In diesem Artikel wird das in den letzten drei Jahren am Institut fur Baustatik und Konstruktion der ETH Zurich entwickelte Computerprogramm FLASH (Finite ELement Analysis of SHells) fur die numerische Berechnung linear-elastischer Flachentragwerke nach der Methode der finiten Elemente vorgestellt.

Matrix Methods in Elasto Mechanics

Das Computerprogramm FLASH

This paper is concerned with the system approach for structural dynamics. First, the concept of dynamic mass is presented. Second, the determination of a dynamic mass is given relative to the reaction forces and moments between two substructures in terms of the cantilever normal modes of one substructure. Third, it is shown how one can simply couple and uncouple substructures for dynamics problems. Fourth, an example is given for the digital simulation of a sine wave test for the purpose of calculating rotational response of the shaker. Fifth, forcing functions are mathematically determined from the measured responses of the space vehicle in flight. Finally, it is shown how one can perform a hybrid test simulation by combining a real-time analog computer with digitally determined structural characteristics, shaker properties and actual control equipment in order to investigate the stability of the control loop.

A Practical Approach to Spacecraft Structural Dynamics

In the early design of compressors and turbines, it was of importance to locate the rotor critical speeds so as to insure that a turbo rotor would not be operating at a critical speed. As compressor and turbine design became more sophisticated, a more detailed analysis of the rotor damped critical speeds and rotor log decrements was necessary. With compressors and turbines operating at higher speeds, under high power levels, and at multiples of the first critical speed, the problem of stability or self-excited whirling is of paramount importance. The onset of self-excited motion may lead to large amplitudes of motion with possible destructions of the rotor or the inability of the compressor to operate at peak power levels. Encountering this phenomenon with a compressor on an off-shore oil platform can mean millions of dollars of lost production. Self-excited whirling can be caused by fluid-film bearings, seals, Alford-type cross-coupling forces, or internal shaft friction, to name a few of the excitation mechanisms. The problem of computing the approximate values of the rotor log decrement under full speed and loading conditions requires the solution of a complex eigenvalue problem. The computation of the rotor complex roots is an order of magnitude more difficult than the problem of undamped critical speed calculations. J. W. Lund presented the first practical numerical procedure for computing turbo-rotor log decrements. The mathematical transfer matrix method pioneered by Lund has allowed industry to develop and stabilize a vast array of rotating machinery leading to the savings to industry of millions of dollars. Without the procedures of Lund, for example, it would not have been possible to resolve stability problems encountered with both the hydrogen and oxygen space shuttle pumps. This paper briefly presents some of the attributes of the Lund stability procedure and its unique characteristics. @DOI: 10.1115/1.1605978#

Lund’s Contribution to Rotor Stability: The Indispensable and Fundamental Basis of Modern Compressor Design

Abstract. In this paper, the free vibration of axially-loaded, multi-cracked Timoshenko beams with differing boundary conditions, namely, hinged-hinged, fixed-fixed, fixed-hinged, and fixed-free is studied. The cracked beam system is represented as several beam segments connected by massless rotational springs with sectional flexibility. Each segment is assumed to obey the Timoshenko beam theory. A simple transfer matrix method is used to derive the characteristic equation of the axially-loaded, multi-cracked beam with differing boundary conditions. The characteristic equation and corresponding mode shapes are a function of natural frequency, crack size and location, and physical parameters of the beam. In this paper, the effects of crack depth, number of cracks, position of cracks, axial load, shear deformation and rotary inertia on the dynamic behavior of multi-cracked beams are studied in detail. It is found that there is good agreement between the results obtained in this study and results available in the literature. Additionally, interesting observations overlooked by other researchers are obtained.

methods

Free vibration of axially loaded multi-cracked Timoshenko beams

Beam structures can be abstracted from many engineering practices. The system needs to be simplified and abstracted in order to obtain its basic characteristics.

Matrix Methods in Elasto Mechanics

Citations

Das Computerprogramm FLASH

A Practical Approach to Spacecraft Structural Dynamics

Lund’s Contribution to Rotor Stability: The Indispensable and Fundamental Basis of Modern Compressor Design

Free vibration of axially loaded multi-cracked Timoshenko beams

WPA for Analyzing Complex Beam Structures

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