192
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
Table 6.27 The Sheremetev–Pelekh model—charts of vibration regimes: (a) without the sizedependent behaviour l/ h = 0; (b) with the size-dependent behaviour l/ h = 0.3 [reprinted with
permission from International Journal of Non-Linear Mechanics publishers]
6.8 Influence of a Type of Kinematic Models of the Zero-,
First- and Third-Order Approximations on the
Scenario of Transition from Periodic to Chaotic
Vibrations
One of the imputation aspects of the investigation of nonlinear dynamics of structural
systems is construction and analysis of scenario of transition from periodic to chaotic
vibrations. The mentioned scenarios of transition have been already analysed for the
beam, plates and shell taking into account the Bernoulli–Euler, Timoshenko and
Sheremetev–Pelekh models but without effects of the size-dependent behaviour [34,
75]. In this given chapter, we have constructed and analysed scenarios of three models
with/without an account of the size-dependent effects, i.e. for l/ h = 0.3 and l/ h = 0
or the following fixed parameters ω p = 9, ε = 1, λ = 30, ν = 0.3.
Scenarios exhibited by the Bernoulli–Euler, Timoshenko and Sheremetev–Pelekh
beams followed the Ruelle-Taken-Newhouse scenario [76] for both cases, i.e. l/ h =
0.3, l/ h = 0.
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
Table 6.27 The Sheremetev–Pelekh model—charts of vibration regimes: (a) without the sizedependent behaviour l/ h = 0; (b) with the size-dependent behaviour l/ h = 0.3 [reprinted with
permission from International Journal of Non-Linear Mechanics publishers]
6.8 Influence of a Type of Kinematic Models of the Zero-,
First- and Third-Order Approximations on the
Scenario of Transition from Periodic to Chaotic
Vibrations
One of the imputation aspects of the investigation of nonlinear dynamics of structural
systems is construction and analysis of scenario of transition from periodic to chaotic
vibrations. The mentioned scenarios of transition have been already analysed for the
beam, plates and shell taking into account the Bernoulli–Euler, Timoshenko and
Sheremetev–Pelekh models but without effects of the size-dependent behaviour [34,
75]. In this given chapter, we have constructed and analysed scenarios of three models
with/without an account of the size-dependent effects, i.e. for l/ h = 0.3 and l/ h = 0
or the following fixed parameters ω p = 9, ε = 1, λ = 30, ν = 0.3.
Scenarios exhibited by the Bernoulli–Euler, Timoshenko and Sheremetev–Pelekh
beams followed the Ruelle-Taken-Newhouse scenario [76] for both cases, i.e. l/ h =
0.3, l/ h = 0.