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.

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.