Upper bound to coupling loss factor for coupling via a generalized point coupling

Abstract

In Statistical Energy Analysis (SEA) the coupling loss factor equals the power of energy flux out of one subsystem into another subsystem coupled to it, nondimensionalized by the product of angular frequency and energy stored in the source subsystem. “Generalized point coupling” indicates any coupling mechanism whose dynamic displacement can be characterized by a single generalized coordinate, in the sense of classical mechanics. Without any other specification of the coupling, an upper bound is found for the sum of power dissipated in the coupling, if any, and power delivered to the other subsystem. The maximum loss factor is given by nmax−1 = 2πωn(ω = 2πfn(f), where ω = 2πf, f is frequency in Hz, and n(f) = 2πn(ω) is the modal density of the source subsystem— i.e., the density in f of modal resonance frequencies. The formula for nmax−1 equals 27.3 times the number of resonances in a tenth‐decade (⅓‐octave) hand. The upper bound is achieved in the case of two parallel thin plates of the same thickness, connected by a rigid, massless, point connection.