The free vibration of a type of tapered beams
In many cases non-uniform beams may exhibit a better distribution of strength and weight than uniform beams. Such beams are used in aeronautical, civil and mechanical engineering. This paper studies vibrational characteristics of tapered beams with continuously varying rectangular cross-section proportional to some power of axial coordinate. It is assumed that the depth and breadth dimensions are small in comparison with the length of beam, so the Bernoulli-Euler theory is valid. Beam functions are obtained by using solutions for the tapered beam under arbitrary static load which is approximated by Taylor series, and the eigenfrequency equation is obtained by Rayleigh-Ritz method.
scientific article; zbMATH DE number 1506865