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02.03 Numerical Methods in Vibro-Acoustics, Part 2

Tutorial on Acoustic Fluid Loading of Structures
Time: 2:00 pm

Author: Stephen Hambric

Abstract ID: 1002

Any vibrating structure is loaded by the fluid surrounding it.  Whether air, water, or something else, the fluid loading adds a spatially distributed resistance (in phase with the vibration) and reactance (out of phase with the vibration) over the structural surfaces.  The resistance absorbs energy, and damps structural vibrations.  The reactance is either mass-like, effectively adding to the structural density, reducing resonance frequencies and vibration amplitudes; or stiffness-like, increasing resonance frequencies.  Usually, mass-like reactance is caused by fluids external to a structure, and stiffness-like reactance is caused by enclosed volumes of fluids.  This tutorial uses analytic methods to compare and contrast external and internal fluid loading on a flat rectangular plate and demonstrates the effects of fluid loading on plate vibration and radiated sound.  The well-known stiffening effect of the internal Helmholtz resonance is demonstrated for a thin panel and a shallow entrained cavity.  The differences between heavy (water) and light (air) external fluid loading are also demonstrated, with significant reductions in resonance frequencies and peak vibration amplitudes for water loading.

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A hybrid method for broadband vibroacoustic simulations
Time: 2:40 pm

Author: Scott Sommerfeldt

Abstract ID: 2236

Many methods for simulating acoustic responses of vibrating systems are only suitable for limited frequency ranges, providing either an accurate low frequency or high frequency response. A hybrid method is presented to combine a low frequency modal response and a high frequency statistical energy response to obtain a unified broadband response. The method is designed to produce an auralizable response. An experimental setup is used to validate the method. Listening tests are conducted to assess the realism of the auralizations compared to measurements. The listening tests confirm that the method is able to produce realistic auralizations, subject to a few limitations.

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Computing Radiated Sound Power using Quadratic Power Transfer Vector (QPTV)
Time: 2:20 pm

Author: Rajendra Gunda

Abstract ID: 2643

Pressure Acoustic Transfer Functions or Vectors (PATVs) relate the surface velocity of a structure to the sound pressure level at a field point in the surrounding fluid. These functions depend only on the structure geometry, properties of the fluid medium (sound speed and characteristic density), the excitation frequency and the location of the field point, but are independent of the surface velocity values themselves. Once the pressure acoustic transfer function is computed between a structure and a specified field point, we can compute pressure at this point for any boundary velocity distribution by simply multiplying the forcing function (surface velocity) with the acoustic transfer function. These PATVs are usually computed by application of the Reciprocity Principle, and their computation is well understood. In this work, we present a novel way to compute the Velocity Acoustic Transfer Vector (VATV) which is a relation between the surface velocity of the structure and fluid particle velocity at a field point. To our knowledge, the computation of the VATV is completely new and has not been published in earlier works. By combining the PATVs and VATVs at a number of field points surrounding the structure, we obtain the Quadratic Power Transfer Vector (QPTV) that allows us to compute the sound power radiated by a structure for ANY surface velocity distribution. This allows rapid computation of the sound power for an arbitrary surface velocity distributions and is useful in designing quiet structures by minimizing the sound power radiated.

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Power balance analysis of nonperiodic structural components from a model converted from FEM to SEA.
Time: 3:20 pm

Author: Mathias Hinz

Abstract ID: 2791

Using Statistical Energy Analysis (SEA) to characterize the power flow within a vibroacoustic system is a challenging task when the subsystems have irregular shape and complex construction. Retrieving analytical solutions for the ordinary SEA parameters is nearly impractical without restricting simplifications and periodicity is usually not exploitable due to the lack of repetition patterns. A promising option to perform the power balance for such cases is to filter part of the information contained in a Finite Element Method (FEM) model of the system, in order to convert it into a SEA model. In this paper, the Lorentzian Frequency Average and the Nonparametric Random Matrix Theory are applied to randomize the dynamic stiffness matrix of the FEM components from a system of industrial application. The obtained direct field dynamic stiffness matrices are employed along the diffuse field reciprocity relationship as a general framework to determine the energetic content of each component. The results obtained with this procedure are evaluated against the ones from classical SEA and Monte Carlo techniques.

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SEA model for structural acoustic coupling by means of periodic finite element models of the structural subsystems
Time: 3:00 pm

Author: Luca ALIMONTI

Abstract ID: 3044

Statistical Energy Analysis (SEA) often relies on simplified analytical models to compute the parameters required to build the power balance equations of a coupled vibro-acoustic system. However, the vibro-acoustic of modern structural components, such as thick sandwich composites, ribbed panels, isogrids and metamaterials, is often too complex to be amenable to analytical developments without introducing further approximations. To overcome this limitation, a more general numerical approach is considered. It was shown in previous publications that, under the assumption that the structure is made of repetitions of a representative unit cell, a detailed Finite Element (FE) model of the unit cell can be used within a general and accurate numerical SEA framework. In this work, such framework is extended to account for structural-acoustic coupling. Resonant as well as non-resonant acoustic and structural paths are formulated. The effect of any acoustic treatment applied to coupling areas is considered by means of a Generalized Transfer Matrix (TM) approach. Moreover, the formulation employs a definition of pressure loads based on the wavenumber-frequency spectrum, hence allowing for general sources to be fully represented without simplifications. Validations cases are presented to show the effectiveness and generality of the approach.

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