Stochastic Stability Analysis of Coupled Viscoelastic Systems with Nonviscously Damping Driven by White Noise

Abstract

Nonviscously damped structural system has been raised in many engineering fields, in which the damping forces depend on the past time history of velocities via convolution integrals over some kernel functions. This paper investigates stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents. Using the coordinate transformation, the coupled Itô stochastic differential equations of the norm of the response and angles process are obtained. Then the problem of the moment Lyapunov exponent is transformed to the eigenvalue problem, and then the second-perturbation method is used to derive the moment Lyapunov exponent of coupled stochastic system. Lyapunov exponent also can be obtained according to the relationship between moment Lyapunov exponent and Lyapunov exponent. Finally, the effects of various physical quantities of stochastic coupled system on the stochastic stability are discussed in detail. These results are validated by the direct Monte Carlo simulation technique.

A Hybrid Approach for Project Crashing Optimization Strategy with Risk Consideration: A Case Study for an EPC Project

“…Hulett [6] stated that CPM scheduling tools, which include manual and software-based systems, cannot handle the uncertainty that exists in the real world regarding project activity durations because these tools assume that activity durations are with certainty as singlepoint numbers. A stochastic risk analysis technique called Monte Carlo simulation can be applied to evaluate project uncertainties [14][15][16][17]. Monte Carlo simulation is suitable for determining the project completion date because the date is determined by the uncertainty in the duration of many activities that have already been linked logically in the CPM schedule [6].…”

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Lyapunov stability of suspension bridges in turbulent flow

“…Among these, remarkable contributions are those by Doyle and Sri Namachchivaya [40] and Sri Namachchivaya et al [41], who examined the p-th moment stability through moment Lyapunov exponents (MLE) in a two-degree-of-freedom system with stiffness coupling, parametrically excited by a small noise characterized by a realistic spectrum. Liu et al [42] employed MLE to study the stochastic stability of coupled elastic systems with non-viscous damping, driven by a white noise. Additionally, MLE were calculated by Li and Liu [43] for the airfoil model previously considered in [34].…”

Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise

“…Liu et al introduced a transfer entropy and surrogate data algorithm to identify the nonlinearity level of the system by using a numerical solution of nonlinear response of beams, the Galerkin method was applied to discretize the dimensionless differential governing equation of the forced vibration, and then the fourth-order Runge-Kutta method was used to obtain the time history response of the lateral displacement [13]. Liu et al investigated the stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents, obtained the coupled Itô stochastic differential equations of the norm of the response and angles process by using the coordinate transformation, and discussed the effects of various physical quantities of stochastic coupled system on the stochastic stability [14]. Nutting, Gemant and Scott-Blair et al [15][16][17] first proposed the fractional derivative models to study the constitutive relation of viscoelastic materials and the research on the viscoelastic materials with fractional derivative is also increasing, and so far, it is still a research hotspot [18][19][20][21][22][23][24][25].…”