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The mathematical modelling of a vibrating stamp interaction with a flexible restrained end wall (bellows) of a narrow channel via a viscous incompressible fluid is carried out. The narrow channel formed by two parallel walls and filled with a viscous liquid is investigated. The liquid motion in the channel is considered as a laminar one. The bottom channel wall is absolutely rigid, and the top one is the absolutely rigid vibrating stamp. At the right edge of the channel, the end wall with flexible restraint (bellows) is installed, and at the left one, there is a free liquid flow. The problem of longitudinal hydroelastic vibrations of the channel end wall is formulated and solved analytically. The distribution laws of velocities and pressure in the fluid layer along the channel are found. The motion law of the channel end wall is determined. The amplitude frequency and phase frequency responses of the end wall for steady-state harmonic oscillations are constructed. The mathematical modelling has shown the possibility of damping the channel end wall (bellows) vibrations by changing the distance between the channel walls or by changing the liquid viscosity in the channel.

Hydroelastic Response of an End Wall Interacting with a Vibrating Stamp via a Viscous Liquid Layer