TOOL C-14 · v1.0.0 · FREE · NO SIGN-UP
C-14 · DYNAMICS · CLOSED-FORM SOLUTIONS
Natural frequency
Natural frequencies of spring–mass systems, beams with five end conditions, beams carrying a point mass and thin plates — the first check before a floor, a support frame or a machine skid meets something that shakes it.
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v1.0.0 · verified against 12 reference cases
f₁ · FIRST NATURAL FREQUENCY28.12 Hz
ω₁176.7 rad/s
T₁ · PERIOD0.0356 s
| Mode | λ | f Hz | ω rad/s | T s |
|---|---|---|---|---|
| 1 | 3.14159 | 28.123 | 176.70 | 0.03556 |
| 2 | 6.28319 | 112.492 | 706.81 | 0.00889 |
| 3 | 9.42478 | 253.106 | 1590.31 | 0.00395 |
| 4 | 12.56637 | 449.966 | 2827.22 | 0.00222 |
| 5 | 15.70796 | 703.072 | 4417.53 | 0.00142 |
- Modes 3, 4, 5: half a wavelength is shorter than ten section depths (3.00 m). There Euler–Bernoulli theory overestimates the frequency — shear deformation and rotary inertia matter; check with a model that includes them.
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References: Blevins, Formulas for Natural Frequency and Mode Shape; Leissa, Vibration of Plates (NASA SP-160, 1969); Rayleigh's method for the point-mass cases.
BEYOND ONE MODE