Transversal vibrations of beams with boundary damping in the context of animal vibrissae

Mice and rats use a sophisticated sensory system to acquire tactile information about their surroundings. Vibrissae, located in the mystacial pad, are either used passively to sense environmental forces (e.g., wind) or actively, when they rhythmically scan objects or surfaces. Some approaches to the biological paradigm vibrissa use rigid body systems in which a rod-like vibrissa is supported by a combination of spring and damping elements modeling the viscoelastic properties of the follicle-sinus-complex. However, these models can only offer limited information about the functionality of the biological sensory system, as they neglect its determining property: the inherent elasticity of the tactile hair. To increase the accuracy and the applicability of the gathered information, the vibrissa is modeled as an elastic beam in this paper. The classical differential equation (derived from the Euler-Bernoulli-equations) is applied to vibrissa beam models with varying supports using discrete and continuously distributed spring and damping elements. The eigenfrequency spectrum of such beams are being determined analytically and numerically, while varying the viscoelastic properties of the support.