The free and forced response of a relief valve system has been analyzed. The valve system consists of a valve having a mass, resting on a seat having nonlinear spring characteristics, and retained by a helical spring which is considered to be a distributed parameter element. The response curves of the first and third harmonic and one-third subharmonic, the amplitudes of which vary with the frequency of the external force, are investigated and presented graphically. It is found that harmonic, higher-harmonic, and subharmonic response of the system may become unstable within certain frequency ranges. Jump and hysteresis phenomena analogous to that of nonlinear single-degree-of-freedom systems are observed. It is also observed that subharmonic vibration may exist in a number of specified frequency ranges.

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