In contrast to the structural modes, which describe the physical motion of vibrating structures, acoustic radiation modes describe the radiated sound power. Radiation modes are beneficial in active noise control because reducing an efficiently radiating radiation mode guarantees the reduction of radiated sound power. Much work has been done to calculate the radiation modes for simple geometries, where analytic solutions are available. In this work, isogeometric analysis (IGA) is used to provide a tool capable of analyzing the radiation modes of arbitrarily complex geometries. IGA offers increased accuracy and efficiency by using basis functions generated from Non-Uniform Rational B-Splines (NURBS) or T-Splines, which can represent geometries exactly. Results showing this increased accuracy and efficiency with IGA using T-Splines are shown for a sphere to validate the method, comparing with the exact analytical solution as well as results from a traditional boundary element method. A free cylindrical shell is also analyzed to show the usefulness of this method. Expected similarities, as well as expected differences, are observed between this free shell and a baffled cylindrical shell.

Driven by the need to reduce the sound transmitted into aircraft cabins from the power plant, this thesis investigates the active control of sound transmitted through a structure into coupled enclosures. In particular, it examines alternatives to conventional microphone and accelerometer error sensors. This study establishes a design framework for the development and analysis of an active noise control system which can be applied to any complex vibro-acoustic system. The design approach has focused on using techniques presently used in industry to enable the transfer of the active noise control technology from the research stage into practical noise control systems. The structural and acoustic sub-systems are modelled using FEA to estimate the in vacuo structural modal response of the structure and the acoustic pressure modal response (with rigid boundary conditions) of the interior cavity. The acoustic and structural systems are then coupled using modal coupling theory. Within this framework, two novel error sensors aimed at overcoming observability problems suffered by traditional microphone and accelerometer sensors are investigated: namely, acoustic energy density sensors and shaped radiation modal vibration sensors. The principles of the measurement of energy density are discussed and the errors arising from its measurement using two and three-microphone sensor configurations are considered for a one-dimensional reactive sound field and a plane wave sound field. The error analysis encompasses finite separation effects, instrumentation errors (phase and sensitivity mismatches, and physical length errors), diffraction and interference effects, and other sources of error (mean flow and turbulence, temperature and humidity, statistical effects). Following the one-dimensional study, four 3-axis energy density sensor designs are proposed and error analysis is conducted over the same acoustic fields as for the one-dimensional study. The design and construction of the simplest arrangement of the 4 three-axis sensors is discussed with reference to design issues, performance and limitations. The strategy of using energy density control is investigated numerically for a purely acoustic system and a coupled panel-cavity system. Energy density control is shown to provide greater local and global control compared to that possible using an equivalent number of microphones. The performance of the control system is shown to be relatively insensitive to the placement of the energy density sensor. For an enclosed cavity system with high modal overlap, the zone of local control achieved by minimising energy density is found to be approximately the same as the zone of local control obtained when min-imising pressure and pressure gradient in a diffuse sound field. It is also shown that if there is only one control source used per energy density sensor, global control will be almost optimum. The addition of further control sources leads to an improvement in global control, however, the control is no longer optimal. The control system is found to be very tolerant of errors in the estimate of the energy density and thus the use of simpler energy density sensor designs is justified. Finally, an experiment is presented in which the global performance achieved by controlling a three-axis energy density sensor is compared with the performance achieved by minimising the acoustic potential energy and minimising the sum of squared pressures at a finite number of microphones. The experimental results are found to reflect the numerical results. The active minimisation of harmonic sound transmission into an arbitrarily shaped enclosure using error signals derived from structural vibration sensors is investigated numerically and experimentally. It is shown that by considering the dynamics of the coupled system, it is possible to derive a set of "e;structural radiation"e; modes which are orthogonal with respect to the global potential energy of the coupled acoustic space and which can be sensed by structural vibration sensors. Minimisation of the amplitudes of the "e;radiation modes"e; is thus guaranteed to minimise the interior acoustic potential energy. The coupled vibro-acoustic system under investigation is modelled using Finite Element Analysis which allows systems with complex geometries to be investigated rather than limiting the analysis to simple, analytically tractable systems. Issues regarding the practical implementation of sensing the orthonormal sets of structural radiation modes are discussed. Specific examples relating to the minimisation of the total acoustic potential energy within a curved rectangular panel and a coupled cavity are given, comparing the performance offered using vibration sensing of the radiation modes on the structure with the more traditional error sensing; namely, the discrete sensing of the structural kinetic energy on the structural boundary and the acoustic potential energy in the enclosed space approximated by the mean squared pressures at several locations. / Thesis (Ph.D.)--Mechanical Engineering, 1999.

