Pipeng Toolbox : Rotated Beam Natural Frequency Calculators Login
Short Cuts
GO
Main ±
Beams ±
References ±
Fluid Flow ±
Fluid Properties ±
Maths ±
Materials ±
Pipelines ±
Soils ±
Subsea ±
Data ±
Units ±
Help ±
Demo

Rotated Beam Natural Vibration Frequency

Calculate the damped and undamped beam lateral natural vibration frequency for rotated general beams (simply supported, fixed, and cantilever beams).

Enter the moment of inertia for two perpendicular axes (Il and Im), and the product of inertia about the centroid (Hlm). For the principal axes the product of inertia is zero. The rotated moment of inertia and bending modulus (EI) can be calculated for:

  • user defined rotation
  • perpendicular to user defined rotation
  • principal axis 1 (I1)
  • principal axis 2 (I2)
  • axis l (Il)
  • axis m (Im)
  • Minimum I
  • Maximum I

The lateral natural vibration frequency beam end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, pinned free ends, and free ends (unsupported beams). For beams on a soft foundation such as soil, use the effective length factor to allow for movement at the beam ends. For defined beam ends such as structures, the effective length factor should be set to one. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). The buckling load is dependent on the end type, and is used for mode 1 vibration only. Buckling normally occurs on the axis with lowest stiffness (I1 or I2). The bending axis for buckling can be defined separately for cases where vibration and buckling are not parallel:

  • parallel to vibration
  • perpendicular to vibration
  • principal axis I1
  • principal axis I2
  • axis l
  • axis m
  • minimum I
  • maximum I
  • user defined angle
  • perpendicular to user defined angle

The mode factor k is dependent on the mode number, and the beam end type. The k factors have been taken from the Shock and Vibration handbook. The damping factor should be set to zero for undamped vibration or set greater than zero and less than or equal to one for damped vibration.

Use the Result Table and Result Plot options to display tables and plots. Refer to the figures and help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

Change Module :

[FREE] tools are free in basic mode with no login (no plots, tables, goal seek etc). Login or Open a free account to use the tools in plus mode (with plots, tables, goal seek etc).
[PLUS] tools are free in basic CHECK mode with Login or Open a free account (CHECK values no plots, tables, goal seek etc). Buy a Subscription to use the tools in plus mode (with plots, tables, goal seek etc).
Try plus mode using the Plus Mode Demo tools with no login.   Help Using The Pipeng Toolbox (opens in the popup workbook)

Links : ±
CALCULATOR : Beam Added Mass Coefficient (General Beam) [FREE]   ±

Calculate general beam added mass coefficient and added mass from gap height and characteristic length.

Added mass is included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The added mass coefficient is calculated in accordance with DNVGL RP F105. The equation is suitable for undamped vibration of circular pipes in still fluid. For circular pipes the diameter should be used as the characteristic length. For other profile shapes the width can be used as the characteristic length. The method may not be valid for other profile shapes (engineering judgement is required). Refer to the help pages for more details.

Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website)

Tool Input

  • cmtype : Added Mass Coefficient Type
    • Cmu : User Defined Added Mass Coefficient
  • mb : Beam Mass Per Unit Length
  • ρe : External Fluid Density
  • W : Beam Characteristic Length
  • G : Gap Height
  • AX : Beam Cross Section Area

Tool Output

  • Cm : Added Mass Coefficient
  • G/W : Gap Over Characteristic Length Ratio
  • m : Total Mass Per Unit Length
  • ma : Added Mass Per Unit Length
CALCULATOR : Beam Lateral Natural Vibration Frequency (General Beam) [FREE]   ±

Calculate beam damped and undamped lateral natural vibration frequency for general beams (user defined properties - with axial load or no axial load). Beam unit mass bending stiffness modulus and axial load are user defined.

Select the load type, end type, and vibration mode number (modes 1 to 5 for beams with no axial load, or mode 1 for beams with axial load. The end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, also pinned free ends, and free ends (unsupported beams). For beams with axial load the natural frequency equals zero for compressive axial loads greater than or equal to the buckling load.

The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). Buckling normally occurs on the axis with lowest stiffness modulus. The buckling stiffness modulus and the vibration stiffness modulus can be defined independently for cases where vibration is not parallel to buckling.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam 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 natural frequency equals zero for critical damping.

Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, beam length and end type, or axial load and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. Refer to the figures and help pages for more details.

Tool Input

  • eitype : Bending Modulus Type
    • EIvu : User Defined Vibration Bending Modulus (E x I)
    • EIbu : User Defined Buckling Bending Modulus (E x I)
  • loadtype : Axial Load Type
    • Fau : User Defined Axial Load
  • fbtype : Buckling Load Type
  • endtype : End Type
  • MN : Mode Number
  • 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)
  • AX : Cross Section Area
  • m : Unit Mass
  • Lo : Nominal Length
  • SY : Yield Stress

Tool Output

  • EIb : Buckling Bending Modulus (E x I)
  • EIv : Vibration Bending Modulus (E x I)
  • Fa : Axial Load
  • Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
  • Fb : Buckling Load
  • Le : Effective Length
  • Lt : Transition Length (Short to Long Beam)
  • fd : Damping Factor
  • fn : Natural Frequency
  • k : Natural Frequency K Factor
CALCULATOR : Beam Vibration Yield Stress [FREE]   ±

Calculate beam yield stress (SMYS) and tensile stress (SMTS).

Select one of the API, ASME or DNV stress table options. Use the Result Table option to display the stress values for the selected stress table.

