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Figure 3. Reflection coefficient versus frequency when « = | for (a) 0 = 5°, (b) 0 = 45°, (c) 0 = 90°, and (d) 0 = 180°. VUPLTIEIETIE Is HOt do All TTI ALOL,. LL Vall UY LCAIVUIAIEU TUTE Ue Lela AN [UH QU/U WY). For the numerical example, a beam is assumed to be made of aluminum with p =2:7 x 10° kg/m’ and E = 7:1 x 10!° N/m’. The beam has an average thickness, /) 1 cm and a width, 6 = 5cm. The geometric periodicity is built in such a way that the beam wavenumber is equal to twice the wavenumber of the flexural wave propagating at a frequency of 1250 Hz. Then, the periodicity of the beam is described as b = S{l + ¢6 sin (5-15x + @) — sin (5-15x)] cm. Hence, the wavelength of the periodic beam is A = 1:22 cm. The small parameter ¢ is taken to be 0-1, and the length of the periodic section is assumed to be ¢ = 10A.

Figure 3 Reflection coefficient versus frequency when « = | for (a) 0 = 5°, (b) 0 = 45°, (c) 0 = 90°, and (d) 0 = 180°. VUPLTIEIETIE Is HOt do All TTI ALOL,. LL Vall UY LCAIVUIAIEU TUTE Ue Lela AN [UH QU/U WY). For the numerical example, a beam is assumed to be made of aluminum with p =2:7 x 10° kg/m’ and E = 7:1 x 10!° N/m’. The beam has an average thickness, /) 1 cm and a width, 6 = 5cm. The geometric periodicity is built in such a way that the beam wavenumber is equal to twice the wavenumber of the flexural wave propagating at a frequency of 1250 Hz. Then, the periodicity of the beam is described as b = S{l + ¢6 sin (5-15x + @) — sin (5-15x)] cm. Hence, the wavelength of the periodic beam is A = 1:22 cm. The small parameter ¢ is taken to be 0-1, and the length of the periodic section is assumed to be ¢ = 10A.

Related Figures (3)

Figure 1. Beam geometry. by substituting equation (4) into equation (3) and equating each of the coefficients of é° and «! to zero, to obtain
Figure 1. Beam geometry. by substituting equation (4) into equation (3) and equating each of the coefficients of é° and «! to zero, to obtain
Figure 2. Resonant reflection coefficient versus the phase angle 0 when « = 1.
Figure 2. Resonant reflection coefficient versus the phase angle 0 when « = 1.
Figure 4. Reflection coefficient versus N (number of resonant wavelengths of the periodic section of the beam)
Figure 4. Reflection coefficient versus N (number of resonant wavelengths of the periodic section of the beam)
Related topics:
EngineeringSound and VibrationReflection Coefficient
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