence of real- world structures and as such poor judges of the performance of a few method. There clearly is a gap between theoretical research and practical application. This paper would be considerably helpful for future research, and especially beneficial for the development of a structural monitoring system in choosing an applicable and realistic method as a basis.

Timoshenko Beam Modeling for Parameter Estimation of NASA Mini-Mast Truss

In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss is proposed. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure and the computational effort for the estimation of modal characteristics are improved. A maximum likelihood estimator for the Timoshenko beam model is also developed. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from other approaches.

Deflection control of beam-like structures by using a piezoelectric sensor and actuator

A finite element model for piezo-layer bonded beams, based on general finite element approach, has been developed. The modified model has been applied to the deflection controller design of a cantilevered beam supporting a distributed load q, by using piezoelectric layer as both sensors and actuators. The sensors generate electric voltages caused by the deflection of the loaded beam and the voltages through amplifiers apply to the actuators which generate control bending moments on the composite beam. A numerical examples for deflection control of a composite beam with seven elements is presented in detail in this paper.

Vibration suppression of a flexible manipulating system by using transfer matrix method

This paper models a two-arm flexible manipulating system by a set of generic partial differential equations, from which the transfer matrices for the flexible arms and revolute joints have been constructed. Based upon the compatibility conditions at the connecting points, the global system dynamic equation has been derived. Joint moments are used as the control actions. A typical control problem for end-effector vibration suppression has been investigated. Control law computation proceeds in the frequency domain based on the pole- placement method. The effectiveness of the vibration suppression by using distributed parameter modeling technique along with the application of transfer matrix method is indicated by means of the decay of the end-effector response time history computed based upon the modal expansion method.

A strain-energy criterion for recognition of identified modes of continuous structural models

Abstract In structural modal analysis and modal testing, an important but difficult task is to match the identified natural frequencies and the corresponding modal deflections. This process is called the modal recognition in this paper. There were some treatments towards this problem for the lumped parameter structural models. For the distributed parameter models, however, little research has been reported on the modal recognition problem. In this paper, a strain-energy criterion for modal recognition has been developed. As an example, a distributed parameter model for a two-beam structural system has been formulated, which is expected to simulate the dynamics of a two-arm manipulating system fixed on a shuttle. Transfer matrix method has been used to set up the dynamic equation of the system. The natural frequencies are obtained from the solution of the characteristics equation. Consequently, the mode shape functions are found out analytically. Strain energy can be viewed as a measure of the structural deformation. When performing modal analysis, we always assume that the structural system is vibrating at a particular natural frequency. The strain energy is, therefore, stored in the deflection caused by such a harmonic motion. The vibration at a particular natural frequency will not produce any strain energy in the other modal components. On the other hand, if a particular mode shape is contributed mostly by the deformation of a specific component of the global structural system, then the great percentage of the total strain energy will be stored in the deformation of that component. Based upon the calculation of the strain energy in the structural components we can find out which component is deformed most and in what motion it is deformed, thereby, the mode shape can be detected. The computer simulation demonstrated that the strain energy indicated an essentially perfect recognition of the identified natural frequencies with the corresponding mode shapes. The creation of the strain-energy criterion consummates the procedure of the distributed parameter modeling, modal identification and parameter estimation.

Distributed-parameter estimation for NASA Mini-Mast truss through displacement measurements

Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.