Xiaoling Jin

Response and stability of SDOF viscoelastic system under wideband noise excitations

Abstract The response and stability of a single degree-of-freedom (SDOF) viscoelastic system with strongly nonlinear stiffness under the excitations of wideband noise are studied in this paper. Firstly, terms associated with the viscoelasticity are approximately equivalent to damping and stiffness forces; the viscoelastic system is approximately transformed to SDOF system without viscoelasticity. Then, with application of the method of stochastic averaging, the averaged Ito differential equation is obtained. The stationary response and the largest Lyapunov exponent can be analytically expressed. The effects of different system parameters on the response and stability of the system are discussed as well.

Non-linear stochastic optimal control of acceleration parametrically excited systems

Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.

First-passage failure of preisach hysteretic systems

The first-passage failure of a single-degree-of-freedom hysteretic system with non-local memory is investigated. The hysteretic behavior is described through a Preisach model with excitation selected as Gaussian white noise. First, the equivalent nonlinear non-hysteretic system with amplitude-dependent damping and stiffness coefficients is derived through generalized harmonic balance technique. Then, equivalent damping and stiffness coefficients are expressed as functions of system energy by using the relation of amplitude to system energy. The stochastic averaging of energy envelope is adopted to accept the averaged Itô stochastic differential equation with respect to system energy. The establishing and solving of the associated backward Kolmogorov equation yields the reliability function and probability density of first-passage time. The effects of system parameters on first-passage failure are investigated concisely and validated through Monte Carlo simulation.

Stochastic stabilization of quasi-generalized Hamiltonian systems:

A procedure for designing a feedback control to asymptotically stabilize, with probability one, quasi-generalized Hamiltonian systems subject to stochastically parametric excitations is proposed. First, the motion equations of controlled systems are reduced to lower-dimensional averaged Itô stochastic differential equations by using the stochastic averaging method. Second, a dynamic programming equation for the averaged system with an appropriate performance index (with undetermined parameters in cost function) is established based on the dynamic programming principle, and the optimal control law is derived from a minimization condition with respect to control. Third, the Lyapunov function method is adopted to evaluate the stability boundary of asymptotic stability with probability one for the uncontrolled/controlled systems. Finally, the parameters in cost function are selected to guarantee the sufficient stability of the controlled systems. Numerical results for a nine-dimensional mathematical system and a three-dimensional practical system, which describes a structure including viscoelastic element, illustrate the effectiveness of the feedback control strategy, and stability domains can be obviously enlarged when imposing the feedback controls on the original systems.