In this thesis, we study the scattering problem of a vertically offset dielectric slab waveguide, using continuous radiation modes. The calculation of radiation modes of an arbitrarily layered waveguide has been thoroughly investigated in the literature. Most approaches were based on launching two incident waves: one from above and one from below, resulting in two transmitted waves and two reflected waves. Radiation modes were obtained by algebraic adjustments of each incident wave¡¦s amplitude and phase. These radiation modes formed standing waves in both the substrates and superstrates. This implies that walls are located an infinite distance far from the first and the last interfaces. In addition to physical conflicts of simultaneous existence of the incident wave and the walls, the derivation details are complicated and non-intuitive. In our thesis, with a given propagation constant for an arbitrarily layered dielectric waveguide, we propose an intuitive method to obtain two independent radiation mode solutions. We also construct a specific procedure to orthogonalize and normalize these two radiation modes. The second part of this thesis is focused on applying these radiation modes into a customized coupled transverse mode integral equation formulation (CTMIE), to the study of vertically offset slab waveguides. CTMIE requires two artificial boundaries placed in the substrate and superstrate. We choose to compute discretized radiation modes with the periodic boundary conditions. Under these circumstances, modes correspond to different spatial frequencies and thereby do not inter-couple. This means the matrix of the overlap integral between these two groups of modes (slightly vertically shifted) are block-diagonally dominated. The off-diagonal elements are two orders of magnitude smaller than the diagonal ones. As a result, when the two artificial boundaries are pushed towards infinity in the CTMIE formulation, we may obtain an exact inverse of the Greene¡¦s matrix without relying on numerical inversion.

The search for a convenient connection between vibration patterns on a structure and the sound radiated from that structure is ongoing in structural acoustics literature. Common techniques are wavenumber domain methods, or representation of the vibration in terms of some basis, such as structural modes or elementary radiators, and calculating the sound radiation in terms of the basis. Most choices for a basis in this situation exhibit strong coupling between the basis functions, but there is one choice which does not: Acoustic radiation modes are by definition the basis that orthogonalizes the radiation operator, meaning the radiation modes do not exhibit any coupling in radiation of sound.Acoustic radiation modes are coming up on their 30th anniversary in the literature, but still have not found wide use. This is largely due to the fact that most radiation modes must be calculated through the computationally intensive boundary element method or boundary integral equations. Analytical expressions for radiation modes, or for the radiation resistance matrix from which they are derived, are only available for a few geometries. This thesis meets this problem head on, to develop additional analytical expressions for radiation resistance matrices of cylindrically curved structures.Radiation modes are developed in the context of their use to calculate sound power. Experimental and computational sound power calculations are presented in order to validate the use of the modes developed here. In addition, the properties and trends of the developed modes are explored.

The International Organization for Standardization (ISO) provides no vibration-based sound power measurement standard that provides Precision (Grade 1) results. Current standards that provide Precision (Grade 1) results require known acoustic environments or complex setups. This thesis details the Vibration Based Radiation Mode (VBRM) method as one approach that could potentially be used to develop a Precision (Grade 1) standard. The VBRM method uses measured surface velocities of a structure and combines them with the radiation resistance matrix to calculate sound power. In this thesis the VBRM method is used to measure the sound power of a single-plate and multiple plate system. The results are compared to sound power measurements using ISO 3741 and good alignment between the 200 Hz and 4 kHz one-third octave band is shown. It also shows that in the case of two plates separated by a distance and driven with uncorrelated sources, the contribution to sound power of each individual plate can be calculated while they are simultaneously excited. The VBRM method is then extended to account for acoustically radiating cylindrical geometries. The mathematical formulations of the radiation resistance matrix and the accompanying acoustic radiation modes of a baffled cylinder are developed. Numberical sound power calculations using the VBRM method and a boundary element method (BEM) are compared and show good alignment. Experimental surface velocity measurements of a cylinder are taken using a scanning laser Doppler vibrometer (SLDV) and the VBRM method is used to calculate the sound power of a cylinder experimentally. The results are compared to sound power measurements taken using ISO 3741.

Active Structural Acoustic Control (ASAC) is a subcategory of the more widely known field of Active Noise control (ANC). ASAC is different from traditional ANC methods because it seeks to attenuate noise by altering the noise producing structure instead of altering the acoustic waves traveling through the air. The greatest challenge currently facing ASAC researchers is that a suitable parameter has not yet been discovered which can be easily implemented as the minimization quantity in the control algorithms. Many parameters have been tried but none effectively attenuate the sound radiation in a way that can be easily implemented. A new parameter was recently developed which showed great potential for use as a minimization quantity. This parameter has been termed the "weighted sum of spatial gradients" (WSSG) and was shown by previous researchers to significantly reduce noise emissions from a vibrating simply supported plate in computer simulations. The computer simulations indicate that WSSG-based control provides as good or better control than volume velocity and does so with a single point measurement which is relatively insensitive to placement location. This thesis presents the experimental validation of the WSSG computer simulations. This validation consists of four major components. First, additional research was needed in to extend the use of WSSG from computer simulations to experimental setups. Second, the WSSG-based control method was performed on simply supported plates to validate the computer simulations. Third, the WSSG-based control method on was used on clamped plates to validate the computer simulations, and fourth, the WSSG-based control method was validated on plates with ribs. The important results are discussed and conclusions summarized for each of these sections. Recommendations are made for future work on the WSSG parameter.

