Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

Table 1

Terminal slope 𝜃(0) of cantilever beam under normal follower forces (𝛼=𝜋/2).

𝜆	𝜃(0)^∘ [51]	S.M. [53]	NDHPM (29)	HPM (35)	LPHPM (37)	NDHPM (41)	LPNDHPM (43)	HPM [50]
0.7010	20	19.50	20.0016	19.9981	19.9981	19.998	19.9981	19.9981
1.4195	40	39.03	39.9784	39.9957	39.9958	39.9487	39.9957	39.9976
2.1755	60	58.61	59.9681	59.9964	59.9975	56.1523	59.9959	60.0066
2.9941	80	78.25	79.9905	79.9947	80.0057	−36.9334	79.9934	80.0233
3.9117	100	98.00	100.0498	99.9943	100.0610	−2104.49	99.9999	100.0504
4.9872	120	117.88	120.1375	120.001	120.2963	−33644.8	120.0574	120.0812
6.3339	140	137.93	140.2400	140.57	141.1245	−523001	140.3214	140.1092
8.2421	160	158.27	160.2464	221.529	163.5890	−1.13840𝑒+07	161.2001	160.1172
13.7500	180	179.97	178.7521	240146	179.1119	−5.39274𝑒+09	180.0345	179.8075