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

Table 4

Relative error (RE) comparison for 𝑇 of nonlinear pendulum (see Table 3).

𝛼^∘	𝑇 (55)	R.E. HPM (50)	R.E. LPHPM	R.E. NDHPM (29)
1.00000000	1.5708262330620782	−4.355𝑒−16	1.087𝑒−10	−3.247𝑒−20
10.00000000	1.5737921309247680	7.021𝑒−12	1.089𝑒−06	−3.260𝑒−12
50.00000000	1.6489952184785310	2.224𝑒−08	0.0007012	−8.872𝑒−07
100.00000000	1.9355810960047220	−2.691𝑒−05	0.01151	0.0005187
120.00000000	2.1565156474996432	0.0001385	0.02289	0.006003
130.00000000	2.3087867981671961	0.0002996	0.03019	0.01645
140.00000000	2.5045500790016340	−7.097𝑒−05	0.03811	0.03964
150.00000000	2.7680631453687676	−0.001557	0.0459	0.08404
160.00000000	3.1533852518878388	−0.001147	0.05221	—
170.00000000	3.8317419997841462	0.00633	0.05401	—
175.00000000	4.5202232749476581	0.002732	0.05038	—
177.00000000	5.0298609371127860	−0.86468𝑒−2	0.4671132𝑒−1	—
179.00000000	6.127778824526868	0.244151	0.3922706𝑒−1	—
179.90000000	8.430255141254121	—	0.28651749𝑒−1	—
179.99999000	17.64055690983073	—	0.1369703𝑒−1	—
179.99999999	24.548351581120853	—	0.01222747	—