Abstract
The hybrid deterministic-statistical energy analysis method has proven to be a versatile framework for modeling built-up vibro-acoustic systems. The stiff system components are modeled deterministically, e.g., using the finite element method, while the wave fields in the flexible components are modeled as diffuse. In the present paper, the hybrid method is extended such that not only the ensemble mean and variance of the harmonic system response can be computed, but also of the band-averaged system response. This variance represents the uncertainty that is due to the assumption of a diffuse field in the flexible components of the hybrid system. The developments start with a cross-frequency generalization of the reciprocity relationship between the total energy in a diffuse field and the cross spectrum of the blocked reverberant loading at the boundaries of that field. By making extensive use of this generalization in a first-order perturbation analysis, explicit expressions are derived for the cross-frequency and band-averaged variance of the vibrational energies in the diffuse components and for the cross-frequency and band-averaged variance of the cross spectrum of the vibro-acoustic field response of the deterministic components. These expressions are extensively validated against detailed Monte Carlo analyses of coupled plate systems in which diffuse fields are simulated by randomly distributing small point masses across the flexible components, and good agreement is found.
Highlights
Effective vibro-acoustic analysis tools are essential for the design of engineering systems with good noise and vibration performance, both in terms of safety and human comfort
Straightforward application of deterministic field-based analysis techniques such as finite element or boundary element analysis is possible at low frequencies, as the wavelength of deformation is long in all system components and the vibro-acoustic response is dominated by a limited number of eigenmodes [1,2]
The hybrid deterministic-statistical energy analysis (SEA) method for vibro-acoustic analysis has been extended to predict the variance of band-averaged energetic response quantities
Summary
Effective vibro-acoustic analysis tools are essential for the design of engineering systems with good noise and vibration performance, both in terms of safety and human comfort. By making extensive use of this generalization in a first-order perturbation analysis, explicit expressions are derived for the cross-frequency and band-averaged variance of the vibrational energies of the diffuse components and for the cross-frequency and band-averaged variance of the cross spectrum of the vibro-acoustic field response of the deterministic components.
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