Calculate beam damped and undamped torsional natural vibration frequency for a circular beam with an end mass.
The system is modelled as a beam fixed at one end, with a mass at the other (free) end. The circular beam mass moment of inertia is calculated from the beam inside diameter, outside diameter, length and density. The mass moment of inertia of the end mass is calculated for either a soid circular mass, or a hollow circular mass. The natural frequency is calculated from the mass moment of inertia ratio of the beam and the end mass for modes 1 to 8. The ᵞ factor is calculated so that ᵞ tan(ᵞ) equals the inertia ratio. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration.
Use the Result Table option to display the natural frequency versus either the mode number, or wall thickness type. Use the Result Plot option to display the natural frequency versus beam length and mode number, natural frequency versus inertia ratio, or ᵞ versus inertia ratio.
Tool Input
- schdtype : Line Pipe Schedule Type
- diamtype : Diameter Type
- ODpu : User Defined Pipe Outside Diameter
- IDpu : User Defined Pipe Inside Diameter
- wtntype : Wall Thickness Type
- tnpu : User Defined Pipe Wall Thickness
- modptypea : Pipe Material Property Type
- Gpu : User Defined Pipe Shear Modulus
- ρpu : User Defined Pipe Density
- jptype : Pipe Mass Moment Of Inertia Type
- Jpu : User Defined Pipe Mass Moment Of Inertia
- modptypeb : End Mass Material Property Type
- Gmu : User Defined End Mass Shear Modulus
- ρmu : User Defined End Mass Density
- jmtype : End Mass Moment Of Inertia Type
- ODmu : User Defined End Mass Outside Diameter
- IDmu : User Defined End Mass Inside Diameter
- Lmu : User Defined End Mass Length
- Jmu : User Defined End Mass Mass Moment Of Inertia
- jojtype : Mass Moment Of Inertia Type
- Jb/Jmu : User Defined Mass Moment Of Inertia Ratio
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- L : Length
Tool Output
- β : Vibration β Value
- ρm : End Mass Density
- ρp : Pipe Density
- CVG : Convergence Check (≥ 1)
- Gm : End Mass Shear Modulus
- Gp : Pipe Shear Modulous
- Jm : End Mass Moment Of Intertia
- Jp : Pipe Mass Moment Of Intertia
- Jp/Jm : Mass Moment Of Inertia Ratio
- ODp : Pipe Outside Diameter
- fd : Damping Factor
- fn : Natural Frequency
- idp : Pipe Inside Diameter
- tnp : Pipe Wall Thickness