ARTICLE IN PRESS Analysis of sensitivity and robustness of forced response for nonlinear dynamic structures E.P. Petrov à Mechanical Engineering Department, South Kensington Campus, London SW7 2AZ, UK article info Article history: Received 16 April 2007 Received in revised form 7 March 2008 Accepted 7 March 2008 Available online 16 March 2008 Keywords: Friction contact Nonlinear vibration Multiharmonic Sensitivity Robustness abstract An effective method is developed for calculation of the sensitivity and robustness of the forced response levels for strongly nonlinear structures. The sensitivity coefficients are determined with respect to parameters of friction contact interfaces, parameters of linear components of an assembled structure, frequency and level of excitation forces. Equations for determination of first- and second-order sensitivity coefficients of the forced response are derived analytically from a nonlinear multiharmonic equation of motion. The analytical derivation allows accurate and fast evaluation of the sensitivity coefficients. The sensitivity coefficients are calculated in frequency domain for each excitation frequency over the frequency range analysed simultaneously with the force response levels. The developed highly efficient method allows calculation of sensitivity characteristics without a noticeable increase of the computation time in addition to the time required for the forced response calculation. A measure of the forced response robustness is introduced. Sensitivity-based method for assessment of the forced response robustness for given ranges of uncertainty of structural and operating parameters is proposed. The methodology developed is illustrated on a set of problems including cases of forced response analysis for realistic strongly nonlinear gas-turbine structures. & 2008 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Sensitivity analysis for forced response In order to make a justified choice of design parameters for jointed structures, there is a need to determine not only the levels of displacement and stresses which are caused by excitation forces but also how sensitive those forced response levels are to variations of the design parameters. Information about the sensitivity of the forced response facilitates choosing those parameters that can be changed in order to provide the required forced response level. Furthermore, in many practical applications, there is often a need to find an optimum set of the design parameter values for a structure which gives a minimum of the forced response or satisfies other criteria formulated by the designer. The optimisation problems can be efficiently solved when sensitivity characteristics are determined and, hence, sensitivity analysis is an important and in many cases unavoidable part of the optimisation process. Due to importance of determination of sensitivity coefficients, efforts of many investigators were devoted to this problem which has taken Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jnlabr/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2008.03.008 à Tel.: +44 20 75941920. E-mail address: y.petrov@imperial.ac.uk Mechanical Systems and Signal Processing 23 (2009) 68– 86