Analysis of the vibrissa parametric resonance causing a signal amplification during whisking behaviour

The paper deals with the mechanical vibrational motion of vibrissae during natural exploratory behaviour of mammals. The theoretical analysis is based on a mechanical model of a cylindrical beam with circular natural configuration under an applied periodic force at the tip, which corresponds to the surface roughness of an investigated object. The equation of motion of the beam is studied using the Euler-Bernoulli beam theory and asymptotic methods of mechanics. It is shown that from the mechanical point of view the phenomenon of parametric resonance of the vibrissa is possible. It means that the amplitude of forced vibrations of a vibrissa increases exponentially with time, if it is stimulated within a specific resonance frequency range, which depends on biomechanical parameters of the vibrissa. The most intense parametric resonance occurs, when the excitation frequency is close to the doubled natural frequency of free vibrations. Thus, it may be used to distinguish and amplify specific periodic components of a complex roughness profile during texture discrimination.