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 animals body. Mystacial vibrissae are distributed over a whiskerpad on a muzzle. 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. 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 dur- ing natural exploratory behaviour from the mechanical point of view. The phenomenon of the parametric resonance of the vibrissa is investigated the- oretically 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 circu- lar natural configuration of the cylindrical beam. Within these models, the small transverse vibration of the beam under a periodic following force at the tip 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 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 am- plitude of the periodic excitation. / Tesis

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 animals body. Mystacial vibrissae are distributed over a whiskerpad on a muzzle. 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. 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 dur- ing natural exploratory behaviour from the mechanical point of view. The phenomenon of the parametric resonance of the vibrissa is investigated the- oretically 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 circu- lar natural configuration of the cylindrical beam. Within these models, the small transverse vibration of the beam under a periodic following force at the tip 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 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 am- plitude of the periodic excitation. / Tesis

The somatosensory system of mammals includes sensory hairs (vibrissae) for tactile perception during near field exploration. Interacting with the environment, the tactile hair transfers mechanical stimuli to the hair follicle (follicle-sinus complex). The follicle-sinus complex transduces the singnals and transmits them to the central nervous system. Rats, e.g., are able to characterize objects with regard to their surface and geometric shape. Inspired by the biological paragon, the implementation of a vibrissa-like tactile sensor is an object of engineering research. According to the sensory organ, the function of a technical vibrissa is based on the recording of stimuli by the artificial hair shaft and their measurement at the support. This enables the detection of technically relevant information. In this context, the present work focuses on the task of object contour reconstruction. For that purpose, the support reactions are determined during scanning of an object. Previous investigations have been restricted on scanning objects with convex contours. This is due to the limitation of mechanical models to single-point contact scenarios. Goal of the present work is the consideration of multiple contact points between sensor shaft and object contour. The sensor shaft is modelled as a Euler-Bernoulli beam. The mathematical/theoretical description of the deformation of the beam during quasi-static scanning results in a multipoint boundary value problem with switching point. In order to simulate scanning sweeps along two different object types, the corresponding multipoint boundary value problems are solved by applying a shooting method incooperating a Runge Kutta Method of 4th order. The support reactions are calculated during scanning. It shows that multi-point contacts can be identified in the support reactions. The simulation is validated by experiments using selected examples.