Compliance Matrix of a Single-Bent Leaf Flexure for a Modal Analysis

Table 3

Theoretical and FEA results with various lengths , thicknesses , and widths under loads , , and .

(mm)	FEA	Theory	Error (%)	(mm)	FEA	Theory	Error (%)	(mm)	FEA	Theory	Error (%)
(a) Rotation (rad)
5	0.00114	0.00108	5.59	0.25	0.01795	0.01762	1.86	2	0.00568	0.00561	1.34
6.5	0.00152	0.00145	4.04	0.325	0.00833	0.00815	2.15	2.6	0.00404	0.00397	1.66
8	0.00189	0.00183	3.07	0.4	0.00455	0.00445	2.28	3.2	0.00312	0.00306	1.91
9.5	0.00226	0.00221	2.40	0.475	0.00277	0.00270	2.50	3.8	0.00254	0.00248	2.13
11	0.00263	0.00258	1.91	0.55	0.00183	0.00178	2.71	4.4	0.00213	0.00208	2.36
12.5	0.00301	0.00296	1.53	0.625	0.00127	0.00123	2.89	5	0.00183	0.00179	2.61
14	0.00338	0.00334	1.23	0.7	0.00093	0.00090	3.03	5.6	0.00161	0.00156	2.88
15.5	0.00375	0.00371	0.99	0.775	0.00070	0.00068	3.16	6.2	0.00143	0.00138	3.18
17	0.00412	0.00409	0.78	0.85	0.00054	0.00052	3.25	6.8	0.00128	0.00124	3.49
18.5	0.00450	0.00447	0.60	0.925	0.00043	0.00042	3.33	7.4	0.00116	0.00112	3.83
20	0.00487	0.00485	0.45	1	0.00035	0.00034	3.39	8	0.00106	0.00102	4.19
(b) Rotation (rad)
5	0.00089	0.00084	4.77	0.25	0.01605	0.01583	1.34	2	0.00540	0.00533	1.33
6.5	0.00126	0.00122	3.08	0.325	0.00744	0.00732	1.60	2.6	0.00376	0.00371	1.35
8	0.00163	0.00159	2.11	0.4	0.00407	0.00399	1.77	3.2	0.00285	0.00281	1.39
9.5	0.00200	0.00197	1.49	0.475	0.00248	0.00243	2.01	3.8	0.00228	0.00224	1.46
11	0.00237	0.00235	1.06	0.55	0.00163	0.00159	2.23	4.4	0.00188	0.00185	1.59
12.5	0.00274	0.00272	0.74	0.625	0.00114	0.00111	2.46	5	0.00158	0.00155	1.77
14	0.00312	0.00310	0.49	0.7	0.00083	0.00081	2.69	5.6	0.00136	0.00133	2.00
15.5	0.00349	0.00348	0.29	0.775	0.00063	0.00061	2.92	6.2	0.00118	0.00116	2.29
17	0.00386	0.00385	0.13	0.85	0.00049	0.00047	3.16	6.8	0.00104	0.00101	2.62
18.5	0.00423	0.00423		0.925	0.00039	0.00037	3.41	7.4	0.00092	0.00090	2.99
20	0.00460	0.00461		1	0.00032	0.00030	3.65	8	0.00082	0.00080	3.39
(c) Rotation (rad)
5	0.00328	0.00348	5.71	0.25	0.05405	0.05573	3.02	2	0.01365	0.01393	2.00
6.5	0.00432	0.00453	4.70	0.325	0.02462	0.02537	2.94	2.6	0.01047	0.01072	2.31
8	0.00535	0.00557	4.03	0.4	0.01320	0.01361	2.95	3.2	0.00848	0.00871	2.66
9.5	0.00638	0.00662	3.58	0.475	0.00789	0.00813	2.94	3.8	0.00711	0.00733	3.01
11	0.00741	0.00766	3.25	0.55	0.00508	0.00523	2.93	4.4	0.00612	0.00633	3.37
12.5	0.00845	0.00871	3.02	0.625	0.00346	0.00357	2.93	5	0.00537	0.00557	3.72
14	0.00948	0.00975	2.84	0.7	0.00246	0.00254	2.93	5.6	0.00477	0.00498	4.06
15.5	0.01051	0.01080	2.71	0.775	0.00182	0.00187	2.94	6.2	0.00430	0.00449	4.39
17	0.01153	0.01184	2.61	0.85	0.00138	0.00142	2.96	6.8	0.00391	0.00410	4.70
18.5	0.01256	0.01289	2.53	0.925	0.00107	0.00110	2.98	7.4	0.00358	0.00377	5.01
20	0.01359	0.01393	2.47	1	0.00084	0.00087	3.01	8	0.00330	0.00348	5.31