Natural Frequency of a Beam
Natural Frequency of a Beam
(OP)
I have two different equations that indicate how to calculate the natural frequency of a beam. The first eqtn is from my old college books that simply indicate the frequency calculation for a simple beam as f = sqrt(g/deflection), where as a diffent book of mine indicates that the natural frequency of a beam is calculated as f = 0.18*sqrt(g/deflection). The first book is simply a dynamic mechanics book and the later is a concrete design book that references the 0.18 eqtn to 'Commentary A, Serviceability Criteria for Deflections & Vibrations,' Supplement to the National Building Code of Canada 1990, NRCC 30629, Nat'l Research Council of Canada, Ottawa, 1990, pgs 134-140. Obviously an 80% reduction is pretty significant and beyond the reasonability of just using the conservative frequency calculation.
Does anyone know what the 0.18 factor is for, and which eqtn is the correct one to use to determine the natural frequency of a beam?
Does anyone know what the 0.18 factor is for, and which eqtn is the correct one to use to determine the natural frequency of a beam?






RE: Natural Frequency of a Beam
No matter what the formulas you have I recommend that you check out Roark's Formulas for Stress and Strain for a complete treatment of beams, loadings and boundary conditions.
Regards,
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RE: Natural Frequency of a Beam
To get to 0.18 (actually 0.1792), you first convert to Hz by dividing by 2*pi, observe that m=w/g, and substitute Delta=5wL^4/(384EI) and simplify. You end up with 0.1792*sqrt(g/Delta).
I actually hate this equation. It goes a long way toward decreasing physical understanding of vibrations. The original form isn't THAT bad. fn=pi/2*sqrt(EI/mL^4). It's the *mass* that affects the natural frequency, not the *load*.
There are two redeeming qualities for this equation. First, it's easier to remember. Second, it applied approximately for other conditions such as cantilevered beams, without having to know another equation.
RE: Natural Frequency of a Beam
RE: Natural Frequency of a Beam
The coefficient is very close to 0.18 for hinged-hinged, fixed-fixed and fixed-hinged; it is closer to 0.20 for a cantilever, and it is 0.16 (again very close) even for a single concentrated mass supported by any elastic structure.
The first equation must be an expression for the angular frequency ω=2πf: it is exact for a single concentrated mass, and approximate for beams as noted above.
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