Hydroelastic analysis of a ship with forward speed using orthogonal polynomials as mode functions of timoshenko beam

Abstract Legendre polynomials and Chebyshev polynomials are adopted as simpler mode functions to replace the dry eigen-modes of the Timoshenko beam. Then the mode-expansion method is applied to prove that a superposition of orthogonal mathematical functions can represent the flexural deflection of a ship in waves, despite a fact that each of these mathematical functions does not satisfy the required boundary conditions and has no physical meaning. Validation of obtained results with Euler-beam and Timoshenko-beam approximations is performed through comparison with the experimental results of a flexible barge conducted by Malenica et al. (2003) as well as the numerical results of Kim et al. (2009b), Kim et al. (2009a) implemented using the direct coupling method in the experimental wave-frequency range. For the forward-speed case, by means of the Rankine panel method (RPM), validation in a wide range of wave frequency is performed through comparison of computed results for the modified Wigley model between dry eigen-modes and orthogonal polynomials used as the mode function. From this comparison, the rationality of consistency in the proposed method is proven and availability in various engineering fields can be expected. The ratio of flexural and shear rigidities is intentionally increased in a numerical study to see the effect of shearing force on various related quantities using Legendre polynomials. Limitation and convergence of the proposed mode functions are also discussed.