Vibration analysis of mechanical structures with a new formulation of the isogeometric collocation method

We propose and validate a new formulation of the isogeometric collocation method, IGA-C in short, for the dynamical analysis of mechanical structures with ideal and special boundary conditions. Precisely, a new method of imposing the boundary conditions is developed. We apply this new formulation to selected models of thick beams, helical springs and composite beams. The detailed results are discussed and compared to recently published works in the aim of appreciating the presented models and determining the parameters of their optimal use. In particular, our results are compared with those obtained by different methods as isogeometric Galerkin, Tchebyshev pseudo-spectral, transfer matrix and finite element methods. In this paper, our method is developed based on IGA-C. However, it can be based on other numerical methods as well. In addition, it may be of great help for developing automatic algorithms in simulation software.