Nonlinear Mechanical Coupling of Harmonic Oscillators Applied for a Vibrational AND Function

This report describes a nonlinear mechanical coupling scheme for two perpendicular motions by means of a conventional spring. The nonlinear coupling scheme is applied for the design of a purely mechanical AND function that couples a superposition of two parallel input vibrations to an output oscillator that vibrates orthogonally to the input oscillators. The performance of the AND function was numerically simulated for a variety of coupling parameters and input amplitudes. Upper limits on the coupling strength were found for fixed input amplitudes, and, similarly, upper limits of the input amplitudes exist for fixed coupling parameters. Beyond these critical values, the motion of the output was found to become chaotic. A modified version of the AND function acting as a mechanical modulator was numerically investigated for application as a mechanical power amplifier. In a frequency up-converter configuration, a significant amplification of the vibrational power fed into the modulator can be achieved. The feasibility of the nonlinear mechanical coupling and its application for a vibrational AND function were demonstrated in an experimental setup.

Additional keywords: Durig, Duerig, Zuger, Zueger