Calculate pipeline damped and undamped lateral natural vibration frequency with axial load for multi layer pipeline sections.
For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long sections), or the Johnson equation (suitable for short sections). For tension loads, the natural frequency increases with increasing tension. The axial load can either be calculated from temperature and pressure, or user defined.
Pipeline unit mass and EI are calculated with external coatings and or internal liners. Unit mass can be calculated with or without added mass. Added mass is included in the unit mass for submerged pipelines to account for the fluid which is displaced by the pipeline. The added mass coefficient is calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. The effective length factor should be used for sections on a soft foundation such as soil, where the section ends are poorly defined. For defined section ends, such as structures, the effective length factor should be set to one (fe = 1). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration.
The bending stifness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating.
Enter the wall thickness for all layers. Only enter the elastic modulus for layers which will contribute to EI.
Select the end type, and vibration mode number (mode 1 only). Use the Result Table option to display the natural frequency versus either mode number, end type, or line pipe wall thickness. Use the Result Plot option to display the natural frequency versus axial load and end type, or section length and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes.
Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website)
Tool Input
- schdtype : Line Pipe Schedule Type
- diamtype : Line Pipe Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Line Pipe Wall Thickness Type
- tnu : User Defined Wall Thickness
- syutype : Line Pipe Stress Type
- mattype : Material Type
- SMYSu : User Defined Specified Minimum Yield Stress
- sectype : Section Properties Type
- EAαu : User Defined E x A x alpha
- νu : User Defined Pipe Poisson's Ratio
- eitype : E x I Type
- Kcu : User Defined Coating Factor
- CSFu : User Defined Concrete Stiffness Factor
- EIu : User Defined Pipe E x I
- mmtype : Mass Type
- ρe : User Defined External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Mass Type
- mu : User Defined Beam Unit Mass
- loadtype : Axial Load Type
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- WTi : Pipe Liner Wall Thickness
- ρi : Pipe And Liner Density
- Ei : Pipe And Liner Elastic Modulus
- αi : Pipe And Liner Thermal Expansion Coefficient
- νi : Pipe And Liner Poisson's Ratio
- WTo : Pipe Coating Wall Thickness
- ρo : Pipe Coating Density
- Eo : Pipe Coating Elastic Modulus
- ρf : Internal Fluid Density
- Lo : Nominal Length
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Force
Tool Output
- ν : Effective Poisson Ratio
- AX : Effective Cross Section Area
- CSF : Concrete Stiffness factor
- Cm : Added Mass Coefficient
- EAα : E x A x alpha
- EI : Effective E x I
- EIc : Concrete E x I
- EIp : Pipe E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- IID : Pipe Inside Diameter Including Liner
- Kc : Coating Factor
- Le : Effective Length
- Lt : Transition Length (Short to Long Beam)
- OD : Line Pipe Diameter
- OOD : Pipe Outer Diameter Including Coatings
- SMYS : Yield Stress
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Nominal Mass Per Unit Length
- md : Displaced Unit Mass
- mla : Added Unit Mass
- mlc : Contents Unit Mass
- mlp : Pipe Unit Mass Including Liner And Coating
- tn : Line Pipe Thickness