Tool Input

  • syutype : Stress Table Type
  • mattype : Material Type
    • SMYSu : User Defined Specified Minimum Yield Stress
    • SMTSu : User Defined Specified Minimum Tensile Stress

Tool Output

  • SMTS : Specified Minimum Tensile Stress
  • SMTS/SMYS : Tensile Stress Over Yield Stress Ratio
  • SMYS : Specified Minimum Yield Stress
  • SMYS/SMTS : Yield Stress Over Tensile Stress Ratio
CALCULATOR : Beam Vibration Material Property [FREE]   ±

Calculate beam elastic modulus, shear modulus, bulk modulus, density, and thermal expansion coefficient.

The table values of Poisson ratio and bulk modulus are calculated from the elastic modulus and shear modulus. Use the Result Table option to display a table of properties versus material type.

Tool Input

  • modptype : Material Type
    • Eu : User Defined Elastic Modulus
    • Gu : User Defined Shear Modulus
    • Ku : User Defined Bulk Modulus
    • νu : User Defined Poisson Ratio
    • ρu : User Defined Density
    • αu : User Defined Thermal Expansion Coefficient

Tool Output

  • α : Thermal Expansion Coefficient
  • ν : Poisson Ratio
  • ρ : Density
  • E : Elastic Modulus
  • G : Shear Modulus
  • K : Bulk Modulus
CALCULATOR : Beam Lateral Natural Vibration Frequency (Rotated General Beam) [PLUS]   ±

Calculate beam damped and undamped lateral natural vibration frequency for rotated general beams (user defined properties - with axial load or no axial load). Beam unit mass bending stiffness modulus and axial load are user defined.

Enter the moment of inertia for two perpendicular axes (Il and Im), and the product of inertia about the centroid (Hlm). For the principal axes the product of inertia is zero. Select the vibration axis, buckling axis, load type, end type, and vibration mode number (modes 1 to 5 for beams with no axial load, or mode 1 for beams with axial load. The end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, also pinned free ends, and free ends (unsupported beams). For beams with axial load the natural frequency equals zero for compressive axial loads greater than or equal to the buckling load.

The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). Buckling normally occurs on the axis with lowest stiffness modulus. The buckling axis and the vibration axis can be defined separately for cases where vibration is not parallel to buckling.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam 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 natural frequency equals zero for critical damping.

Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, beam length and end type, or axial load and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. Refer to the figures and help pages for more details.

Tool Input

  • modptype : Material Property Type
    • Eu : User Defined Elastic Modulus
  • loadtype : Axial Load Type
    • Fau : User Defined Axial Load
  • fbtype : Buckling Load Type
  • leftype : Effective Length Type
    • feu : User Defined Effective Length Factor
  • endtype : End Type
  • MN : Mode Number
  • fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
    • fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
  • angtype : Vibration Axis Type
    • θvu : User Defined Vibration Axis Angle
  • eitype : Buckling Axis Type
    • θbu : User Defined Buckling Axis Angle
  • Ax : Cross Section Area
  • Il : Moment Of Inertia L
  • Im : Moment Of Inertia M
  • Hlm : Product Of Inertia
  • Lo : Nominal Length
  • m : Unit Mass
  • Sy : Yield Stress

Tool Output

  • θb : Buckling Axis Angle Relative To Axis L
  • θv : Vibration Axis Angle Relative To Axis L
  • E : Elastic Modulus
  • EIb : Buckling Bending Modulus (E x Ib)
  • EIv : Vibration Bending Modulus (E x Iv)
  • Fa : Axial Load
  • Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
  • Fb : Buckling Load
  • Ib : Buckling Moment Of Inertia
  • Iv : Vibration Moment Of Inertia
  • Le : Effective Length
  • Lt : Transition Length (Short to Long Beam)
  • fd : Damping Factor
  • fn : Natural Frequency
  • k : Natural Frequency K Factor
CALCULATOR : Beam Cross Section Rotated Moment Of Inertia (General Beam) [FREE]   ±

Calculate beam rotated moment of inertia and product of inertia about any point for a general beam.

The cross section area (Ax), the moments of inertia (Il and Im) and the product of inertia (Hlm) are user defined at any suitable point (either the centroid or an offset). If the axis l and m are pricipal axis, the product of inertia Hlm equals zero.

I1 and I2 are the principal moments of inertia (H12 = 0). θ1 is the angle between the X axis and the principal axis 1. θ2 is the angle between the X axis and the principal axis 2, perpendicular to θ1.

The rotated moments of inertia (Iu and Iv) and the rotated product of inertia (Huv) can be calculated for either the user defined rotation angle (θ), perpendicular to the user defined rotation angle, the principal axis angle θ1, or the principal axis angle θ2. Use the Result Plot option to display a plot of the rotated moment of inertia and product of inertia versus rotation angle.

Tool Input

  • angtype : Rotation Angle Type
    • θu : User Defined Rotation Angle
  • Ax : Cross Section Area
  • Il : Moment Of Inertia L
  • Im : Moment Of Inertia M
  • Hlm : Product Of Inertia

Tool Output

  • θ : Rotation Angle
  • θ1 : Principal Axis Angle 1
  • Huv : Product Of Inertia Rotated
  • I1 : Principal Moment Of Inertia 1
  • I2 : Principal Moment Of Inertia 2
  • Ip : Polar Moment Of Inertia
  • Iu : Moment Of Inertia U Rotated
  • Iv : Moment Of Inertia V Rotated
pipeng.com 2025 (696 μs : 6 ms : 0.751 MB) Pengu CMS ©