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.

Interpreting Proper Orthogonal Modes in Vibrations

We investigate the interpretation of proper orthogonal modes (POMs) of displacements in both linear and nonlinear vibrations. The POMs in undamped linear symmetric systems can represent linear natural modes if the mass distribution is known. This is appoximately true in a distributed system if it is discretized uniformly. If a single mode dominates, the dominant POM approximates the dominant mode. This is also true if a distributed system is discretized arbitrarily. Generally, the POMs represent the principal axes of inertia of the data in the coordinate space. For synchronous nonlinear normal modes, the dominant POM represents a best fit of the nonlinear modal curve. Linear and nonlinear simulation examples are presented.

Nonlinear Normal Modes of Buckled Beams: Three-to-One and One-to-One Internal Resonances

Nonlinear normal modes of a buckled beam about its first buckling mode shape are investigated. Fixed-fixed boundary conditions are considered. The cases of three-to-one and one-to-one internal resonances are analyzed. Approximate expressions for the nonlinear normal modes are obtained by applying the method of multiple scales to the governing integro-partial-differential equation and boundary conditions. Curves displaying variation of the amplitude with the internal resonance detuning parameter are generated. It is shown that, for a three-to-one internal resonance between the first and third modes, the beam may possess either one stable mode, or three stable normal modes, or two stable and one unstable normal modes. On the other hand, for a one-to-one internal resonance between the first and second modes, two nonlinear normal modes exist. The two nonlinear modes are either neutrally stable or unstable. In the case of one-to-one resonance between the third and fourth modes, two neutrally stable, nonlinear normal modes exist.

An Approach for the Dynamics of Robotic Manipulators With Structural Flexibility of Links and Joints

In this paper, an approach is presented for the dynamic modeling and analysis of robotic manipulators having structural flexibility in the links and joints. The formulation allows the user to include different types of flexibilities, as required. This approach includes the dynamic effects of joint driving systems by considering the mass and moments of inertia of their elements, the rotor-link interactions, and the gear reduction ratios; all of which can have significant influences on the behavior of the manipulator. Both distributed-discrete and discretized-discrete parameter models of a robot can be analysed. In the discretized-discrete case, dynamic equations of motion are developed for four model types: rigid link - rigid joint, rigid link - flexible joint, flexible link - rigid joint, and flexible link - flexible joint. An example of a two-link manipulator is considered. Simulation results are presented for different models (flexible joint - rigid link, rigid joint - flexible link, flexible joint - flexible link) of the manipulator. The computations show the influence of joint and link flexibilities on the manipulator performance.

The Wide World of Translating Webs

Our webs are wide, very thin, two-dimensional, continua arising commonly as a material in transport in machine systems. Though they are thin, webs often require modeling as plates or shells, albeit very thin and flexible ones, because even small bending stiffness distinguishes their behaviors from membranes in critical ways. Technological applications generating interest in web mechanics include the manufacture and handling of paper where wide sheets are transported by rollers at the highest possible speed, thereby maximizing productivity. Material handling problems of a similar type also arise with tissues, films, magnetic media, textiles, fabrics, polymer sheets, and the like. In a technical world pressing for ever higher speeds of stable transport, the web instabilities of wrinkling and flutter commonly bound the productivity of a technological process. These instabilities can result in permanent damage or rupture of the material and disruption of the manufacturing process. Consequently, the presentation today addresses some findings on webs that relate to their modeling, the prediction and causes of wrinkling, and the effect of roller misalignment on web behavior during transport. To allow us to maintain this focus, the rich collection of works on membrane structures, including modeling of inflated membranes, space structures and fiber reinforced membranes will not be part of our discussion. For attention to interesting membrane developments readers might examine Reissner (1938), Steigmann and Pipkin (1989), Jenkins and Leonard (1991), Li and Steigmann (1993), and Haseganu and Steigmann (1994). The most important topic of web flutter caused by air flows over the web surfaces will not be addressed, though recent experimental findings can be found in Chang and Moretti (1992) and Nguyen (1993). Theories modeling the flow and web in these coupled problems tend to underestimate the flutter speeds. This problem area is one of great importance.

Mode Localization and Delocalization in Constrained Strings and Beams

The free vibration response of a string and a Euler-Bernoulli beam supported by intermediate elastic constraints is studied and analyzed by the transfer function method. The constrained system consists of three subsystems coupled by constraints imposed at the subsystem interfaces. For both the string and beam systems, curve veering and mode localization are observed in the lower modes when the distance between the elastic constraints is varied. As the mode number increases, the modes of the system become extended indicating that the coupling springs have little effect on the system at higher modes. A wave analysis is employed to further investigate the behavior of the systems at high frequencies. Reflection and transmission coefficients are formulated to show the effects of the constraints on the coupling of the subsystems. The weakly bi-coupled beam produces an interesting phenomena where a particular mode experiences no localization while neighboring modes are localized. The frequency at which this occurs is termed the delocalization frequency. Only one delocalization frequency exists and it occurs where the reflection coefficient of the propagating wave becomes zero.