Precise integration method for natural frequencies and mode shapes of ocean risers with elastic boundary conditions

Abstract

• A relatively new precise integration method for modal analysis of ocean risers is developed. • It is suitable for ocean risers with variable tension and cross-section and various boundaries. • The results are proved to be very accurate by comparing the analytical solution and literature. • Computing time is quite short and the method exhibits good convergence and high efficiency. • Effects of elastic constraints simulating damaged and undamaged boundaries on natural frequencies and mode shapes are investigated. The effects of the elastic constraints simulating damaged and undamaged boundaries on the natural frequencies and mode shapes of ocean risers with a variable axial tension are investigated using the precise integration method (PIM). The classical high-order variable-coefficient partial-differential governing equation of the free vibration of ocean risers is reduced to a set of first-order ordinary differential equations and efficiently solved by the PIM. The main advantages of the PIM are that the numerical results can be calculated with high accuracy even when total element number n , number of iterations N and Taylor expansion terms r are small. Moreover, the computing time is quite short. Various boundary conditions are modeled as linear elastic constraints using a pair of translational and torsional springs, and four types of boundary damage coefficients are proposed to investigate the effects of a damaged boundary on the natural frequencies. The results for specific boundary conditions show agreement with those reported in the literature, and the calculation errors are very small in comparison with the analytical solution. Overall, the methodology of PIM is applicable for the investigation of the natural frequencies and mode shapes of ocean risers with a variable axial tension and cross-section and various boundary conditions.