'Twixt Earth and Sky with Rod and Tube
The Journal of the Acoustical Society of America, 26 (1):
140 (Jan 1, 1954)DOI: 10.1121/1.1917782
Abstract
The techniques which comprise the mobility method of vibration computation are introduced into the classical impedance analogy; instead of drawing an analogous classical electrical schematic, a new set of mechanical and acoustical symbols is introduced which permits the drawing of a (classical) hydraulic schematic directly by cautious inspection of the structure to identify the elements and their terminals. In a mobility schematic, a straight line represents an ideal rigid massless rod; in a hydraulic schematic, a line represents a tube of unit cross section filled with ideal massless incompressible liquid which can sustain either tension or compression. Revised mobility schematic symbols are provided for mechanical and acoustical elements, and hydraulic schematic symbols for the same elements have been visualized as tubes filled with mercury or molasses, or chambers filled with methane (or air); all of these symbols resemble their analogous electrical symbols. Rigid and hydraulic junctions are distinguished by different symbols. Correct mobility schematics are obtained by inspection through considering each mass as having one terminal fixed in a frame of reference called the ground, which has zero mobility and infinite mass; correct hydraulic schematics are obtained by inspection through considering each spring as having one terminal fixed in a force of reference (P0 etc.) called the sky, which has zero impedance and infinite compliance (in both cases the analogous electrical element is a conducting sphere in free space, not a condenser). While it is recommended that analogous electrical circuits not be used, they can be copied directly from a mobility schematic by considering mechanical ground analogous to electrical ground, or copied directly from a hydraulic schematic by considering mechanical sky analogous to electrical ground.