Mobilities and impedances of structures. Part 1: Compendium of frequency response functions.
Abstract:The aim of the Item is to provide a visual record of the mobilities of structures, such as beams, plates and cylinders. Information on both point and transfer mobilities is given as graphs of the modulus of mobility against frequency and as loci in the complex plane. Further data are provided on basic elements, such as springs, dampers and rigid bodies. The visual information is provided in Tables at the end of the Item. In the first part of the Item the background to mobility and impedance is considered and the rules for obtaining the mobilities and impedances of connected structures explained. The basic elements may be combined to form single and two degree of freedom systems. Beams and plates with single degree of freedom and other systems attached at a point are considered. For all these systems graphical records of their mobilities are provided. The building-block approach to the mobility of built-up structures is emphasised. Structures with different types of dampers and springs can be easily analysed from the data provided. The building block approach is used to account for the effect of foundations on systems designed to provide vibration isolation. The graphical information allows the detail of the mobilities to be appreciated. For example, in the case of a point mobility there is an alternating sequence of resonances and antiresonances that is shown in a graph of modulus of mobility as a function of frequency. Transfer mobilities have a different sequence. Similarly, in the complex plane the point mobility may be approximated by circles with only positive real values, whereas the approximate circles for transfer mobilities can have both positive and negative values on the real axis. Such differences are useful in assessing and checking the validity of measurements of mobility on a real structure. The graphs of the modulus of mobility have been estimated for beams and plates with hysteretic damping and include a large number of modes of vibration, so that the high frequency limit of the mobility can be studied. This high frequency limit is the same as that for an infinite structure and is of particular interest in Statistical Energy Analysis. Mobilities of infinite structures are the subject of Part II of the Item.
|Data Item ESDU 04009|