OBRABOTKAMETALLOV Vol. 24 No. 2 2022 TECHNOLOGY The amplitude frequency response of the vibration system (Fig. 2) was taken at the end of the waveguide using a dial indicator. The resonance frequency is f = 21,800 Hz. Fig. 2. Amplitude-frequency characteristic PMS-2.0-22 A differential equation for the bending vibrations of the plate [28]: 2 2 4 2 0 0 4 2 2 2 0. m m m d d dx c c dx Where m is the vibration amplitude, 0 is the angular frequency of self-induced vibrations, x is the plate coordinate in the longitudinal direction, c is the propagation rate of longitudinal vibrations, is the cross-section inertia radius. / . I S Where I is the moment of inertia relative to the axis, S is the cross-section area. For the rectangular plate being used (30×4 mm): 3 / 0.0012. 12 bh bh If the condition of 2 2 0.05 l is met (0.0006 for the case under consideration), the rotary inertia can be neglected, and the equation of steady-state vibrations looks as follows: 2 4 0 4 2 0. m m d dx c This equation was solved by Krylov (1936): 1 2 3 4 , m x x x x C A C B C C C D where C1, C2, C3, C4 are the constants of integration that are found from boundary conditions: ( ) cos( ) / 2, x A ch kx kx ( ) sin( ) / 2, x B sh kx kx
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