In this study, the chaotic behavior of a viscoelastic plate under integrated non-Gaussian additive and multiplicative bounded noise is investigated with an analytical approach. First, the governing equation of motion of the system was derived by introducing a set of dimensionless parameters. After that, the modified version of Melinkov’s function in terms of statistical indices was obtained, and then, for a spectrum of bounded noises, the boarder curves of chaotic areas were obtained. The model of sine/cosine Wiener was chosen for the bounded noise which enables the researcher to produce a range of wide and narrowband noises. For the case that the excitation is only additive, or only multiplicative, and that both excitations exist simultaneously, the effect of variations in structural properties and noise characteristics on the chaos area were investigated. It was shown that at frequencies close to the natural frequency of the corresponding linear system, narrowband excitations affected the chaotic behavior more than the wideband ones and vice versa. To validate the results, a numerical simulation was also made.
AbediMAsnafiA (2015) To reduce the instability region in the nonlinear transverse vibration of randomly excited plates using orthotropic P-FG material. Nonlinear Dynamics80: 1413–1430.
2.
AbediMAsnafiAKaramiK (2014) To obtain approximate probability density functions for a class of axially moving viscoelastic plates under external and parametric white noise excitation. Nonlinear Dynamics78: 1717–1727.
3.
AlijaniFAmabiliM (2013) Nonlinear vibrations of laminated and sandwich rectangular plates with free edges. Part 1: theory and numerical simulations. Composite Structures105: 422–436.
4.
AmabiliM (2008) Nonlinear Vibrations and Stability of Shells and Plates. New York: Cambridge University Press.
5.
AmabiliM (2016) Nonlinear vibrations of viscoelastic rectangular plates. Journal of Sound and Vibration362: 142–156.
6.
AmabiliM (2018a) Nonlinear damping in large-amplitude vibrations: modelling and experiments. Nonlinear Dynamics: 1–14.
7.
AmabiliM (2018b) Nonlinear damping in nonlinear vibrations of rectangular plates: derivation from viscoelasticity and experimental validation. Journal of the Mechanics and Physics of Solids118: 275–292.
8.
AmabiliM (2018c) Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials. New York: Cambridge University Press.
9.
AsnafiA. (2019) Chaotic analysis of Kelvin–Voigt viscoelastic plates under combined transverse periodic and white noise excitation: an analytic approach. Acta Mechanica: 1–16.
10.
BalasubramanianPFerrariGAmabiliM, et al. (2017) Experimental and theoretical study on large amplitude vibrations of clamped rubber plates. International Journal of Non-Linear Mechanics94: 36–45.
11.
D'onofrioA (2013) Bounded Noises in Physics, Biology, and Engineering. New York: Springer.
12.
DengJZhongZLiuA (2019) Stochastic stability of viscoelastic plates under bounded noise excitation. European Journal of Mechanics-A/Solids78: 103849.
13.
FarokhiHGhayeshMH (2017) Nonlinear resonant response of imperfect extensible Timoshenko microbeams. International Journal of Mechanics and Materials in Design13: 43–55.
14.
FarokhiHGhayeshMHGholipourA (2017) Dynamics of functionally graded micro-cantilevers. International Journal of Engineering Science115: 117–130.
15.
GhayeshMH (2012a) Nonlinear dynamic response of a simply-supported Kelvin–Voigt viscoelastic beam, additionally supported by a nonlinear spring. Nonlinear Analysis: Real World Applications13: 1319–1333.
16.
GhayeshMH (2012b) Subharmonic dynamics of an axially accelerating beam. Archive of Applied Mechanics82: 1169–1181.
17.
GhayeshMH (2018a) Dynamics of functionally graded viscoelastic microbeams. International Journal of Engineering Science124: 115–131.
18.
GhayeshMH (2018b) Functionally graded microbeams: simultaneous presence of imperfection and viscoelasticity. International Journal of Mechanical Sciences140: 339–350.
GhayeshMH (2019h) Viscoelastic nonlinear dynamic behaviour of Timoshenko FG beams. The European Physical Journal Plus134: 401.
28.
GhayeshMHAmabiliM (2013a) Nonlinear dynamics of an axially moving Timoshenko beam with an internal resonance. Nonlinear Dynamics73: 39–52.
29.
GhayeshMHAmabiliM (2013b) Nonlinear vibrations and stability of an axially moving Timoshenko beam with an intermediate spring support. Mechanism and Machine Theory67: 1–16.
30.
GhayeshMHYourdkhaniMBalarS, et al. (2010) Vibrations and stability of axially traveling laminated beams. Applied Mathematics and Computation217: 545–556.
31.
GhayeshMHKazemiradSDarabiMA, et al. (2012) Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system. Archive of Applied Mechanics82: 317–331.
32.
GhayeshMHFarokhiHAliciG (2015) Subcritical parametric dynamics of microbeams. International Journal of Engineering Science95: 36–48.
33.
GhayeshMHFarokhiHGholipourA, et al. (2017) Nonlinear bending and forced vibrations of axially functionally graded tapered microbeams. International Journal of Engineering Science120: 51–62.
34.
KazemiradSGhayeshMHAmabiliM (2013) Thermo-mechanical nonlinear dynamics of a buckled axially moving beam. Archive of Applied Mechanics83: 25–42.
35.
LakesRLakesRS (2009) Viscoelastic Materials. New York: Cambridge University Press.
36.
LinY-KCaiGQ (1995) Probabilistic Structural Dynamics. Advanced Theory and Applications. New York: McGraw-Hill.
37.
MottPHRolandCM (2009) Limits to Poisson’s ratio in isotropic materials. Physical Review B80: 132104.
38.
PotapovVD (2011) Nonlinear vibrations and stability of elastic and viscoelastic systems under random stationary loads. Mechanics of Solids46: 444.
39.
TimoshenkoSPWoinowsky-KriegerS (1959) Theory of Plates and Shells. New York: McGraw-Hill.
40.
WangC-JLinQ-FYaoY-G, et al. (2019) Dynamics of a stochastic system driven by cross-correlated sine-Wiener bounded noises. Nonlinear Dynamics95: 1941–1956.
41.
WigginsS (2013) Global Bifurcations and Chaos: Analytical Methods. New York: Springer Science & Business Media.
42.
YounesianDNorouziH (2016) Chaos prediction in nonlinear viscoelastic plates subjected to subsonic flow and external load using extended Melnikov's method. Nonlinear Dynamics84: 1163–1179.
