(iv) The Cauchy problem was solved by numerous methods and the fourth-order
Runge-Kutta method was chosen as the most efficient. The optimal step was
chosen using the Runge principle.
(v) Based on the tests carried out for numerous wavelets (Daubechies, Gauss,
Haar and Morlet), the Morlet wavelets were chosen as the most feasible for
our problem.
(vi) The static analysis was carried out for three values of temperature and two
values of size-dependent parameter. The investigated “frequency-deflection”
dependency exhibits different results for homogeneous and non-homogeneous
(optimized) beams for all values of the length-dependent parameter.
(vii) The use of beams with the optimized microstructure allows for an increase
in the range of working loads regimes compared to homogeneous beams for
which the vibration regimes are either periodic or quasi-periodic.
(viii) The analysis of the scenarios of transition from periodic to chaotic vibrations was carried out. In all cases, the transition into chaotic vibrations
followed a scenario similar to the classical Pomeau-Manneville scenario (a
few exceptions were observed for some values of temperature and the
length-dependent parameter).
Introduction
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