Some general effects of strong high-frequency excitation: stiffening, biasing, and smoothening

Mechanical high-frequency (HF) excitation provides a working principle behind many industrial and natural applications and phenomena. This paper concerns three particular effects of HF excitation, that may change the apparent characteristics of mechanical systems: 1) stiffening, by which the apparent linear stiffness associated with an equilibrium is changed, along with derived quantities such as stability and natural frequencies; 2) Biasing, by which the system is biased towards a particular state, static or dynamic, which does not exist or is unstable in the absence of the HF excitation; and 3) smoothening, referring to a tendency for discontinuities to be effectively "smeared out" by HF excitation. Illustrating first these effects for a few specific systems, analytical results are provided that quantify them for a quite general class of mechanical systems. This class covers systems that can be modeled by a finite number of second order ordinary differential equations, generally nonlinear, with periodically oscillating excitation terms of high frequency and small amplitude. The results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems, for calculating effects for specific systems using well-defined formulas, and for possibly designing systems that display prescribed characteristics in the presence of HF excitation.