Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method

Table 2

Comparison of the convergence study of the Ritz method using Chebyshev and algebraic polynomials in of a completely free annular plate with for the first five eigenvalue parameters ().

CR	10 × 10	1.442	2.669	3.568	5.591	6.462
AR	10 × 10	1.442	2.669	3.556	5.585	6.467
CR	11 × 11	1.441	2.668	3.546	5.585	6.448
AR	11 × 11	2.051	2.182	5.828	6.419	6.786
						(ill-conditioned)
CR	12 × 12	1.437	2.668	3.522	5.579	6.415
AR	12 × 12	210.5i	162.9i	1.957 + 118.5i	1.957−118.5i	80.77i
						(ill-conditioned)

CR: results worked by the Chebyshev–Ritz method. AR: results worked by the Ritz method using algebraic polynomial as the admissible function. .