Apparent masses of a lattice of plates in an incompressible fluid

Abstract

The apparent masses of a plane lattice of plates in an incompressible fluid were determined by Gurevich (for the case of cophased translational vibrations [1]) and by Samoilovich (for cophased and antiphased translational and torsional vibrations of plates [2]). However, in a number of applications it is necessary to calculate apparent masses both for more complex forms of vibrations and also for different values of the phase shift between the vibrations of neighboring plates. In the present paper we present a calculation algorithm for the apparent masses of the lattice of plates that vibrate according to an arbitrary law with a constant phase shift between the vibrations of neighboring plates. The forms of the vibrations are approximated by trigonometric polynomials, which allows us to represent the apparent masses in the form of series in some standard coefficients. Results are given for the calculation of these coefficients over a wide range of variations of thickness, stagger, and phase shift.