Engineering Transactions, 64, 2, pp. 197–211, 2016
10.24423/engtrans.302.2016

### Isogeometric Approximation for Dynamics of Infinite String Using Difference Equation Method

Jerzy RAKOWSKI
Poznan University of Techlology Institute of Structural Engineering ul. Piotrowo 5 60-965 Poznan Poland
Poland

Przemyslaw WIELENTEJCZYK
Poznan University of Techlology Institute of Structural Engineering ul. Piotrowo 5 60-965 Poznan Poland
Poland

An efficient method of vibration investigation of an infinite string using the isogeometric analysis (IGA) with B-spline basis functions is considered. The research objective is to compare IGA, finite element method (FEM) and exact formulation approaches. In the IGA approximation a system is divided into a set of regularly distributed coordinates assembled in a uniform knot vector. Transverse displacements are described by linear, quadratic, cubic and quartic B-spline basis functions. The geometrical and mass matrices are found for all types of approximations. The equilibrium conditions for an arbitrary interior element are expressed in the form of one difference equation equivalent to the infinite set of equations obtained by numerical IGA formulation for this dynamic problem. Assuming the wavy nature of a vibration propagation phenomenon the dispersive equations are obtained. The ranges of vibration frequencies for the dispersive and reactive cases are determined. The influences of the adopted discretization, mass distribution and initial axial force effects on the wave propagation phenomenon are examined.
Keywords: FEM; FDM; NURBS; IGA
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

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DOI: 10.24423/engtrans.302.2016