A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

Table 1

The linear and nonlinear frequency ratio and the contribution coefficients of stepped beam (b) subjected to a free vibration.

Wmax	a1
0.968	0.5	1.23	3.43E−03	−4.21E03	1.42E−04	−4.52E−04	−2.912E−05	−1.04E−04	−2.77E−05	−2.96E−05	1.39E−05
1.166	0.6	1.32	5.64E−03	−7.01E−03	2.69E−04	−7.74E−04	−4.449E−05	−1.79E−04	−4.61E−05	−5.07E−05	2.36E−05
1.365	0.7	1.42	8.48E−2	−1.06E−02	4.65E−03	−1.21E−03	−6.058E−05	−2.83E−04	−7.03E−05	−7.98E−05	3.66E−05
1.566	0.8	1.53	1.19E−2	1.51E−02	7.48E−04	−1.78E−03	−7.46E−05	−4.19E−03	−1.00E−04	1.17E−04	5.32E−05