Beam Torsional Vibration Calculators

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Beam Torsional Vibration Frequency

Calculate beam torsional natural vibration frequency from for modes 1 to 8.

The torsional natural vibration frequency for a beam can be calculated by

`fn = k / (2 L) √(G / ρ) `

where :

fn = natural frequency [Hz]
k = mode factor
L = beam length
G = beam shear modulus
ρ = beam density

The mode factor k is dependent on the mode number and the beam end type. The torsional natural frequency is independent of the cross section profile. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes.

Use the Result Table and Result Plot options to display tables and plots. Refer to the 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

Calculate beam damped and undamped torsional natural vibration frequency from beam shear modulus, density and length.

The torsional natural frequency is independent of the cross section profile. Select the end type, and vibration mode number (modes 1 to 8). The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. 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 mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type.

Tool Input

modptype : Material Property Type
- Gu : User Defined Shear Modulus
- ρpu : User Defined Density
endtype : End Type
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

ρ : Density
G : Shear Modulous
fd : Damping Factor
fn : Natural Frequency
k : Natural Frequency K Factor

Beam Torsional Vibration Frequency

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