L'objectif de ce travail de thèse est la conception d'un système de haut-parleurs transportable, capable de générer un champ sonore prédéfini et focalisé avec un contraste spatial élevé. Ce système doit permettre à terme d'effectuer différents types d'études, par exemple des essais de transparence acoustique ou encore des essais vibratoires en conditions non-anéchoïques. La minimisation du nombre de canaux à piloter ainsi que du nombre des transducteurs est l'un des enjeux principaux du travail. Le choix du nombre de sources et la sélection de leurs positions optimales afin de générer un champ acoustique cible n'a pas de solution triviale. Pour répondre à cette question, la méthode proposée se base sur la décomposition du rayonnement d’une source en série de fonctions orthogonales indépendantes (les"modes de rayonnement"), construits numériquement via une décomposition en valeurs singulières de la matrice d'impédance. En filtrant les termes évanescents, le champ lointain peut être reconstruit à l'aide d'un faible nombre de termes. De plus, la méthode permet d'estimer une distribution de débit efficace pour générer le champ cible. La méthode proposée étant relativement peu étudiée dans la littérature, la première partie de la thèse a été consacrée au problème de la validation expérimentale de la méthode directe et à l'étude des principaux paramètres en influençant le résultat. La problématique du positionnement des sources permettant de synthétiser un champ sonore prédéfini et focalisé est abordée dans la deuxième partie du travail. / The goal of this thesis is the design of a transportable speaker system, able to generate a predefined and focused sound field with a high spatial contrast. This system has eventually to allow carrying out different types of studies, for example acoustic transmission loss tests or vibration tests in non-anechoic conditions. The minimization of the number of driven channels and the number of transducers is one of the main goals of the work. The choice of the number of sources and the selection of their optimal positions in order to generate a target acoustic field has no trivial solution. To answer this question, the proposed method is based on the decomposition of the source radiation into a series of independent orthogonal functions (the "radiation modes"), constructed numerically via a singular value decomposition of the impedance matrix. By filtering the evanescent terms, the far field can be reconstructed using a small number of terms. In addition, the method allows the estimation of an efficient flow distribution to generate the target field. With the proposed method having been scarcely studied in the literature, the first part of the thesis is devoted to the problem of the experimental validation of the direct method and the study of the main parameters that are influencing the result. The problem of sources positioning in order to synthesize a predefined and focused sound field is discussed in the second part of the thesis.

This dissertation advances the Vibration-Based Sound Power (VBSP) method for measuring the sound power of vibrating structures, expanding its applicability to a wider range of geometries and acoustic environments. The research addresses limitations of traditional sound power measurement techniques by developing an alternative method that achieves near Precision (Grade 1) accuracy while maintaining feasibility for in situ testing under uncontrolled acoustic conditions. After reviewing the current VBSP method in Unit 1, Unit 2 introduces stitching techniques for Scanning Laser Doppler Vibrometer (SLDV) measurements, enabling accurate 3D scans and extending the method to complex geometries. Experimental validation is provided for baffled simply curved plates and arbitrarily curved plates. The method also estimates sound power in uncontrolled acoustic environments, where traditional approaches are less effective. Initial work on thin unbaffled flat plates is presented, with a practical demonstration using pickleball paddles as a representative unbaffled configuration. Unit 3 addresses the computational demand of constructing radiation resistance (R) matrices, a key limitation of the VBSP method. Symmetry-based techniques leveraging acoustic reciprocity and geometric symmetries are applied to reduce computational demands by up to 75% for unbaffled structures. For baffled configurations, translational symmetry of acoustic reciprocity between elements results in the R matrix having Toeplitz symmetry, reducing the computational complexity from n^2 to n, where n is the number of mesh elements. Unit 4 introduces an indirect VBSP (I-VBSP) method to estimate sound power from encased sources, achieving near Precision (Grade 1) accuracy relative to the ISO 3741 standard using only a single surface scan. Validated on a Bluetooth speaker, this approach provides a simplified alternative to conventional methods, offering a practical solution for sound power measurement in structures with encased noise sources. Overall, this dissertation demonstrates that the VBSP method serves as a viable alternative to conventional sound power techniques, effectively applied across various geometries and scenarios. While the current VBSP method does not accommodate structures with multiple vibrating surfaces in contact, the I-VBSP method can theoretically achieve this by enclosing a structure and scanning one vibrating side. This research lays the foundation for future studies through the development of a generalized R matrix and application of foundational symmetries, enhancing the understanding of acoustic radiation from vibrating structures. Ultimately, this work aims to reduce noise pollution in consumer products through improved acoustic design and measurement strategies.