# How does one calculate the natural frequency of the vibrofeeder supported on a rubber coated helical spring having varying stiffness?

The total weight of the feeder is 19000 kg and it is mounted on 22 springs in parallel with each spring having variable stiffness varying from 50N/mm to 450N/mm for compression of 3mm to 36mm.

## All Answers (3)

Lars-Göran Sjökvist· SP Technical Research Institute of SwedenJoerg Wallaschek· Leibniz Universität HannoverThe best way to analyze your problem would be to first calculate the static equilibrium deflection (operation point) of the system and then expand the force-deflection characteristics in a Taylor series around the operation point. The linear term gives you the small-amplitude linearized stiffness of the system, which is a good starting point for the calculation of the natural frequency. The higher order terms determine whether the system is of a hardening or of a softening type and they are needed to calculate the natural frequency of the nonlinear system. How this is done is described in textbooks on nonlinear vibrations, like e.g. Hagedorn or Nayfeh/Mook.

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