53/58:153 Lecture 25 Fundamental of Vibration ______________________________________________________________________________ - 1 - Lecture 25: Large scale systems Reading materials: 10.1 and 10.2 1. Guyan Reduction Finite element discretization results in a large dynamic system. Therefore, computation is intensive. One approach is reducing the size of the eigenvalue problem that must be solved to compute the mode shapes and frequencies. Generalized eigenvalue problem In the reduction process, choosing an appropriate set of DOFs that are to be retained. Those DOFs are called master DOFs while the ones eliminated are called slave DOFs. Relationship between the total DOFs (#n) and the master DOFs (#m)s Static equilibrium equations53/58:153 Lecture 25 Fundamental of Vibration ______________________________________________________________________________ - 2 - Example 153/58:153 Lecture 25 Fundamental of Vibration ______________________________________________________________________________ - 3 - Reduced matrices53/58:153 Lecture 25 Fundamental of Vibration ______________________________________________________________________________ - 4 - For original problem 2. Inverse iteration An iterative method to compute frequencies and modes shapes for multi-degree freedom systems. Rearrange Dynamic matrix53/58:153 Lecture 25 Fundamental of Vibration ______________________________________________________________________________ - 5 - Example 253/58:153 Lecture 25 Fundamental of Vibration ______________________________________________________________________________ - 6
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