This study focusses on developing a novel reduced order model for dynamic analysis of an acousto-elastic system, such as an impeller housed in a pressurised incompressible fluid filled chamber. Resolving the coupled dynamics of such systems require high-fidelity numerical models for both the structure and the fluid and are typically modelled using finite elements (FE) leading to FE equations with large ordered asymmetric matrices. The parameters for the system are obtained from measurements which are susceptible to uncertain errors and biases. This study proposes the development of a stochastic reduced order FE model based on integrating arbitrary PCE with SEREP. Numerical results reveal that the proposed method results in significant reduction in computational costs for dynamic analysis without compromising on accuracy. The reduced order model is shown to be useful for proper orthogonality check for quantifying the degree of correlation between experimentally observed and model based modes. © 2018 Elsevier Ltd

Sayan Gupta

Department of Applied Mechanics

Sunetra Sarkar

Department of Aerospace Engineering

Hridya P. Lal

ELASTICITY

Numerical methods

Stochastic models

Stochastic systems

Uncertainty analysis

ARBITRARY POLYNOMIAL

ELASTIC SYSTEMS

Orthogonality

Reduced order modelling

SEREP

finite element method

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Probabilistic Engineering Mechanics

Use of heavy gases in centrifugal compressors for enhanced oil extraction have made the impellers susceptible to failures through acousto-elastic instabilities. This study focusses on understanding the dynamical behavior of such systems by considering the effects of the bounded fluid housed in a casing on a rotating disc. First, a mathematical model is developed that incorporates the interaction between the rotating impeller - modelled as a flexible disc - and the bounded compressible fluid medium in which it is immersed. The nonlinear effects arising due to large deformations of the disc have been included in the formulation so as to capture the post flutter behavior. A bifurcation analysis is carried out with the disc rotational speed as the bifurcation parameter to investigate the dynamical behavior of the coupled system and estimate the stability boundaries. Parametric studies reveal that the relative strengths of the various dissipation mechanisms in the coupled system play a significant role that affect the bifurcation route and the post flutter behavior in the acousto-elastic system. © 2016 Elsevier Ltd

Journal of Sound and Vibration

Bifurcation and response analysis of a nonlinear flexible rotating disc immersed in bounded compressible fluid

Accurate determination of acousto-elastic natural frequencies in centrifugal compressors is important in order to avoid resonance events that may lead to machine failure. Compressors operating with CO2 at high pressures, especially near its transition to supercritical state, deal with a wide variation in density and speed of sound. Natural frequency behavior under these conditions is studied here. A finite element method (FEM) based coupled acousto-elastic solver has been developed to study the modal coupling and interactions between the impeller and the side-cavity modes for an idealized compressor geometry. Pressure in the side-cavities is increased up to a very high value of 20 MPa and existence of fluid-A nd structure-dominant acousto-elastic modes is observed. The variation of the natural frequencies of these modes with pressure exhibits contrasting trends as CO2 transitions from gaseous to supercritical state. © 2017 by ASME.

Journal of Vibration and Acoustics, Transactions of the ASME

Acousto-Elastic Interactions in High-Pressure CO2 Centrifugal Compressors

This study focuses on the development of reduced order models for stochastic analysis of complex large ordered linear dynamical systems with parametric uncertainties, with an aim to reduce the computational costs without compromising on the accuracy of the solution. Here, a twin approach to model order reduction is adopted. A reduction in the state space dimension is first achieved through system equivalent reduction expansion process which involves linear transformations that couple the effects of state space truncation in conjunction with normal mode approximations. These developments are subsequently extended to the stochastic case by projecting the uncertain parameters into the Hilbert subspace and obtaining a solution of the random eigenvalue problem using polynomial chaos expansion. Reduction in the stochastic dimension is achieved by retaining only the dominant stochastic modes in the basis space. The proposed developments enable building surrogate models for complex large ordered stochastically parametered dynamical systems which lead to accurate predictions at significantly reduced computational costs. © 2017 Elsevier Inc.

Applied Mathematical Modelling

Stochastic model order reduction in randomly parametered linear dynamical systems

Multilayer fibre reinforced composites exhibit significant spatial variabilities in their response due to the variations in the individual lamina properties. Uncertainty quantification of these structures can be carried out using the polynomial chaos based stochastic finite element method (SFEM). The variations in the individual laminae properties are modelled as independent random fields. The SFEM method involves two stages of discretisation. First, the displacement fields are discretised into variables along the spatial dimension using traditional FEM. Next, the random fields are discretised into a vector of correlated random variables using polynomial chaos expansions. As the random field discretisation is carried out for each individual laminae, the number of random variables entering the formulation becomes large, making uncertainty quantification computationally prohibitive. This study focusses on the development of model order reduction strategies that enable reducing the stochastic dimensionality of the problem and enable faster computations. This is achieved by developing a probabilistically equivalent structure scale model using two approaches - one based on probabilistic equivalence of a nodal response and the other seeking equivalence on the probabilistic characteristics of the constitutive matrix. A set of numerical examples are presented to highlight the salient features of the proposed developments. © 2015 Elsevier Ltd.

Composite Structures

Stochastic model order reduction in uncertainty quantification of composite structures

Journal of Engineering Mechanics

Linear Random Vibration of Structural Systems with Singular Matrices

Reduced order modelling in stochastically parametered acousto-elastic system using arbitrary PCE based SEREP

Journal	Data powered by TypesetProbabilistic Engineering Mechanics
Publisher	Data powered by TypesetElsevier Ltd
ISSN	02668920
Open Access	No