L=225 w=28 t=3 h=17+3/2 (实际上是梯形的)}
k N = 1 4 Y w ( t L ) 3 = 1 4 ( 160000 ) 28 ( 3 225 ) 3 = 2. 654 8 {\displaystyle k_{N}={\frac {1}{4}}Yw\left({\frac {t}{L}}\right)^{3}={\frac {1}{4}}\left(160000\right)28\left({\frac {3}{225}}\right)^{3}=2.\,654\,8}
f [ H z ] = t β i 2 4 π L 2 Y 3 ρ = ( 3 ∗ 10 − 6 ) ( 1.875 ) 2 4 π ( 225 ∗ 10 − 6 ) 2 ( 160 ∗ 10 9 ) 3 ∗ 2330 = 79318. H z {\displaystyle f[Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(3\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(225\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=79318.Hz}
2 ( w h t L ) 2 = 2 ( 28 ∗ 18.5 3 ∗ 225 ) 2 = 1. 177 8 {\displaystyle 2\left({\frac {wh}{tL}}\right)^{2}=2\left({\frac {28\ast 18.5}{3\ast 225}}\right)^{2}=1.\,177\,8} 所以 k l a t k t o r . {\displaystyle k_{lat}~k_{tor}.}
k t o r = k N 1 2 ( L h ) 2 = 2.65 1 2 ( 225 18.5 ) 2 = 195. 99 {\displaystyle k_{tor}=k_{N}{\frac {1}{2}}\left({\frac {L}{h}}\right)^{2}=2.65{\frac {1}{2}}\left({\frac {225}{18.5}}\right)^{2}=195.\,99}
k l a t = 1 4 Y t w 3 L 3 = 1 4 ( 160000 ) 3 ( 28 225 ) 3 = 231. 26 {\displaystyle k_{lat}={\frac {1}{4}}Y{\frac {tw^{3}}{L^{3}}}={\frac {1}{4}}\left(160000\right)3\left({\frac {28}{225}}\right)^{3}=231.\,26}
规格：13 kHz，0.45 N/m : L=440 w=30 t=4 h=17.5+2 (实际上是梯形的??)
k N = 1 4 Y w ( t L ) 3 = 1 4 ( 160000 ) 30 ( 4 440 ) 3 = 0.901 58 {\displaystyle k_{N}={\frac {1}{4}}Yw\left({\frac {t}{L}}\right)^{3}={\frac {1}{4}}\left(160000\right)30\left({\frac {4}{440}}\right)^{3}=0.901\,58}
f {\displaystyle f} [ H z ] = t β i 2 4 π L 2 Y 3 ρ = ( 4 ∗ 10 − 6 ) ( 1.875 ) 2 4 π ( 440 ∗ 10 − 6 ) 2 ( 160 ∗ 10 9 ) 3 ∗ 2330 = 27655. H z {\displaystyle [Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(4\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(440\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=27655.Hz}
2 ( w h t L ) 2 = 2 ( 30 ∗ 19.5 4 ∗ 440 ) 2 = 0.220 96 {\displaystyle 2\left({\frac {wh}{tL}}\right)^{2}=2\left({\frac {30\ast 19.5}{4\ast 440}}\right)^{2}=0.220\,96} 因此 k l a t < k t o r . {\displaystyle k_{lat}<k_{tor}.}
k t o r = k N 1 2 ( L h ) 2 = 0.9 1 2 ( 440 19.5 ) 2 = 229. 11 {\displaystyle k_{tor}=k_{N}{\frac {1}{2}}\left({\frac {L}{h}}\right)^{2}=0.9{\frac {1}{2}}\left({\frac {440}{19.5}}\right)^{2}=229.\,11}
k l a t = 1 4 Y t w 3 L 3 = 1 4 ( 160000 ) 4 ( 30 440 ) 3 = 50. 714 {\displaystyle k_{lat}={\frac {1}{4}}Y{\frac {tw^{3}}{L^{3}}}={\frac {1}{4}}\left(160000\right)4\left({\frac {30}{440}}\right)^{3}=50.\,714}
规格：50 kHz，1.5 N/m : L=215 w=30 t=4 h=17.5+2 (它实际上是梯形的吗？)
k N = 1 4 Y w ( t L ) 3 = 1 4 ( 160000 ) 30 ( 4 215 ) 3 = 7. 727 6 {\displaystyle k_{N}={\frac {1}{4}}Yw\left({\frac {t}{L}}\right)^{3}={\frac {1}{4}}\left(160000\right)30\left({\frac {4}{215}}\right)^{3}=7.\,727\,6}
f {\displaystyle f} [ H z ] = t β i 2 4 π L 2 Y 3 ρ = ( 4 ∗ 10 − 6 ) ( 1.875 ) 2 4 π ( 215 ∗ 10 − 6 ) 2 ( 160 ∗ 10 9 ) 3 ∗ 2330 = 1. 158 2 × 10 5 H z {\displaystyle [Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(4\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(215\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=1.\,158\,2\times 10^{5}Hz}
