Dissipative Joints Research Articles

Eigenfrequencies of the non-collinearly coupled Euler-Bernoulli beam system with dissipative joints

In this paper, we will compute asymptotically the eigenfrequencies for the in-plane vibrations of the general non-collinear Euler-Bernoulli beam equation with dissipative joints. Many different kinds of dampers are allowed, even within the same structure. This generalizes a previous result for collinear structures. Matrix techniques are used to combine asymptotic analysis with the wave propagation method. We will find that if the lengths of the beams are rational, there will be a finite number of “streams” of eigenfrequencies, and, like the collinear case, each lies asymptotically to a vertical line.

Eigenfrequencies of the three dimensional euler-bernoulli beam system with dissipative joints

In this paper, we will compute the transfer matrices to find the eigenfrequencies for the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beam structure with dissipative joints. We will allow the structure to be three dimensional, and thus we must consider all types of vibrations simultaneously, including longitudinal and torsional vibrations. The general structure considered will consist of any number of beams joined end to end to form a chain. Many different kinds of dampers are allowed, even within the same structure. We also will allow different materials within the structure as well as different beam widths. We then will show that asymptotic estimates can be used to find the eigenfrequencies approximately.

Eigenfrequencies of curved Euler-Bernoulli beam structures with dissipative joints

In this paper, we will compute asymptotically the eigenfrequencies for the in-plane vibrations of an Euler-Bernoulli beam system with dissipative joints, which allow the beams to be curved into an arc of a circle. This enhances the author’s previous result for structures involving straight beams, given in his preprint “Eigenfrequencies of the non-collinearly coupled Euler-Bernoulli beam system with dissipative joints". Matrix techniques are used to combine asymptotic analysis with a form of the wave propagation method.

Exponential Stability of Coupled Beams with Dissipative Joints: A Frequency Domain Approach

Two examples of coupled Euler–Bernoulli beams with a dissipative joint are considered. The joint placements that lead to exponential stability for these systems are characterized. The technique used shows input-output stability of a related controlled, observed system, and then shows that in these examples, input-output stability implies exponential stability. In the first example, the energy dissipation arises from a discontinuity in the shear at the joint. In the second example, the energy dissipation arises from a discontinuity in the bending moment at the joint. The analysis of this system involves a complete spectrum analysis of the zero dynamics of the associated controlled, observed system.

Asymptotic eigenfrequency distributions for the N-beam Euler-Bernoulli coupled beam equation with dissipative joints

In this paper, we will compute asymptotically the eigenfrequencies of the general collinear Euler-Bemoulli beam equation with linear joints. We will discover in the process that many different types of joints are equivalent, that is, if one joint of a structure is replaced by an equivalent type of joint, the eigenfrequencies to leading order would remain the same for both structures. Also, if the lengths of the beams are rational, there will be a finite number of “streams” of eigenfrequencies, each lying asymptotically to a vertical line.

Efficiency of percussive drilling of rock with dissipative joints

The nonlinear dissipative spring mass (NDSM) model for a percussive drill rod joint of the coupling sleeve (CS) type has been implemented into a Modula-2 program with the aid of which percussive drilling of rock is simulated. Transmission and dissipation of energy are first studied when a rectangular stress wave, generated through the impact by a uniform hammer, is transmitted through a single joint. The efficiency of energy transmission increases from 81 to 94% and the relative energy dissipation decreases from 8 to 1 or 2% when the length of the hammer varies from relatively short to relatively long. The effect of the joint preload is weak in the range from medium to relatively high preload. The efficiency of the percussive drilling process decreases with the number of joints but depends little on the joint preload. For soft rock, the efficiency increases with hammer length, whereas for medium and hard rock the dependence of efficiency on hammer length is not monotonic. This is because soft rock requires a long incident wave for efficient conversion of energy to work at the bit, whereas the reverse is true for hard rock. It is also found that the efficiency of the percussive drilling process may be considerably underestimated if the effects of each joint on the length and shape of the transmitted wave and of multiple reflections within the drill string are neglected.

Analysis, Designs, and Behavior of Dissipative Joints for Coupled Beams

In the construction of modern large flexible space structures, active and passive damping devices are commonly installed at joints of coupled beams to achieve the suppression of vibration. In order to successfully control such dynamic structures, the function and behavior of dissipative joints must be carefully studied. These dissipative joints are analyzed by first classifying them into types according to the discontinuities of physical variables across a joint. The four important physical variables for beams are displacement $( y )$, rotation $( \theta )$, bending moment $( M )$, and shear $( V )$. Dissipative joints can be classified into the following four types: (1) M and V are continuous, y and $\theta $ are discontinuous; (2) y and M are continuous, $\theta $ and V are discontinuous; (3) y and $\theta $ are continuous, M and V are discontinuous; (4) $\theta $ and V are continuous, y and M are discontinuous,according to the conjugacy of these variables. Mechanical designs have been achieved for all these dissipative joints of the linear passive type. The spectrum of two identical coupled beams with a linear dissipative joint shows an interesting pattern. It is proven that there are two families of eigenvalues, asymptotically appearing alternately and parallel to the imaginary axis with eigenfrequencies spaced vertically with gap $O( {n^2 } )$. This interesting spectral behavior has also been observed and studied in experiments conducted at the Modelling, Information Processing and Control Facility of the University of Wisconsin. Numerical simulations using the Legendre spectral method have also confirmed these spectral properties. All of the aforementioned mechanical designs, experimental, and numerical results are presented in this paper.

Modelling, analysis and testing of dissipative beam joints -experiments and data smoothing

The modelling, analysis and design of beam joints are important in the study of control and stabilization of modern large flexible space structures. In this paper we first briefly summarize our recent findings in the modelling of dissipative beam joints and their vibration eigenfrequency analysis. We then present beam joint experiments and the recorded data. We process the data by least square smoothing. The smoothed data shows strong consistency with the theoretical estimates. This in turn supports the correctness of our modelling as well as the accuracy of experimental measurements.

Dynamical control of industrial robots with elastic and dissipative joints

In this report some problems about dynamical control of industrial robots performing high speed continuous movement are presented. At first, automatic generation of robot dynamical models is dealt with and a new code, DYMIR, developed at Rome University is presented. In new DYMIR an extension that takes into account gear-boxes elasticity is included. Thereafter a study is presented on robot control systems based on a nonlinear feedback from local joint variables that makes the system decoupled and linear in nominal condition. The influence of the control implementation via a discrete algorithm, of joint elasticity (neglected in the control design) and of parameter variation is evaluated by using simulation.