DETERMINATION OF THE FREQUENCY OF ANTISYMMETRIC FORMS OF FREE OSCILLATIONS OF A RECTANGULAR CFCF – PLATE

To find the natural frequencies of antisymmetric oscillation patterns of a rectangular plate, two opposite sides of which are pinched and the other two are free (CFCF plate), a method of sorting frequency values («shooting method») in combination with the method of successive approximations is proposed. The deflection function is represented by two hyperbola-trigonometric series along two coordinates. When all the conditions of the boundary value problem are met, a homogeneous infinite system of linear algebraic equations is obtained with respect to the indeterminate coefficients of these series, which contains the oscillation frequency as a parameter. To find nontrivial solutions of the corresponding reduced system, an iterative process of parameter iteration is organized. Numerical results are obtained for the first two antisymmetric eigenforms. The influence of the number of series terms and the number of iterations on the accuracy of the results is investigated. A comparison with the results of other authors and experimental data is given.