Efficient prediction of the forced response statistics of mistuned bladed discs

Abstract

This paper presents two efficient reduced-order modelling techniques for predicting the forced response statistics of bladed disc assemblies. First, the formulation presented in (1) is extended to the forced response problem. Component modes for a blade-disc sector are used as basis vectors, leading to a reduced model of the same size as the number of sectors and allowing for pass-band calculations. For each realization of the random system parameters, a reduced system of equations is solved to compute the displacement vector for each frequency band of interest. Statistics of responses at each frequency point can be therefore estimated by performing Monte Carlo Simulations of cost comparable to single degree-of-freedom mass-spring systems. Second, a stochastic reduced basis approach is applied to the mistuning analysis problem. Here, the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors which span the preconditioned stochastic Krylov Subspace (2,3). Orthogonal stochastic projection schemes are employed for computing the undetermined coefficients in the stochastic reduced basis representation. These schemes lead to explicit expressions for the response to be obtained, thereby allowing the efficient computation of the response statistics