A pressure vessel subject to an external force or ground motion, due to forces such as the wind or an earthquake, will deflect to a specific shape and then return to its original position once the applied force is dissipated or removed. The extent of deflection is proportional to the applied force. The vessel, or its support, will act as a spring. As the force dissipates, the vessel will vibrate through its various modes.
The period of vibration (POV) is the time it takes the vessel to deflect through one mode and return to its original position and is measured in seconds. The frequency, which is the inverse of POV, is the number of cycles per second. The POV of a pressure vessel is a function of the vessel weight, diameter, height, weight distribution, temperature, flexibility, type of support, damping mechanisms and location (if supported in a structure). Typically, when discussing the period of vibration for a vessel the “first” period of vibration, or the first “natural” or “fundamental” period of vibration is implied.
Example of the vibration modes of a cantilever beam, which can be applied to slender pressure vessels.
Generally, vessels with a POV less than 0.3 seconds (f>3.33 Hz) are considered rigid. Vessels with a POV between 0.3 and 0.75 seconds (1.33 Hz < f < 3.33 Hz) are semi-rigid. Between 0.75 and 1.25 seconds (0.8 Hz < f < 1.33 Hz) vessels are semi-flexible and for a POV greater than 1.25 seconds (0.80 Hz) vessels are considered to be flexible.
A vessel will have a different POV when empty or when full. It will have a different POV for the new and corroded conditions. It will have a different POV for hot and cold conditions due to the varying modulus of elasticity of the steel at each temperature.
Vertical vessels on legs and skirts are the most flexible. Vessels on lugs and rings are normally supported in structures and therefore would be subject to the harmonics of the structure itself. Horizontal vessels vibrate with their supports and as well are also impacted by deflections in their piers/foundations.
The POV depends on the vessel’s weight, diameter, height, weight distribution, temperature, flexibility, type of support, etc. To calculate the POV the mass distribution and exact size/shape of each component must be known, which is not feasible at early design stages. A good practice and recommended short cut to determine the POV can be found in “Pressure Vessel Design Manual” by Dennis Moss, described below.
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