176
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
Table 6.8 Numerical results for the Timoshenko model (l/ h = 0.3, t ∈ [300; 1600]) [reprinted
with permission from International Journal of Non-Linear Mechanics publishers]
Table 6.9 Numerical results for the Timoshenko model (l/ h = 0.3, t ∈ [1600; 5300]) [reprinted
with permission from International Journal of Non-Linear Mechanics publishers]
Comparison of the tables allows to conclude that increase of the power of
frequency ω 2 and occurrence of the frequencies ω 2 , ω 5 of the end of interval
t ∈ [300; 2500] changes the vibration characteristics qualitatively. The previous periodic signal becomes complex and unperiodic. The previous phase portrait of the limit
cycle is transformed into node.
6.6.1.2 The Bernoulli–Euler Model for l/h = 0
Table 6.4 presents results associated with the study of time window t ∈ [300; 5300],
whereas Tables 6.5 and 6.6 report the results of time windows t ∈ [300; 3100] and
t ∈ [3100; 5300], respectively.
The frequency spectrum contains the following frequencies: ω 1 = 1.15, ω 2 =
1.941, ω 3 = 2.732, ω 4 = 3.523, ω 5 = 4.315, ω 6 = 5.11, ω 7 = 7.42, ω 8 = 8.21
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
Table 6.8 Numerical results for the Timoshenko model (l/ h = 0.3, t ∈ [300; 1600]) [reprinted
with permission from International Journal of Non-Linear Mechanics publishers]
Table 6.9 Numerical results for the Timoshenko model (l/ h = 0.3, t ∈ [1600; 5300]) [reprinted
with permission from International Journal of Non-Linear Mechanics publishers]
Comparison of the tables allows to conclude that increase of the power of
frequency ω 2 and occurrence of the frequencies ω 2 , ω 5 of the end of interval
t ∈ [300; 2500] changes the vibration characteristics qualitatively. The previous periodic signal becomes complex and unperiodic. The previous phase portrait of the limit
cycle is transformed into node.
6.6.1.2 The Bernoulli–Euler Model for l/h = 0
Table 6.4 presents results associated with the study of time window t ∈ [300; 5300],
whereas Tables 6.5 and 6.6 report the results of time windows t ∈ [300; 3100] and
t ∈ [3100; 5300], respectively.
The frequency spectrum contains the following frequencies: ω 1 = 1.15, ω 2 =
1.941, ω 3 = 2.732, ω 4 = 3.523, ω 5 = 4.315, ω 6 = 5.11, ω 7 = 7.42, ω 8 = 8.21