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Natural Frequency of a Steel Shaft
Free-Free Vibration of a Steel Shaft
Introduction
This experiment investigates how accurately we can measure the natural frequency of an object through the use of specialised equipment.
Theory
The natural frequencies of bodies with a continuous distribution of mass and elasticity can be described in terms of partial differential equations can be separated into a time function and a displacement function. The displacement function is a fourth order ordinary differential equation of the form:
d4y/dx4 - Ć4y = 0 Where Ć4 = AĉčN2 / EI Equation (1)
Which can be rearranged to give an equation for the natural frequency, čN.
ƒçN = „©(ƒÜ4EI / Aƒâ) Equation (2)
Where A is the cross-sectional area of the shaft, ƒâ is its density, ƒç is a natural frequency, E is Young¡¦s modulus and I is the second moment of area of the cross section.
I = ĈD4 / 64 ...
Free-Free Vibration of a Steel Shaft
Introduction
This experiment investigates how accurately we can measure the natural frequency of an object through the use of specialised equipment.
Theory
The natural frequencies of bodies with a continuous distribution of mass and elasticity can be described in terms of partial differential equations can be separated into a time function and a displacement function. The displacement function is a fourth order ordinary differential equation of the form:
d4y/dx4 - Ć4y = 0 Where Ć4 = AĉčN2 / EI Equation (1)
Which can be rearranged to give an equation for the natural frequency, čN.
ƒçN = „©(ƒÜ4EI / Aƒâ) Equation (2)
Where A is the cross-sectional area of the shaft, ƒâ is its density, ƒç is a natural frequency, E is Young¡¦s modulus and I is the second moment of area of the cross section.
I = ĈD4 / 64 ...
Posted by: Cinthia De Ruiz
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