Analysis of structural systems in the mid-frequency range
Abstract
The need for information on structural vibrations spanning the entire frequency range has led to the investigation of many new analytical techniques. The focus of this investigation is the mid frequency range as it applies to structural systems. Until recently, this area has received little attention and focused research effort. The literature in related areas is reviewed and the current state of the art discussed. The definition of the mid frequency range is discussed, and a definition in terms of averaged responses is proposed. The equations necessary for the analysis of several types of vibrations in terms of energy and energy flow are developed. The areas of application of these equations are longitudinal and torsional vibrations in rods and flexural vibrations in beams. The simplification and assumptions necessary to arrive at the governing equations are discussed and shown to be acceptable. For each type of vibration, appropriate boundary conditions are derived and related to the classical displacement conditions for the problem. Compatibility equations necessary for the coupling of multiple members are also developed and verified. The governing equations are modified to allow for the analysis of systems excited in the mid frequency range. This is done for both longitudinal vibration in rods and flexural vibration in beams. In the case of the beam vibration, the newly developed method is compared to a previously developed approximate solution. The comparison shows the new method to perform favorably and to offer advantages.
Degree
Ph.D.
Advisors
Bernhard, Purdue University.
Subject Area
Mechanical engineering
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