On the application of curve reparameterization in isogeometric vibration analysis of free-from curved beams

In the present paper, an innovative approach based on a curve reparameterization technique is developed to solve the natural frequency problem of free-form Euler-Bernoulli curved beams using isogeometric analysis (IGA). The method is beneficial in modifying the probably inappropriate initial parameterization of input geometries. For this purpose, a transformation from the initial parametric domain to a new reparameterized one is adopted, creating a pseudo arc-length parameterization that is suitable for IGA. An auxiliary one-dimensional B-spline curve is utilized as the parametric transfer function (PTF). A combination of curve rectification and B-spline approximation techniques is implemented to construct the PTF. The number of elements in the proposed approach is based on the knot vector of the PTF that is not dependent on the knot vector of the input NURBS curve defining the geometry. The method is tested on different numerical examples that prove the validity and applicability of the formulations.