Theories and experiments on the stiffening effect of high-frequency excitation for continuous elastic systems

One effect of strong mechanical high-frequency excitation may be to apparently “stiffen” a structure, a well-described phenomenon for discrete systems. The present study provides theoretical and experimental results on this effect for continuous elastic structures. A laboratory experiment is set up for demonstrating and measuring the stiffening effect in a simple setting, in the form of a horizontal piano string subjected to longitudinal high-frequency excitation at the clamped base and free at the other end. A simplest possible theoretical model is set up and analyzed using a hierarchy of three approximating theories, each providing valuable insight. One of these is capable of predicting the vertical string lift due to stiffening in terms of simple expressions, with results that agree very well with experimental measurements for a wide range of conditions. It appears that resonance effects cannot be ignored, as was done in a few related studies—unless the system has very low modal density or heavy damping; thus first-order consideration to resonance effects is included. Using the specific example with experimental support to put confidence on the proposed theory, expressions for predicting the stiffening effect for a more general class of continuous systems in differential operator form are also provided.