OBRABOTKAMETALLOV Vol. 24 No. 2 2022 TECHNOLOGY Let’s calculate from the condition fp ≈ 21,800 Hz for various n and include the calculation values in Table 4. Ta b l e 4 Dependence of the resonant length of the plate on n at frequency of 21,800 Hz n 1 2 3 4 5 6 7 8 lp 0.031 0.052 0.072 0.093 0.114 0.134 0.155 0.176 k 151.6 Thus, the size of the plate, which provides vibrations at a resonant frequency of 21,800 Hz, corresponds to the 7th vibration mode and is 155 mm (this size was chosen for research). The coeffi cient k allows associating the frequency and propagation rate of bending vibrations CB: B , k C where B 2 904.5 C f c . Where E c is the rod rate of longitudinal vibrations (5,157 m/s for AMg4). If the rate and frequency are known, the bending wavelength can be found (4): B B p 41.3 mm C f . (4) In this manner, when ultrasonic vibrations are communicated, the plate length fi ts / 3.75 p B l bending waves. Taking into account that plate ends are free and can’t have zero vibrations, let’s build the diagram of vibration distributions over the plate (Fig. 4). Vibration nodes where the amplitude is equal to zero are located at the half-wave length with a shift by 1/8 of the wave length x1 = (B/2) I + B/8 (I = 0, 1, 2…), and antinodes with the maximum amplitude are located at 1/4 of the wave length from nodes x2 = (B/2) I + B/8 – B/4. The weld locations and ultrasonic vibration application points should be selected according to distance x2. Fig. 4. Distribution of vibrations over the welded plate
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