Temporal Response of Coupled One-Dimensional Dynamic Systems
Research and development rept.
DAVID TAYLOR RESEARCH CENTER BETHESDA MD
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A formalism is presented which describes the response of a complex of coupled one-dimensional dynamic systems to an impulse drive. The formalism is based on an impulse response operator which relates a drive applied to one point in the complex to the response at any point in the complex. The formalism is derived directly in the time domain, and the impulsive drives which can be accommodated must be finite in time and applied at a spatial point. The constituent systems must be one-dimensional and possess a pulse propagation velocity which is not a function of position within the system. Systems interact through junctions which also define their spatial extents. The junctions are characterized by reflection and transmission coefficients which modulate the amplitude of reverberant components and by delays in the reflections and transmissions. Propagation in the systems is characterized by losses. Several simplistic examples are calculated and presented to illustrate the type of information which the formalism can provide. Keywords Transient propagation Pulse propagation Multiple dynamic systems Dynamic systems.