We study the stability of solutions to initial–boundary-value problems for coupled systems of partial differential equations that describe the dynamics of deformable structural elements interacting with a gas-liquid medium. The definitions of stability of deformable bodied adopted in this work correspond to the concept of the Lyapunov stability of dynamic systems. The stability of deformable elements of vibration devices interacting with subsonic and supersonic flows is examined. The influence of a gas or liquid (in the model of an ideal compressible medium) is determined from asymptotic equations of aerohydromechanics. For the description of the dynamics of elastic elements, we use nonlinear models of solid deformable bodies with transverse and longitudinal deformations. Models are described by coupled nonlinear systems of partial differential equations. The study of stability is based on the construction of positive-definite Lyapunov-type functionals corresponding to these systems; sufficient conditions for the stability of their solutions are obtained.
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