Recommendations for books addressing complex eigenvalue problems in finite element method (FEM) analysis include W.T. Thomson's "Theory of Vibration with Applications" and the "Shock and Vibration Handbook" by McGraw-Hill. These texts cover the theory behind eigenvalue problems, including damping, which is relevant in fields like composite materials and aerospace engineering, particularly in relation to phenomena such as wing flutter and brake squeal. Additionally, the documentation of specific FEA software often provides insights into the complex eigenvalue extraction process. Zienkiewicz, Taylor, and Zhu also touch on complex eigenvalues in their work, specifically in sections discussing dynamic stability and the governing equation Mu" + Cu' + ku = 0.
