H. Baruh

Dynamics and Control of a Translating Flexible Beam With a Prismatic Joint

The complete dynamic model of a translating flexible beam, with a tip mass at one end and emerging from or retracting into a rigid base at the other, is presented. The model considers the effect of elastic and translational motions of the beam on each other. The properties of the eigenfunctions of a fixed-free beam are exploited to obtain closed-form expressions for several domain integrals that arise in the model.

Actuator placement in structural control

The placement of force and torque actuators for structural control problems is considered. Objective functions are defined based on the elements of the actuator influence matrix, and optimization studies are conducted. The performance of the control is compared. The results indicate that a relatively even distribution of the actuators gives satisfactory results, whereas a close spacing of the actuators leads to excessive fuel and energy use. In all cases, several evenly spaced actuator distributions are found to be suitable. In addition, torque actuators are found to be less desirable than force actuators because they excite the higher modes to a greater degree. The efficiency of piecewise-continuous actuators is analyzed. Piecewise-continuous actuators are more realistic models than point actuators and they reduce stress levels. However, if their contact area is too large, they use more fuel.

A closed-form solution procedure for circular cylindrical shell vibrations

Abstract A systematic procedure for obtaining the closed-form eigensolution for thin circular cylindrical shell vibrations is presented, which utilizes the computational power of existing commercial software packages. For cylindrical shells, the longitudinal, radial, and circumferential displacements are all coupled with each other due to Poissons ratio and the curvature of the shell. For beam and plate vibrations, the eigensolution can often be found without knowledge of absolute dimensions or material properties. For cylindrical shell vibrations, however, one must know the relative ratios between shell radius, length, and thickness, as well as Poissons ratio of the material. The mode shapes and natural frequencies can be determined analytically to within numerically determined coefficients for a wide variety of boundary conditions, including elastic and rigid ring stiffeners at the boundaries. Excellent agreement is obtained when the computed natural frequencies are compared with known experimental results.

Modal sensing of circular cylindrical shells using segmented piezoelectric elements

In this computational study, we investigate the use of thin piezoelectric films to detect the vibration of circular cylindrical shells. Rather than use complicated sensor shapes for modal filtering, we consider simple rectangular shapes and leave the measurement filtering and reconstruction of the system dynamics to full order modal observers. Simulations indicate that decreasing the magnitude of the real part of the observer gain leads to slower convergence but to the desired mode. Larger values lead to faster convergence but to the actual sensor measurements, indicating the occurrence of minimal signal filtering. Increasing the number of sensors can improve observer performance provided that they are placed intelligently on the shell. If a sensor cannot adequately detect the mode which it was intended to sense, sensor output cancelation may affect the behavior of all modal observers. In addition to the signal measurement analysis, the contribution of different mode types within different frequency bands is also investigated, as well as the determination of an adequate number of vibrational modes to include in the simulations.

Gibbs phenomenon in structural mechanics

The concepts of complementary boundary condition and interior condition are discussed. Guidelines are developed to eliminate the Gibbs effect when selecting trial functions for the series expansion

Another look at admissible functions

Abstract Problems associated with using global admissible functions in boundary value problems are discussed. It is shown that if care is not taken, it is possible to construct sets of trial functions that yield inaccurate results which take too long to converge. The concept of complementary boundary conditions is introduced, and their existence is established. Complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries. It is shown that trial functions that yield incorrect or very slowly converging results are those that violate the complementary boundary conditions. A revision for the definition of admissible and comparison functions is proposed that takes the complementary boundary conditions into consideration.

Analytical perturbations in Markov chains

Abstract The problem of recomputing the steady-state probabilities in a Markov chain is considered, after a small deviation is introduced to the original infinitesimal generator. Approximate expressions are developed to calculate the corresponding perturbed vector of probabilities. Computational stability and accuracy issues associated with the approximation are discussed. As an application, the perturbation approach is incorporated into an optimization scheme to identify workloads that maximize the output rate in a production line, where qualitative and quantitative measures are introduced to control the accuracy of the perturbation.

IDENTIFICATION OF MODAL PARAMETERS IN VIBRATING STRUCTURES

Abstract A method is presented for the identification of the eigensolution associated with vibrating structures. The identification can be performed in the presence of periodic external excitations and noisy measurements. It is assumed that the mass properties of the structure are known, and that the stiffness properties are not known. Linear combinations of the eigensolution obtained with an estimate of the stiffness properties are taken by using unitary transformation matrices to identify the actual eigensolution. The criterion for rotation is based on the number and magnitude of peaks in the frequency spectra of the response of the postulated modal co-ordinates.

Identification of external excitations in self-adjoint distributed systems using modal filters†

A method is presented for the identification of external excitations acting on distributed parameter systems and, for certain special cases, the parameters contained in the equations of motion. By extracting the modal co-ordinates from the system output, and using these modal co-ordinates to identify the modal excitations acting on a number of modes, the actual external disturbances are synthesized. The modal co-ordinates are extracted from the system output by interpolation of the sensors measurements and use of the expansion theorem, a process known as modal filtering. It is shown that the accuracy of the identification improves as the number of sensors is increased. The effects of factors such as measurement noise and interpolation error are analyzed.

Simultaneous maneuver and vibration suppression of flexible spacecraft

Abstract A method is described for the simultaneous large-angle maneuver and vibration suppression of flexible spacecraft. The control action is carried out in two independent systems, one system performing the maneuvers and the other system controlling the elastic motion. The vibration is suppressed using a natural control. It is shown that control of the elastic motion does not distort the maneuver because the spacecraft linear and angular momenta are conserved regardless of spacecraft modeling errors. Thus, the maneuver can be designed and performed independently of the elastic motion control.