A truncated conical beam model for analysis of the vibration of rat whiskers

A truncated conical beam model is developed to study the vibration behaviour of a rat whisker. Translational and rotational springs are introduced to better represent the constraint conditions at the base of the whiskers in a living rat. Dimensional analysis shows that the natural frequency of a truncated conical beam with generic spring constraints at its ends is inversely proportional to the square root of the mass density. Under all the combinations of the classical free, pinned, sliding or fixed boundary conditions of a truncated conical beam, it is proved that the natural frequency can be expressed as f = α(rb/L(2))E/ρ and the frequency coefficient α only depends on the ratio of the radii at the two ends of the beam. The natural frequencies of a representative rat whisker are predicted for two typical situations: freely whisking in air and the tip touching an object. Our numerical results show that there exists a window where the natural frequencies of a rat whisker are very sensitive to the change of the rotational constraint at the base. This finding is also confirmed by the numerical results of 18 whiskers with their data available from literature. It can be concluded that the natural frequencies of a rat whisker can be adjusted within a wide range through manipulating the constraints of the follicle on the rat base by a behaving animal.