Active and passive strategies in dynamic contact point sensing by a flexible beam

A dynamic model of a flexible beam in contact with the environment is considered in this paper. The model serves as a background for a dynamic, active antenna type, contact point sensor. In its simplest realization the sensor can be implemented in the form of a flexible beam rotating in plane. The dynamic model is developed in the nondimensional form and possible sensing strategies, active and passive, are outlined. The main feature of the sensor is the use of the frequency-versus contact point curve which, for some regions, may be a multi-valued function. Basic properties of the sensing curves are formulated, and two points of interest-the point of maximal stiffness and the point of center of impact-are introduced into the analysis. Behaviour of the sensing curves is analyzed with respect to three system parameters-mass, inertia, and stiffness ratios. It is found that in some limiting, but practically attainable cases the sensing curve becomes a single-valued function within the working range of the sensor.