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.