Efficient computational nonlinear dynamic analysis using modal modification response technique Timothy Marinone a,n , Peter Avitabile a , Jason Foley b , Janet Wolfson b a Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA b Air Force Research Laboratory Munitions Directorate Fuzes Branch, Eglin Air Force Base, 306W. Eglin Blvd., Bldg 432, Eglin AFB, FL 32542-5430, USA article info Article history: Received 8 September 2011 Received in revised form 18 January 2012 Accepted 21 February 2012 Available online 15 March 2012 Keywords: Nonlinear analysis Forced nonlinear response Linear components for nonlinear analysis Modal analysis Mode superposition abstract Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by inter- connecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Generally, any nonlinear response analysis involves significant computation, especially if the full analytical model system matrices are used for the forced response problem. These nonlinearities can be broadly broken down into two categories: global and local, with significant effort expended on research of both. Due to the significant computational time required for these nonlinear cases, the analyst may often be unable to investigate the nonlinearities in depth, especially if a set of performance characteristics related to temperature, preload, deflection, etc. characterize the nonlinear connection elements. Thus, there is significant motivation to develop a set of reduced order models that can accurately predict nonlinear response at a substantially reduced computation time. One area of interest involves the dynamic response of systems with nonlinear connections. These systems are typically linear, but the introduction of the local nonlinearity causes the system to become highly nonlinear. Several approaches to this class of problems have been developed and are described herein. A promising approach to this type of problem involves the use of Nonlinear Normal Modes [1]. This extends the concept of linear normal modes to a nonlinear system where the frequency and mode shape of a NNM can vary depending on the state of the nonlinearity (i.e., stiffness, position or time dependent). As a result, these NNMs are no longer orthogonally independent and are not limited to a discrete number of frequencies defined the number of DOFs of the system. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2012.02.011 n Corresponding author. Tel.: þ1 978 934 2990. E-mail address: timothy.marinone@gmail.com (T. Marinone). Mechanical Systems and Signal Processing 31 (2012) 67–93