Natural vibration and instabilility of plane franmes: exact analitycal solutions using power series

Abstract

The objective of this article is to introduce a practical procedure for determining analytical solutions to free vibration and instability problems related to plane frames, by means of extended power series method. Transfer conditions are applied in order to guarantee geometric continuity and simultaneous equilibrium of knots or conexions. This procedure leads to an important reduction in the number of unknowns to be handled. In the problem of eigenvalue calculation of a frame (both in dynamics or statics), the solution corresponds to the nullity of a determinant whose order is substantially smaller compared to the one found by other ways (e.g. finite element method). In order to attain better presición, other procedures require an increase in the quantity of unknowns, however in the case of power series, only the degree of power is increased without enlarging the number of unknowns. A number of examples are presented in order to show the advantages of the present procedure. Moreover comparisons of computational costs are included in the examples.