Vibration of rectangular orthotropic plates

Summary An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate.Nomenclature 2a, 2b sides of the rectangular plate - h plate thickness - E_x, E_y, E, G elastic constants of te orthotropic material - D_x E_xh³/12 - D_y E_yh³/12 - H_xy Eh³/12+Gh³/6 D_x, D_yand H_xyare rigidity constants of the orthotropic plate - mass of the plate per unit area - Poisson's ratio - W deflection of the plate - p circular frequency - b/a ratio - X_m, Y_n characteristic functions of the vibrating beam problem - p²a²b²/H_xythe frequency parameter.