Analysis of subsystem randomness effects on the mid-frequency vibrations of built-up structures

The paper concerns the analysis of subsystem randomness effects on the mid-frequency vibration responses of built-up systems. The system model considered, in the first instance, is a long-wavelength finite element (FE) subsystem connected with a short-wavelength statistical energy analysis (SEA) subsystem via discrete couplings. The randomness effects of the SEA subsystem on both the displacement response of the FE subsystem and the energy response of the SEA subsystem are then investigated under the frame of the hybrid FE/SEA theory [P. Shorter, R. Langley, Vibro-acoustic analysis of complex systems, Journal of Sound and Vibration, 288 (2005) 669–700]. It is found that the subsystem randomness effects may be well indicated by a dimensionless parameter α, which is a function of the number of coupling points, the dynamic mismatch between the FE and SEA subsystems and the modal overlap factor of the SEA subsystem. The smaller the value of α is, the more insignificant the randomness effects are. As a result, a so-called “α-criterion” is derived which states that, if a built-up structure satisfies the condition of α⪡1, the randomness effects of the SEA subsystem can be neglected. In this case, the SEA subsystem can be simply treated as an infinite (or semi-infinite as appropriate) structure regardless of its mode count being sufficiently high or not. Numerical examples are presented to illustrate the validity of the present theory.