Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning

Table 3

Comparison of approximate solutions obtained by the proposed algorithm for different cases of scenarios 2 and 3 of angular displacement of a homogenous circular sector.

Case I				Case II		Case III		Case I		Case II		Case III
t	Numerical	CNN-BLMA		Numerical	CNN-BLMA	Numerical	CNN-BLMA	Numerical	CNN-BLMA	Numerical	CNN-BLMA	Numerical	CNN-BLMA
0	0.392699082	0.392685093	0.392699082		0.392670786	0.392699082	0.392661944	0.39269908	0.392624275	0.39269908	0.39259210	0.39269908	0.39256229
10	0.083388890	0.083389783	−0.053232122		−0.053235250	−0.151961836	−0.151961785	−0.36749090	−0.367653662	−0.36374462	−0.36345803	−0.22287067	−0.22264354
20	−0.358208978	−0.358210302	−0.378788375		−0.378796623	−0.278995466	−0.279004381	0.29461331	0.294685021	0.28024739	0.28022323	−0.14975320	−0.14978926
30	−0.234800091	−0.234800409		0.155649427	0.155648690	0.363640049	0.363652579	−0.18251243	−0.182477435	−0.15297185	−0.15299577	0.38443195	0.38481916
40	0.260262179	0.260262109		0.337907757	0.337907826	−0.000819025	−0.000819677	0.04540274	0.045441209	0.00077900	0.00061557	−0.28550774	−0.28569189
50	0.343613202	0.343612501		−0.246351630	−0.246347082	−0.363030749	−0.363041240	0.09803384	0.098023706	0.15154292	0.15147925	−0.06938614	−0.06961510
60	−0.115291291	−0.115290537		−0.272637949	−0.272634926	0.280132157	0.280142714	−0.22786478	−0.227850757	−0.27917225	−0.27905960	0.35986908	0.35952351
70	−0.391351734	−0.391304302		0.318824563	0.318825376	0.150454989	0.150457157	0.32678376	0.326762802	0.36317118	0.36298554	−0.33516516	−0.33536112
80	−0.050882422	−0.050882087		0.187321504	0.187318255	−0.392695353	−0.392577931	−0.38266277	−0.382575699	−0.39269606	−0.39197161	0.01440356	0.01442215
90	0.370322679	0.370323421		−0.368151155	−0.368156176	0.153465671	0.153473754	0.38920766	0.389280863	0.36431245	0.36406319	0.31975532	0.32062675
100	0.207666340	0.207662784		−0.087977218	−0.087990333	0.277853197	0.278105162	−0.34571116	−0.345711854	−0.28131805	−0.28162897	−0.37007441	−0.37007000