Herwig Peters

Modal decomposition of exterior acoustic-structure interaction.

A modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented. The fluid-loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem. The eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented. The modal sound power contributions using both fluid-loaded structural modes and acoustic radiation modes are presented. The results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem.

Modal decomposition of exterior acoustic-structure interaction problems with model order reduction

A numerical technique for modal decomposition of the acoustic responses of structures submerged in a heavy fluid medium using fluid-loaded structural modes is presented. A Krylov subspace model order reduction approach to reduce the computational effort required for a fully coupled finite element/boundary element model is described. By applying the Krylov subspace to only the structural part of the global system of equations for the fully coupled problem, only the frequency independent finite element matrices are reduced. A fluid-loaded cylindrical shell closed at each end by hemispherical end caps is examined. The cylinder is excited by a ring of axial or transverse forces acting at one end. The individual contributions of the cylinder circumferential modes to the sound power and directivity of the radiated sound pressure are observed. The technique presented here provides a tool for greater physical insight into exterior acoustic-structure interaction problems using fully coupled numerical models, with significantly reduced computational effort.

Surface contributions to radiated sound power

This paper presents a method to identify the surface areas of a vibrating structure that contribute to the radiated sound power. The surface contributions of the structure are based on the acoustic radiation modes and are computed for all boundaries of the acoustic domain. The surface contributions are compared to the acoustic intensity, which is a common measure for near-field acoustic energy. Sound intensity usually has positive and negative values that correspond to energy sources and sinks on the surface of the radiating structure. Sound from source and sink areas partially cancel each other and only a fraction of the near-field acoustic energy reaches the far-field. In contrast to the sound intensity, the surface contributions are always positive and no cancelation effects exist. The technique presented here provides a method to localize the relevant radiating surface areas on a vibrating structure. To illustrate the method, the radiated sound power from a baffled square plate is presented.

ENFORCING RECIPROCITY IN NUMERICAL ANALYSIS OF ACOUSTIC RADIATION MODES AND SOUND POWER EVALUATION

By identifying the efficiently radiating acoustic radiation modes of a fluid loaded vibrating structure, the storage requirements of the acoustic impedance matrix for calculation of the sound power using the boundary element method can be greatly reduced. In order to compute the acoustic radiation modes, the impedance matrix needs to be symmetric. However, when using the boundary element method, it is often found that the impedance matrix is not symmetric. This paper describes the origin of the asymmetry of the impedance matrix and presents a simple way to generate symmetry. The introduction of additional errors when symmetrizing the impedance matrix must be avoided. An example is used to demonstrate the behavior of the asymmetry and the effect of symmetrization of the impedance matrix on the sound power. The application of the technique presented in this work to compute the radiated sound power of a submerged marine vessel is discussed.

Three-dimensional analysis of a noise barrier using a quasi-periodic boundary element method

Two-dimensional (2D) numerical models are often used to estimate the environmental noise attenuation of a roadside barrier. The prediction of noise barrier attenuation using a 2D boundary element model assumes an infinitely long barrier with constant cross section. However, for barrier geometries that do not have constant cross section in the third dimension, three-dimensional (3D) models should be used for greater accuracy of noise reduction due to the barrier. The size of a numerical model and hence its computational cost can be significantly reduced using a 3D quasi-periodic structure, whereby the structure is truncated using a finite number of periodic sections. In this study, a quasi-periodic model developed using the boundary element method is used to predict the acoustic performance of 3D noise barriers. The convergence behavior of the quasi-periodic model is discussed. Results from the quasi-periodic model are compared with results from both a 3D analytical model and a 2D finite element model, showing good agreement. Quasi-periodic models of different noise barrier designs are developed and their acoustic performances in terms of frequency and receiver positions are discussed. The quasi-periodic boundary element method provides a computationally efficient tool to examine the acoustic performance of 3D noise barrier designs.

