Maximum speed and displacement criteria for a vibrating straight nozzle

The paper deals with the analytical calculation of the vibrations of industrial piping system nozzles. Its purpose is to provide the maintenance engineer with easy-to-use fatigue criteria as regards onsite speed or acceleration measurements. Monitoring of vibrating piping system nozzles requires the estimation of the bending stress in the nozzle as a function of a measurable value (the displacement, the speed or the acceleration of the valve or the main pipe). A model of a nozzle based on the Timoshenko beam theory has been created. It takes into account the mass and the rotation inertia of the valve. It provides analytical expressions of: • the first natural frequency of a nozzle • the maximum speed of a nozzle as regards endurance limit • the expected lifetime of a nozzle exhibiting a crack at its base • the maximum allowable speed of a nozzle exhibiting a crack at its base as regards fracture toughness.