Development of error criteria for adaptive multi-element polynomial chaos approaches

International audienceThis paper presents and compares different methodologies to create an adaptive stochastic space partitioning in polynomial chaos applications which use a multi-element approach. To implement adaptive partitioning, Wan and Karniadakis first developed a criterion based on the relative error in local variance. We propose here two different error criteria: one based on the residual error and the other on the local variance discontinuity created by partitioning. The methods are applied to classical differential equations with long-term integration difficulties, including the Kraichnan–Orszag three-mode problem, and to simple linear and nonlinear mechanical systems whose stochastic dynamic responses are investigated. The efficiency and robustness of the approaches are investigated by comparison with Monte-Carlo simulations. For the different examples considered, they show significantly better convergence characteristics than the original error criterion used

Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼60%∼60%, it is found that three ring modes of vibration (1θ,2θ1θ,2θ and 3θ3θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2θ2θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping

Wave interaction with defects in pressurised composite structures

There exists a great variety of structural failure modes which must be frequently inspected to ensure continuous structural integrity of composite structures. This work presents a Finite Element (FE) based method for calculating wave interaction with damage within structures of arbitrary layering and geometric complexity. The principal novelty is the investigation of pre-stress effect on wave propagation and scattering in layered structures. A Wave Finite Element (WFE) method, which combines FE analysis with periodic structure theory (PST), is used to predict the wave propagation properties along periodic waveguides of the structural system. This is then coupled to the full FE model of a coupling joint within which structural damage is modelled, in order to quantify wave interaction coeffcients through the joint. Pre-stress impact is quantified by comparison of results under pressurised and non-pressurised scenarios. The results show that including these pressurisation effects in calculations is essential. This is of specific relevance to aircraft structures being intensely pressurised while on air. Numerical case studies are exhibited for different forms of damage type. The exhibited results are validated against available analytical and experimental results

Nonlinear Modal Analysis of Mistuned Periodic Structures Subjected to Dry Friction

International audienceThis paper deals with the dynamics of a cyclic system, representative of a bladed-disk subjected to dry friction forces, and exhibiting structural mistuning. The nonlinear complex modes are computed by solving the eigenproblem associated to the free response of the whole structure, and are then used to better understand the forced response to a traveling wave excitation. Similarly to the underlying linear system, the tuned model possesses pairs of modes that can be linearly combined to form traveling waves, unlike those of the mistuned structure. However, due to the nonlinearity, the modal properties are not constant but vary with the vibration amplitude in both cases. A qualitative analysis is also performed to assess the impact of the mistuning magnitude on the response, and suggests that further statistical investigations could be of great interest for the design of bladed disks, in terms of vibration mitigation and robustness