Free vibration analysis of tapered Timoshenko beam with higher order Haar wavelet method

. In the current study, the higher order Haar wavelet method based formulation is developed for the analysis of the free vibrations of the tapered Timoshenko beam. The clamped-clamped and clamped-pinned boundary conditions are explored and the results with the 4th order and the 6th order of convergence are presented. The results are found to be in good agreement with the corresponding results of the Ritz method. The proposed approach can be considered as the principal improvement of the widely used Haar wavelet method providing the same accuracy with the several magnitudes lower mesh. Thus, the higher order Haar wavelet method has reduced the computational cost in comparison with the widely used Haar wavelet method since the computational complexity of both methods is determined by the mesh used. In the case of the fixed equal mesh used for both methods, the higher order Haar wavelet method results in the several magnitudes lower absolute error without a remarkable increase in computational complexity. The cost needed to pay for higher accuracy is hidden in a certain increase in the implementation complexity compared with the widely used Haar wavelet method.