2 ( w h t L ) 2 = 2 ( 30 ∗ 19.5 4 ∗ 215 ) 2 = 0.925 43 {\displaystyle 2\left({\frac {wh}{tL}}\right)^{2}=2\left({\frac {30\ast 19.5}{4\ast 215}}\right)^{2}=0.925\,43}
因此 k l a t k t o r . {\displaystyle k_{lat}~k_{tor}.}
k t o r = k N 1 2 ( L h ) 2 = 7.7 1 2 ( 215 19.5 ) 2 = 468. 02 {\displaystyle k_{tor}=k_{N}{\frac {1}{2}}\left({\frac {L}{h}}\right)^{2}=7.7{\frac {1}{2}}\left({\frac {215}{19.5}}\right)^{2}=468.\,02}
k l a t = 1 4 Y t w 3 L 3 = 1 4 ( 160000 ) 4 ( 30 215 ) 3 = 434. 68 {\displaystyle k_{lat}={\frac {1}{4}}Y{\frac {tw^{3}}{L^{3}}}={\frac {1}{4}}\left(160000\right)4\left({\frac {30}{215}}\right)^{3}=434.\,68}
规格：200 kHz，20 N/m : L=115 w=30 t=4 h=17.5+2 (它实际上是梯形的吗？)
k N = 1 4 Y w ( t L ) 3 = 1 4 ( 160000 ) 30 ( 4 115 ) 3 = 50. 497 {\displaystyle k_{N}={\frac {1}{4}}Yw\left({\frac {t}{L}}\right)^{3}={\frac {1}{4}}\left(160000\right)30\left({\frac {4}{115}}\right)^{3}=50.\,497}
f {\displaystyle f} [ H z ] = t β i 2 4 π L 2 Y 3 ρ = ( 4 ∗ 10 − 6 ) ( 1.875 ) 2 4 π ( 115 ∗ 10 − 6 ) 2 ( 160 ∗ 10 9 ) 3 ∗ 2330 = 4. 048 4 × 10 5 H z {\displaystyle [Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(4\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(115\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=4.\,048\,4\times 10^{5}Hz}
2 ( w h t L ) 2 = 2 ( 30 ∗ 19.5 4 ∗ 115 ) 2 = 3. 234 6 {\displaystyle 2\left({\frac {wh}{tL}}\right)^{2}=2\left({\frac {30\ast 19.5}{4\ast 115}}\right)^{2}=3.\,234\,6} 因此 k l a t > k t o r . {\displaystyle k_{lat}>k_{tor}.}
k t o r = k N 1 2 ( L h ) 2 = 50.4 1 2 ( 115 19.5 ) 2 = 876. 45 {\displaystyle k_{tor}=k_{N}{\frac {1}{2}}\left({\frac {L}{h}}\right)^{2}=50.4{\frac {1}{2}}\left({\frac {115}{19.5}}\right)^{2}=876.\,45}
k l a t = 1 4 Y t w 3 L 3 = 1 4 ( 160000 ) 4 ( 30 115 ) 3 = 2840. 5 {\displaystyle k_{lat}={\frac {1}{4}}Y{\frac {tw^{3}}{L^{3}}}={\frac {1}{4}}\left(160000\right)4\left({\frac {30}{115}}\right)^{3}=2840.\,5}
![{\displaystyle f[Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(3\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(225\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=79318.Hz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fbeda8a4886164dcd9879d19c8e05c9997cf926)
所以 
![{\displaystyle [Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(4\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(440\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=27655.Hz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/110b10313c8bb8568be844f60cdbb75dd810b0f0)
因此 
![{\displaystyle [Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(4\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(215\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=1.\,158\,2\times 10^{5}Hz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fdacf7a9ea7bbbf1f9325d02fdbc5f081084326f)
![{\displaystyle [Hz]={\frac {t\beta _{i}^{2}}{4\pi L^{2}}}{\sqrt {\frac {Y}{3\rho }}}={\frac {\left(4\ast 10^{-6}\right)\left(1.875\right)^{2}}{4\pi \left(115\ast 10^{-6}\right)^{2}}}{\sqrt {\frac {\left(160\ast 10^{9}\right)}{3\ast 2330}}}=4.\,048\,4\times 10^{5}Hz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a8bcec750635799fc0f1ae50cfa2c33360a8f4f)
因此 
