This paper presents the application of isogeometric analysis to structural vibration problems. Isogeometric analysis is a method that extends finite element analysis by using basis functions from computer-aided design (CAD) systems to represent geometry exactly. The method is applied to various structural models, including rods, thin beams, membranes, and thin plates. The concept of k-refinement is explored, which produces more accurate and robust results than traditional finite elements. Nonlinear parameterization is used to eliminate "optical" branches of frequency spectra, which are known to cause Gibbs phenomena in wave propagation problems and degrade higher modes in p-method finite elements. A geometrically exact model of the NASA Aluminum Testbed Cylinder is constructed and its frequencies and mode shapes are computed and compared with experimental results. The paper also discusses the advantages of isogeometric analysis over traditional finite elements, including the ability to maintain exact geometry and the potential for higher accuracy and efficiency. The paper concludes that isogeometric analysis is a promising approach for structural vibration analysis and that further research is needed to fully realize its potential.This paper presents the application of isogeometric analysis to structural vibration problems. Isogeometric analysis is a method that extends finite element analysis by using basis functions from computer-aided design (CAD) systems to represent geometry exactly. The method is applied to various structural models, including rods, thin beams, membranes, and thin plates. The concept of k-refinement is explored, which produces more accurate and robust results than traditional finite elements. Nonlinear parameterization is used to eliminate "optical" branches of frequency spectra, which are known to cause Gibbs phenomena in wave propagation problems and degrade higher modes in p-method finite elements. A geometrically exact model of the NASA Aluminum Testbed Cylinder is constructed and its frequencies and mode shapes are computed and compared with experimental results. The paper also discusses the advantages of isogeometric analysis over traditional finite elements, including the ability to maintain exact geometry and the potential for higher accuracy and efficiency. The paper concludes that isogeometric analysis is a promising approach for structural vibration analysis and that further research is needed to fully realize its potential.