Prediction of the intramembranous tissue formation during perisprosthetic healing with uncertainties. Part 2. Global clinical healing due to combination of random sources

This work proposes to examine the variability of the bone tissue healing process in the early period after the implantation surgery. The first part took into account the effect of variability of individual biochemical factors on the solid phase fraction, which is an indicator of the quality of the primary fixation and condition of its long-term behaviour. The next issue, addressed in this second part, is the effect of cumulative sources of uncertainties on the same problem of a canine implant. This paper is concerned with the ability to increase the number of random parameters to assess the coupled influence of those variabilities on the tissue healing. To avoid an excessive increase in the complexity of the numerical modelling and further, to maintain efficiency in computational cost, a collocation-based polynomial chaos expansion approach is implemented. A progressive set of simulations with an increasing number of sources of uncertainty is performed. This information is helpful for future implant design and decision process for the implantation surgical act.

Structural and acoustic responses of a fluid loaded shell due to propeller forces

The low frequency structural and acoustic responses of a fluid loaded shell to propeller induced fluid pressures are investigated. The propeller operates in the non-uniform wake field and produces fluctuating pressures on the blades of the propeller. This in turn generates acoustic waves and a near field that excites the surface of the shell. The resulting incident pressure is scattered and diffracted by the shell surface, and also excites structural vibration. A potential flow panel code is coupled with the Ffowcs-Williams and Hawkings acoustic analogy to predict the fluctuating propeller forces, blade pressures and the resulting incident field on the surface of the fluid loaded shell due to operation of the propeller in a non-uniform inflow. The propeller induced incident pressure field is then combined with a coupled three-dimensional finite element/boundary element model of the submerged shell to predict the vibro-acoustic and scattered field responses.

Modal contributions to sound radiated from a fluid loaded cylinder

A modal decomposition technique to compute the individual modal contributions to the sound radiated from a cylindrical shell submerged in water is presented. The wet structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem. A Krylov subspace technique is used to reduce the model size of the structural domain, while the fluid domain remains unchanged. Results for the radiated sound power and sound pressure directivity are presented for groups of circumferential modes with common mode number. Under axial and transverse excitation, the cylinder breathing and bending modes are respectively the major modes contributing to the radiated sound at low frequencies. The contribution of the rigid body modes to the radiated sound is also observed.

Non-negative intensity for coupled fluid–structure interaction problems using the fast multipole method

The non-negative intensity (NNI) method is applied to large-scale coupled fluid-structure interaction (FSI) problems using the fast multipole boundary element method (FMBEM). The NNI provides a field on the radiating structure surface that consists of positive-only contributions to the radiated sound power, thus avoiding the near-field cancellation effects that otherwise occur with the sound intensity field. Thus far the NNI has been implemented with the boundary element method (BEM) for relatively small problem sizes to allow for the full BEM coefficient and inverse matrices to be explicitly constructed and stored. In this work, the FMBEM is adapted to the NNI by calculating the eigenvalue solution of the symmetric acoustic impedance matrix using the FMBEM via a two-stage solution method. The FMBEM implementation of the NNI is demonstrated for a large-scale model of a submerged cylindrical shell. The coupled FSI problem is first solved using a finite element-FMBEM model and the resulting surface fields are then used in the FMBEM calculation of the NNI. An equivalent reactive NNI field representing the evanescent near-field radiation is demonstrated and the effect of the chosen number eigenvectors on the NNI field is investigated.

Flow-Induced Noise Prediction Using a RANS-BEM Technique

A hybrid RANS-BEM technique is applied to calculate the self-noise produced by low Mach number flow past a flat plate. The flow field and turbulence statistics of the flow over the flat plate is predicted using a two-dimensional Reynolds Averaged Navier-Stokes (RANS) simulation. A statistical noise model is used to process the mean velocity, turbulent kinetic energy and turbulent dissipation rate to predict the incident pressure on the flat plate. This incident field is then applied as a load to a three-dimensional boundary element method (BEM) model of the flat plate to predict the far-field sound. Turbulent flow past a flat plate is used to demonstrate the hybrid RANS-BEM technique. The flow has a Reynolds number based on chord \(Re_{c}=2.0\times 10^{5}\) and Mach number \(M=0.044\). The far-field pressure predicted with the hybrid RANS-BEM technique compares favourably with experimental measurements from literature.