6.6 Chaotic Dynamics of the Size-Dependent Flexible Beams
171
Fig. 6.10 Convergence of the results for different numbers of beam length partitions n for the
beam deflection (a) and power spectrum (b) [reprinted with permission from International Journal
of Non-Linear Mechanics publishers]
Fig. 6.11 Result convergence versus different numbers of beam length partition (n =
10, 20, 40, 80) for the longitudinal displacement (a) and Fourier power spectrum (b) [reprinted
with permission from International Journal of Non-Linear Mechanics publishers]
time histories w(0.5, t) (Fig. 6.10a) and u(0.25, t) (Fig. 6.11a) and the Fourier spectra S w (ω) (Fig. 6.10b) and S u (ω) (Fig. 6.11b) for some values of the beam length
partition n are compared. The investigations have been carried out for all models for
the values of scale length material parameter l/ h = 0 and 0.3. Figures 6.10, 6.11
report the results for the Bernoulli–Euler model (6.127) (6.128) with the boundary
conditions (6.129)–(6.131), for l/ h = 0. The sinusoidal transverse load has the form
q = 1050 sin(5.14t).
Convergence of the results in the power spectrum is achieved already for n = 20
though the signals w(0.5, t) and u(0.25, t) exhibit uniform convergence for n = 40.
Therefore, the employed methods and stability algorithms allow to achieve reliable
results.
171
Fig. 6.10 Convergence of the results for different numbers of beam length partitions n for the
beam deflection (a) and power spectrum (b) [reprinted with permission from International Journal
of Non-Linear Mechanics publishers]
Fig. 6.11 Result convergence versus different numbers of beam length partition (n =
10, 20, 40, 80) for the longitudinal displacement (a) and Fourier power spectrum (b) [reprinted
with permission from International Journal of Non-Linear Mechanics publishers]
time histories w(0.5, t) (Fig. 6.10a) and u(0.25, t) (Fig. 6.11a) and the Fourier spectra S w (ω) (Fig. 6.10b) and S u (ω) (Fig. 6.11b) for some values of the beam length
partition n are compared. The investigations have been carried out for all models for
the values of scale length material parameter l/ h = 0 and 0.3. Figures 6.10, 6.11
report the results for the Bernoulli–Euler model (6.127) (6.128) with the boundary
conditions (6.129)–(6.131), for l/ h = 0. The sinusoidal transverse load has the form
q = 1050 sin(5.14t).
Convergence of the results in the power spectrum is achieved already for n = 20
though the signals w(0.5, t) and u(0.25, t) exhibit uniform convergence for n = 40.
Therefore, the employed methods and stability algorithms allow to achieve reliable
results.