The elastic stability of a thin cantilever beam under an articulated tip force—II: Kinetic analysis

Abstract

The problem of applying the kinetic concept of elastic stability for the experimental determination of buckling forces of a thin elastic cantilever beam subjected to a tip force applied via an articulated rod is analysed theoretically in order to establish how the square of the beam natural frequency varies with the tip force applied to the beam. In previously reported work it had been expected that this variation would be approximately linear and that consequently the results could be extrapolated to obtain the buckling force without applying it physically. The experimental results unexpectedly indicated that non-linearity would occur of a kind which effectively prevented extrapolations to be made reliably.The results of the analysis indicate that pronounced non-linearity can be expected when the articulated rod length is negative. For positive rod lengths, on the other hand, the square of frequency is sufficiently linear with tip force to enable the buckling force to be obtained by extrapolation.