POD based computation of Joint Interface Modes Wolfgang Witteveen, University of applied sciences - Wels, Stelzhammerstr. 69, 4600 Wels, Austria, Phone: +43 (0) 7242 72811 3260, wolfgang.witteveen@fh-wels.at Karim Sherif, Linz Centre of Mechatronics GmbH, Altenbergerstr. 69, 4040 Linz, Austria, Phone: +43 (0)70 2468 6117, karim.sherif@lcm.at Nomenclature n number of DOF of FE model x nodel DOF vector of FE model Bf external forces acting on FE model IJ f contact forces inside the joint M mass matrix of FE model K stiffness matrix of FE model nB number of boundary DOF Bx vector of boundary DOF nIJ number of joint DOF IJ x vector of joint DOF r number of Ritz vectors for static reduction X reduction matrix red K reduced stiffness matrix red M reduced mass matrix *,red ĭ full matrix of eigenvectors k considered numbers of eigenvectors red ĭ matrix of considered eigenvectors JIM ĭ matrix of joint interface modes m vector dimension y arbitrary vector Y matrix with column vectors y m number of POM u proper orthogonal mode (POM) i, j index variables J cost function v eigenvector w ratio of considered energy A matrix POD,JIM ĭ matrix of POD based JIM 1. Abstract Recently proposed joint interface modes (JIM), which have been presented at the IMAC 25th, do consider Newton’s 3rd law across a joint already at the stage of mode generation which leads to significant improvements in the subsequent mode based computation where nonlinear contact forces are applied. In the latter publication the computation of the JIM is based on a general eigenvalue problem of a statically reduced mass and stiffness matrix. This approach has certain drawbacks in terms of interpretability and in terms of an ‘a priory’ - estimation of the required number of JIM. In this contribution a prober orthogonal decomposition (POD) based method for the computation of the JIM is introduced. In this context the JIM can be interpreted as kind of ‘energy modes’ so that this procedure holds a meaningful physical interpretation as well as an ‘a priory’ – estimation of the required number of JIM. 2. Introduction and Motivation It is a well known fact that the global stiffness and damping properties of a metallic structure, which consists of jointed substructures, are strongly influenced by the local and nonlinear characteristics of the involved joints such as bolted joints or spot welded seams, see exemplarily [1] and [2]. In the industrial practice this kind of problems are typically investigated either by the direct Finite Element Method (FEM) or a Ritz vector based (commonly called ‘modal’) approach. T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, 19 DOI 10.1007/978-1-4419-9305-2_2, © The Society for Experimental Mechanics, Inc. 2011
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