A general algorithm for the study of the dynamical behaviour of beams

Abstract This paper presents a simple, accurate and flexible general algorithm for the study of a great number of beams vibration problems. The approach is developed based on the Rayleigh–Ritz method with characteristic orthogonal polynomial shape functions. It allows the inclusion of a number of complicating effects such as varying cross-sections, presence of an arbitrarily placed concentrated mass, ends elastically restrained against rotation and translation and presence of an axial, tensile force. Several cases are treated to show the simplicity and great flexibility of this approach, in the determination of frequencies. To demonstrate the accuracy of the present approach natural frequency coefficients are given for beams, from which comparison results are available. New results are also given for tapered beams with several complicating effects.

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