Dynamic Properties of Thin-Walled Structures Under Changing Pressure Conditions in the Contact Fluid
We propose an analytical algorithm to study harmonic oscillation of a rectangular elastic plate in an incompressible fluid, with varying pressure conditions. Application of the two-dimensional Fourier transform leads to a two-dimensional integral equation with a two-dimensional integral as a kernel. The solution of the basic integral equation is represented as a series by the Chebyshev orthogonal polynomials. The problem is reduced to an infinite system of one-dimensional integral equations. The asymptotic approach allows us to solve each equation of the system independently. The solution of the integral equation leads to an ordinary differential equation of the fourth order for the function of the plate vibrations. The obtained solution determines the form of the oscillation. The results are given on example of the aluminum plate oscillations for a number of frequencies by varying air pressure density. The results are compared with experimental data.