The beam is assumed partitioned into several finite elements and the deflection of the beam is required to be a positive quantity along the whole beam so that the related fundamental fourth-order ordinary differential equation can continuously holds good. In this paper, we apply Haar wavelet methods to solve finite-length beam differential equations with initial or boundary conditions known. An operational matrix of integration based on the Haar wavelet is established and the procedure for applying the matrix to solve the differential equations is formulated. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number of variables. Illustrative example is given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

Haar wavelets Ordinary differential equation finite-length beam computationally attractive