A quantitative criterion validating coupling power proportionality in statistical energy analysis

• Published in: Journal of sound and vibration Vol. 330; no. 1; pp. 87 - 109
• Main Author: Finnveden, Svante
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 03.01.2011; Elsevier
• Subjects: Approximation; Coupled element; Coupling power; Coupling strengths; Criteria; Deterministic equations; Dynamic loads; Eigen modes; Eigen-value; Eigenvalues; Eigenvalues and eigenfunctions; Energy management; Ensemble averages; Equations of motion; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Iterative solutions; Joining; Modal analysis; Modal data; Modal interactions; Physics; Quantitative criteria; Random frequency; SEA model; Solid mechanics; Statistical energy analysis; Strength; Structural and continuum mechanics; TECHNOLOGY; TEKNIKVETENSKAP; Uncoupled motions; Unity; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Weak couplings; Energy analysis; Energy flow; Statistical analysis; Mode coupling; Vibration; Probabilistic approach; Equation of motion; Eigenmode; Iterative method; Waveguide; Modeling; Global local method; Large eddy simulation; Eigenvalue problem; Deterministic approach; Strength
• ISSN: 0022-460X; 1095-8568; 1095-8568
• DOI: 10.1016/j.jsv.2010.08.003

The response of two general spring-coupled elements is investigated to develop a unifying approach to the weak coupling criterion in Statistical Energy Analysis (SEA). First, the coupled deterministic equations of motion are expressed in the bases given by the uncoupled elements’ eigenmodes. Then, an iterative solution is expressed as a succession of exchanges between elements, where uncoupled motion provides the start approximation, converging if the ‘coupling eigenvalue’ is less than unity, in which case coupling is said to be weak. This definition is related to whether response is ‘local’ or ‘global’, encompassing a number of previously defined coupling strength definitions, applying for deterministically described structures. A stochastic ensemble is defined by that its members are equal to the investigated structure but the elements have random frequencies. It is required that the coupling eigenvalue be less than unity for all members of the ensemble. This requirement generates the title subject of the article: ‘the modal interaction strength’. It is similar to the previously defined coupling strength criterion characterising the ensemble average energy flow in uni-dimensional waveguides. Finally, SEA models are formulated in terms of the uncoupled elements’ modal data.