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The random‐time‐delay (RTD) occurs inevitably in feedback control, caused by the utilization of a multi‐user network with random demands. This paper is devoted to the stochastic stabilization of multi‐degree‐of‐freedom (MDOF) nonlinear RTD controlled systems. Firstly, a two‐step approximated method is proposed to deal with RTD: by modeling the RTD as a Markov jump process, the RTD control is formulated as the one with discrete jump varying delay; utilizing the randomly periodic characteristic, the Markov jump delay is taken out of the control as a parameter. The stochastic averaging principle is applied to generate a less‐dimensional averaged governing equation of system's energies. Secondly, the dynamical programming principle is applied to the ergodic control problem of the average systems with an undetermined cost function, which is determined by the demand of stabilizing the averaged systems, then the optimal control law is deduced. A largest Lyapunov exponent is introduced to the averaged systems to evaluate the asymptotic stability with probability one. Finally, an example is worked out to demonstrate the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Dielectric elastomers are widely used in many fields due to their advantages of high deformability, light weight, biological compatibility, and high efficiency. In this study, the stochastic dynamic response and bifurcation of a dielectric elastomer balloon (DEB) with viscoelasticity are investigated. Firstly, the rheological model is adopted to describe the viscoelasticity of the DEB, and the dynamic model is deduced by using the free energy method. The effect of viscoelasticity on the state of equilibrium with static pressure and voltage is analysed. Then, the stochastic differential equation about the perturbation around the state of equilibrium is derived when the DEB is under random pressure and static voltage. The steady-state probability densities of the perturbation stretch ratio are determined by the generalized cell mapping method. The effects of parameter conditions on the mean value of the perturbation stretch ratio are calculated. Finally, sinusoidal voltage and random pressure are applied to the viscoelastic DEB, and the phenomenon of P-bifurcation is observed. Our results are compared with those obtained from Monte Carlo simulation to verify their accuracy. This work provides a potential theoretical reference for the design and application of DEs. [ABSTRACT FROM AUTHOR]

An optimal bounded control strategy for strongly nonlinear vibro-impact systems under stochastic excitations with actuator saturation is proposed. First, the impact effect is incorporated in an equivalent equation by using a nonsmooth transformation. Under the assumption of light damping and weak random perturbation, the system energy is a slowly varying process. By using the stochastic averaging of envelope for strongly nonlinear systems, the partially averaged Itô stochastic differential equation for system energy can be derived. The optimal control problem is transformed from the original optimal control problem for the state variables to an equivalent optimal control problem for the system energy, which decreases the dimensions of the optimal control problem. Then, based on stochastic maximum principle, an adjoint equation for the adjoint variable and the maximum condition of partially averaged control problem are established. For infinite time-interval ergodic control, the adjoint variable is assumed to be a stationary process and the adjoint equation can be further simplified. Finally, the probability density function of the system energy and other statistics of the optimally controlled system are derived by calculating the associated Fokker–Plank–Kolmogorov equation. For comparison, the bang–bang control is also investigated and the control results are compared to show the advantages of the developed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics of an axially translating functionally graded cantilever beam (FGCB) with time-varying length are studied under environmental temperature variations. Firstly, the governing partial differential equation for the FGCB under different temperatures is established based on the Euler–Bernoulli beam theory. Secondly, the Galerkin discretization and the assumed mode method (AMM) are employed to derive the vibration equations for each mode. Then, the coupling effects of the axial translation motion and the bending deformation on the vibration response of the FGCB are analyzed through numerical simulation. The results showed that different initial lengths, velocities and accelerations can influence the dynamic response greatly. Moreover, the increase in temperature will increase the response amplitude and decrease the frequency of FGCB, but the increase in functionally gradient parameter will decrease both the amplitude and the frequency of the FGCB. Finally, the wavelet transform (WT) is utilized to perform a time–frequency analysis. It is found that the time-dependent frequency obtained by using WT is consistent with the first-order static frequency obtained theoretically. The variation of frequency with time can be obtained quickly and accurately by using WT. The results of this research are of great significance for the application of composite axially translating beams in practical engineering. [ABSTRACT FROM AUTHOR]

It is inevitable that carbon nanotubes (CNTs) are subjected to random vibrations due to environmental noise, which may impair their mechanical properties. The nonlinear dynamics associated with single-walled carbon nanotubes (SWCNTs) under random noise has been investigated in this work. First, based on the nonlocal theory and the Euler–Bernoulli beam model with fixed supports at both ends, the governed equations and boundary conditions are established according to Hamilton’s principle. Second, the Galerkin method is used to approximate the differential equations of motion and the stochastic averaging method (SAM) is applied to predict the approximate response of the original system. Subsequently, a detailed parametric study is conducted to analyze the nonlinear random vibration response of the SWCNT with nonlocal effects, and the effectiveness of the proposed method is verified by comparing the analytical results with those from the Runge–Kutta method. Finally, by solving the backward Kolmogorov (BK) equation and the generalized Pontryagin (GP) equation simultaneously, the conditional reliability function (CRF) and mean first-passage time (MFPT) for determining the reliability of SWCNT systems are obtained. [ABSTRACT FROM AUTHOR]