Theoretical Analysis of the Shaft

Table 1

Comparison of results between MANFIS, experimental analysis, and numerical analysis.

Relative first natural frequency “inf”	Relative second natural frequency “mnf”	Relative third natural frequency “fnf”	Average relative first mode shape difference “amd”	Average; relative second mode shape difference “bmd”	Average relative third mode shape difference “cmd”	MANFIS relative				Experimental analysis relative				Numerical analysis relative
						1st crack depth “𝛽5”				1st crack depth “𝛽3”				1st crack depth “𝛽1”
						1st crack location “𝛼5”				1st crack location “𝛼3”				1st crack location “𝛼1”
						2nd crack depth “𝛽6”				2nd crack depth “𝑟 𝛽4”				2nd crack depth “𝛽2”
						2nd crack location “𝛼6”				2nd crack location “𝛼4”				2nd crack location “ 𝛼2”
						𝛽5	𝛼5	𝛽6	𝛼6	𝛽3	𝛼3	𝛽4	𝛼4	𝛽1	𝛼1	𝛽2	𝛼2
0.9964	0.9994	0.9988	0.030495	0.031595	0.085795	0.23859	0.23958	0.47628	0.2401	0.10098	0.10197	0.198156	0.100058	0.099	0.099	0.196	0.098
0.9854	0.998	0.991	0.029175	0.0314	0.085365	0.241	0.46948	0.47628	0.4851	0.102	0.19982	0.198156	0.202158	0.1	0.194	0.196	0.198
0.9812	0.9924	0.9948	0.028585	0.03074	0.085919	0.241	0.72358	0.47142	0.735	0.102	0.30797	0.196134	0.3063	0.1	0.299	0.194	0.3
0.965	0.9828	0.9936	0.0257165	0.02954	0.0853925	0.22895	0.93896	0.47871	0.9506	0.0969	0.39964	0.199167	0.396148	0.095	0.388	0.197	0.388
0.9918	0.9996	0.9912	0.03092	0.025875	0.0666	0.46272	0.23232	0.95499	0.4851	0.19584	0.09888	0.397323	0.202158	0.192	0.096	0.393	0.198
0.9946	0.9994	0.9962	0.070885	0.0317	0.109835	0.70372	0.46222	0.98	0.7007	0.29784	0.19673	0.504489	0.292006	0.292	0.191	0.499	0.286
0.97	0.9898	0.9816	0.0278	0.030695	0.085695	0.22895	0.69454	0.60021	0.94815	0.0969	0.29561	0.249717	0.395127	0.095	0.287	0.247	0.387
0.9868	0.9984	0.9898	0.036535	0.08095	0.13391	0.57358	0.23232	0.95	0.94325	0.24276	0.09888	0.450906	0.393085	0.238	0.096	0.446	0.385
0.9888	0.9992	0.9884	0.005305	0.10795	0.10395	0.69408	0.46706	0.971	0.9408	0.29376	0.19879	0.533808	0.392064	0.288	0.193	0.528	0.384
0.9832	0.9938	0.995	0.04377	0.030645	0.08668	0.47718	0.96074	0.991	0.24255	0.20196	0.40891	0.450906	0.101079	0.198	0.397	0.446	0.099