Period Of Vibration At Dead Weight Calculator

Formula Used:

\[ T = 6.35 \times 10^{-5} \times \left(\frac{H}{D}\right)^{3/2} \times \left(\frac{\Sigma Weight}{t_{vesselwall}}\right)^{1/2} \]

Overall Height of Vessel (H):

Diameter of Shell Vessel Support (D):

Weight of Vessel with Attachments and Contents (ΣWeight):

Corroded Vessel Wall Thickness (t_vesselwall):

Period of Vibration at Dead Weight (T):

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1. What is the Period of Vibration at Dead Weight?

The Period of Vibration at Dead Weight is a measure of how quickly the structure will oscillate or vibrate when subjected to an external force or disturbance. It is an important parameter in structural engineering for assessing the dynamic behavior of pressure vessels and support structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T = 6.35 \times 10^{-5} \times \left(\frac{H}{D}\right)^{3/2} \times \left(\frac{\Sigma Weight}{t_{vesselwall}}\right)^{1/2} \]

Where:

\( T \) — Period of Vibration at Dead Weight (s)
\( H \) — Overall Height of Vessel (mm)
\( D \) — Diameter of Shell Vessel Support (mm)
\( \Sigma Weight \) — Weight of Vessel with Attachments and Contents (N)
\( t_{vesselwall} \) — Corroded Vessel Wall Thickness (mm)

Explanation: The formula calculates the natural vibration period of a vessel structure based on its geometric properties and mass distribution.

3. Importance of Vibration Period Calculation

Details: Calculating the vibration period is crucial for structural design, seismic analysis, and ensuring that the vessel can withstand dynamic loads without excessive vibration or resonance.

4. Using the Calculator

Tips: Enter all values in the specified units (mm for dimensions, N for weight). Ensure all values are positive and within reasonable ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why is vibration period important in vessel design?
A: Vibration period helps engineers design structures that can avoid resonance with external forces like wind or seismic activity, preventing structural damage.

Q2: What factors affect the vibration period?
A: The period is influenced by the vessel's height-to-diameter ratio, total weight, and wall thickness - taller, heavier vessels with thinner walls typically have longer periods.

Q3: How does wall thickness affect vibration period?
A: Thicker walls generally result in a shorter vibration period as they increase the structure's stiffness, while thinner walls allow for longer periods and more flexibility.

Q4: When should this calculation be performed?
A: This calculation should be performed during the design phase of pressure vessels and support structures, particularly for installations in seismic zones or areas with significant dynamic loads.

Q5: Are there limitations to this formula?
A: This formula provides an approximation and may need to be supplemented with more detailed finite element analysis for complex structures or critical applications.