Imposing a Node at a Desired Location Along a Beam Under Harmonic Base Excitation: Theory and Experiment

Vibration absorbers are commonly used to reduce unwanted structural vibrations. In this paper, a vibration absorber composed of a sprung mass is used to enforce a location of zero displacement (or node) at a specified location on a Euler-Bernoulli beam under harmonic base excitation. Closed-form expressions for the optimal tuning of the auxiliary spring-mass system are found, and the results are presented for the cases of the attachment and node located at the same and different locations. The assumed modes method is used, so the results can be applied for arbitrary boundary conditions. To aid in the design process, this paper also characterizes the sensitivity of the displacement at the desired node location to parametric variations. Sensitivities are considered with respect to the base excitation frequency and the attachment mass, stiffness, and location. The sensitivities of the system highlight some feasible but less desirable attachment locations. Numerical and experimental results for a cantilever beam are presented to illustrate the proposed method and the effects of mistuning.