The tactile hairs of rodents like rats and mice are noticable located in
the snout region, the mystacial pad, with many other ones. A tactile hair
is used, e.g., for the orientation of the animal in its enviroment and the
localization of objects. The tactile hair consists of a follicle-sinus
complex, an intrinsic musculature which interconnects two follicles and a
vibrissa, which is used as a force transmission element to the follicle,
whereas the follicle serves as a support of the vibrissa. The aim is to
realize the object distance detection with biologically related models in
order to integrate the results into the development of tactile sensors. The
present thesis at hand deals with the development and the detailed analysis
of new vibrissa supports. Vibrissae are modeled as a bending beam,
therefore an insight into the bending vibration theory of an
Euler-Bernoulli beam with small deflections is given. The mathematical
formalism to determine the eigenvalues and associated eigenfrequencies is
explained with respect to three introductory examples. In the following,
the state of the art is analyzed. In focus are the biology of vibrisseae
and their current bionic models. The developed models refer to the
left-side bearing of a bending beam. At first, we consider a
viscoelastically pivoted beam. This support shall model the
follicle-sinus-complex. As an extension of this model, we increase the
complexity of the support in form of an additional viscoelastic translatory
bearing. This support models the elasticity of skin and intrinsic
musculature. The modal analysis of the developed models is treated
analytically from the beginning, because the cross section is constant at
first. In order to verify or to falsify the results and the occurred
atypical behavior of the analytical calculation of the
eigenfrequency–spectra, the models are examined in connection with the
help of a multi-body-system-approximation-method. Until now, it is assumed
that the vibrissa has a cylindrical shape. But, the biological paragon has
a conical longitudinal cut. This longitudinal cut is modeled by means of a
linear or an exponential function for technical vibrissae. The modal
analysis of the eigenfrequency–spectrum is performed using the
multi-body-system-approximation-method. In the previous analyses, all
models have a free right end. Therefore, finally, we take the goal object
distance determination into account. At first, the right-end is simply
supported by a bearing modeling the contact to a rigid body. Then, an
extended the right-end support to a viscoelastic translatory bearing
mimicking the behavior due to a contact to an elastic body/object. The
dependence of the eigenfrequenzy-spectrum on the contact parameters is
analytically analyzed and discussed.