Abstract
This paper proposes the measurement system of cubic nonlinear elasticity of tissues. The system consists of a vibrator, a measuring object and a control circuit. We apply a nonlinear feedback proportional to velocity and displacement squared of the vibrator to actuate the vibrator for inducing van der Pol type self-excited oscillation and control the amplitude of the oscillation by changing the nonlinear feedback gain. When the vibrator touches the measuring object, the frequency shift of the vibrator occurs depending on elasticity of the object. When the object has nonlinear elasticity, it causes a natural frequency shift related to the amplitude of the vibrator. Therefore, by the change of the response amplitude based on the variation of the nonlinear feedback gain, we estimate the nonlinear elasticity of the object. We theoretically examine the validity of the above proposed measurement method for the cubic nonlinear elasticity of the object and experimentally confirm the performance for the cubic nonlinear elasticity of the system with magnetic restoring force.
