Driving‐Point Impedances of Cantilever Beams—Comparison of Measurement and Theory

TLDR: In this paper, the Timoshenko theory was extended to account for the internal damping of the beams in addition to the effects of rotary inertia and shear displacement, and the driving point impedances and natural frequencies of small, rigidly terminated, metal cantilever beams in bending vibration have been measured at low strain amplitudes.

Abstract: The driving‐point impedances and natural frequencies of small, rigidly terminated, metal cantilever beams in bending vibration have been measured at low strain amplitudes. The results show excellent agreement with the predictions of the Timoshenko theory, which has been extended to account for the internal damping of the beams in addition to the effects of rotary inertia and shear displacement. Values of impedance measured at the free end of a magnesium alloy beam have a maximum dynamic range of 6×106; the lowest measured value of impedance was 4.1×10−5 lb‐sec/in. Attempts to avoid the excitation of the third beam mode by driving the beam at a nodal point near its midpoint have proved both successful and straight‐forward. Driving‐point impedance has also been measured at the ends of a manganese‐copper alloy beam and an aluminum beam coated with an unconstrained layer of damping compound. The driving‐point impedance of this damped beam has been closely matched theoretically by the impedance of an equivalen...