Application of Parametric Uncertainty Modeling to a Flexible Structure

We present the results of a study in uncertainty modeling applied to the flexible structure at the University of Minnesota. In addition to additive and multiplicative uncertainty models, we examine parametric uncertainty descriptions in which the weights are obtained directly from input-output data. Two methods are examined, one based on a minimum norm model validation (MNMV) test and another in which the estimated co-variance of the parameters is used to arrive at the uncertainty weights. The resulting uncertainty models are then used to design μ-synthesis controllers, and the resulting closed-loop performance is evaluated. Additional data is taken in a closed-loop setting, and this data is used to refine the model. For the flexible structure studied, we show that the use of parametric uncertainty leads to higher performance than that attainable with purely additive or multiplicative uncertainty. Refinement of the model based on closed-loop data is also shown to result in increased performance.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Reduction of Forced Vibration Response by Optimum Balance of Linkage and Optimum Design of System

This paper proposes a new method to reduce the forced vibration response of frame of linkage. It is that the root-mean-square (RMS) value of binary maximum (Bmax) of forced vibration response at a series of angular velocities is taken as the objective function, and the counterweight mass parameters of links and the stiffness factors are used as design variables. Then, it is found out that the responses are related not only to the Bmax value of shaking forces, but also to the shape of curve of shaking forces. The calculation results are compared with those of two other methods used in the reduction of forced vibration response by optimized balance of linkages, and it is shown that the new method can significantly reduce the responses of frame of linkage.

Analysis of Operating Deflection Shapes Based on Subspace Method

In this paper, we propose the new method to identify the Operating Deflection Shapes (ODSs) from the measurement data of time domain. At first, we present the identification scheme of ODSs based on a state-space model. Then the scheme is extended to identify the ODSs adaptively for the time-varying systems by using the URV Decomposition (URVD). Proposed scheme is able to decompose the deformation of a structure under operating condition into the underlying superposition of well excited frequency components. This paper introduces the algorithm and shows the effectiveness of our proposed scheme applyed for both synthesized and experimental data.

The Surface Variational Principle: A Different Perspective for Structural Acoustic Modeling

This paper surveys the development and application of the surface variational principle (SVP) governing the acoustic interaction between surface pressure and normal velocity. SVP is analogous to the method of assumed modes for vibration analysis, in that it represents the response in terms of a sequence of basis functions that are globally defined. The system equations governing the series coefficients are obtained by requiring that the value of the variational functional be stationary. In the wavenumber-based version of SVP, the pressure and velocity are represented by dual range Fourier series. A brief description of the steps entailed in formulating the SVP equations and coupling them to the equations for an elastic structure is provided. Then the computational requirements of an SVP analysis relative to conventional boundary element and finite element techniques are discussed. This is followed by an example illustrating the convergence properties of SVP. Another example is used to highlight the physical interpretation of the SVP representation of surface response. The evolution of the present version of SVP is surveyed, along with some of its applications. The paper closes with a brief discussion of possible future applications of the method.

Dynamic Modelling and Solutions for a Transmission Mechanism With Flexible Support

In this work, the motion differential equations for a multiple-point meshing mechanism with flexible support are established by the Lagrange formula, and solved using a Laplace transform approach. The stable conditions and the formula for calculating this system’s natural frequencies are given and the general dynamic responses, in analytical form, are developed. The analysis pays special attention to the zero state response to a step function and constant loading inputs. Furthermore, the dynamic torques acting on the basic shaft and torsional bar are also discussed. This research lays the foundation for the analysis and design of this new type of transmission mechanism.

Identification of Viscoelastic Properties of Finite Element Structures With Joints

Identification of the damping and stiffness parameters of the composite joints in finite element structures is analyzed. For the modeling of the viscoelastic properties of the joints the classical Voigt-Kelvin and generalized Maxwell model (three parameter solid) are used. A time domain identification algorithm for classically and non-classically damped dynamic systems is developed. It is based on the application of an extended Kalman filter and least square technique. The algorithm uses complex modal analysis and sparse matrix technology. Both force and base excited systems are considered. Experimental verification of the identification results is carried out on a test structure. The accuracy of the modeling of damping in the joint using the Voigt-Kelvin and generalized Maxwell models is investigated.

Commercialization of Active Isolation for Jet Aircraft

Active Noise and Vibration Control (ANVC) technology is a proven solution for noise and vibration problems in aircraft. The challenges in commercializing this solution range from the development issues of choosing the best actuation, sensor, and control technology to obtaining sufficient flight test time and satisfying FAA requirements. This paper examines significant case histories in the progression of the Lord active vibration control program from conception to market. Throughout the development program, several important discoveries were made regarding the performance, reliability, and economics of Active Isolation Systems (AIS) in jet aircraft. First, practical speaker-based solutions cannot achieve global acoustic noise cancellation for engine tones above about 200 Hz. A comparatively small array of structural actuators placed in the dominant transmission path, such as in or near the engine mounts, are capable of global cancellation in the cabin up to at least 500 Hz. Second, the performance is generally better when cabin microphones are used as error sensor inputs because the AIS control system can compensate for flanking paths better than if accelerometers are used as error sensors. Third, when the actuators are placed in the dominant transmission path and close to the vibration source, the control system will simultaneously achieve global acoustic noise reduction in the cabin and vibration reduction in the aircraft structure without affecting the engine casing vibration levels.

Robust Passive-Active Mounts for Machinery and Equipment

Conventional vibration isolation mounts are not as effective as expected on a practical foundation whose resonant frequencies normally are within the bandwidth of interest. In addition, the low frequency enhancement is a characteristic of the passive mounts. Applying inertia actuators to the bottom attachment plate of the conventional mounts overcomes these shortcomings and enhances their performance significantly. This design concept has universal application since it is applicable to any dynamic system. It requires very little power and force capacity, i.e., a small percentage of the disturbance force, from the actuators to be effective for frequencies higher than the resonant frequency of the mount itself. The effectiveness of the proposed mounts for the machinery is demonstrated on the load transmissibility reduction at the foundation support (fixed end) due to disturbance from machinery above mounts. On the other hand, the vibration magnitude reduction of equipment above mounts due to disturbance from the foundation is used for evaluating the equipment isolation effectiveness. There is no stabilty or degradation problem when a number of the passive-active mounts are used on the same foundation. Furthermore, the more of this type of mounts used on a foundation the more effective the vibration suppression and the smaller actuator force requirement for each passive-active mount.

Development of Structural Identification Accuracy Indicators Using Fuzzy Logic

A fuzzy expert system was developed for autonomous in-space identification of spacecraft modal parameters. The in-space identification can be used to validate analytical predictions, detect structural damage, or tune automatic control systems as required. A fuzzy expert system determines accuracy of vibration data analysis performed autonomously using the Eigensystem Realization Algorithm. Evaluation of the data analysis output is imprecise and somewhat subjective. The expert system was developed using the knowledge provided the co-developer of the Eigensystem Realization Algorithm. The accuracy indicator represents the analyst’s degree of confidence in the analysis results. The fuzzy membership functions of the expert system were parameterized and tuned using numerical optimization.