In nature, vibrissae are tactile hairs of mammals used as sensor
elements for the exploring the surrounding area. These hairs, also known as
whiskers, can be found in different locations on an animal’s body.
Mystacial vibrissae are distributed over a whiskerpad on a muzzle and well
organized in rows and columns. Carpal vibrissae are located on the downside
aspect of the forelimbs of mammals. The vibrissal hair has a conical shape
and grows from a special heavily innervated hair follicle incorporating a
capsule of blood, called follicle-sinus complex. As the hair itself has no
receptors along its length, the vibrissa may be considered as a system for
transmitting forces and torques that arise from the contact between the
hair and an object to sensory receptors inside the follicle.
The present thesis deals with the vibrational motion of vibrissae during
natural exploratory behaviour from the mechanical point of view. The
phenomenon of the parametric resonance of the vibrissa is investigated
theoretically and numerically. In the first part of this thesis, two
mechanical models of an elastic beam are presented based on findings in the
literature. The first model considers a straight beam with the linearly
decreasing radius of the circular cross-section. The second model takes
into account the circular natural configuration of the cylindrical beam.
Within these models, the small transverse vibration of the beam under a
periodic following force at the tip, which corresponds to the surface
roughness of an investigated object, are analysed using the Euler-Bernoulli
beam theory and asymptotic methods of mechanics.
In the second part of the thesis, the numerical analysis of the problems is
performed based on the finite element method using ANSYS 16.2 software. For
each model, the dynamical mechanical response of the system on the
parametric excitation is simulated for different frequency values.
It is shown theoretically and numerically that at specific ranges of the
excitation frequency the phenomenon of the parametric resonance of the beam
takes place. That means that the amplitude of vibrations of the beam
increases exponentially with time, when it is stimulated within one of the
frequency ranges of the parametric resonance. These ranges depend on the
geometrical and material parameters of the beam model, as well as the
amplitude of the periodic excitation.