International audienceThis paper begins with personal recollections of John H. Argyris. The geometrical spirit embodied in Argyris's work is revived in the sequel in applying the newly developed concept of isogeometric analysis to structural vibration problems. After reviewing some fundamentals of isogeometric analysis, application is made to several structural models, including rods, thin beams, membranes, and thin plates. Rotationless beam and plate models are utilized as well as three-dimensional solid models. The concept of k-refinement is explored and shown to produce more accurate and robust results than corresponding finite elements. Through the use of nonlinear parameteri-zation, ''optical'' branches of frequency spectra are eliminated for k-refined meshes. Optical branches have been identified as contributors to Gibbs phenomena in wave propagation problems and the cause of rapid degradation of higher modes in p-method finite elements. A geometrically exact model of the NASA Aluminum Testbed Cylinder is constructed and frequencies and mode shapes are computed and shown to compare favorably with experimental results