Vibraciones mecanicas

STRUCTURAL TESTING Part II: Modal Analysis and Simulation by Ole Døssing, Brüel&Kjær
Experimental Modal Analysis………………………………. 2 All Structures Exhibit Modal Behaviour………………... 4 Single-degree-of-freedom (SDOF) Models……………….. 6 SDOF Models in the Frequency Domain ...............…...... 7 A Closer Look at Pole Location and Residue .....……..... 9 The DOF and MDOF models....….................................... 10 What is a Mode Shape? ................................................. 11 Normal Modes and Complex Modes .......................... 12 How Residues Relate to Mode Shapes ...................... 13 Scaling the Mode Shapes .............................................. 14 Modal Coupling ................................................................ 15 What Does the ModalDescription Assume? ............ 16 Practical Structures ......................................................... 17 The Lumped-parameter Model and Modal Theory . 18 The Modal Space .............................................................. 19 Specifying the Degrees of Freedom (DOFs) ............ 20 DOFs and the Mobility Matrix ...................................... 22 Modal Test on a Simple Structure.............................. 24 Mode Shapes from Quadrature Picking ..................... 26 Parameter Estimation by Curve-fitting ....................... 28 What is Curve-fitting? ..................................................... 29 Curve-fitters for Modal Analysis .................................. 30 Local and Global Curve-fitters ..................................... 32 Computer-aidedModal Testing ..................................... 33 Step 1 - Setting up the Modal Test .......................... 34 Step 2 - Making the Measurements .......................... 36 Step 3 - Parameter Estimation by Curve-fitting .... 37 Step 4 - Documentation of the Test .......................... 38 The Dynamic Modal Model ............................................ 40 Checking and Applying theModel ............................. 41 Considerations of Model Completeness .................... 42 Computer Simulations .................................................... 43 Response Simulation ...................................................... 44 Modification Simulation .................................................. 46 Applying Modifications................................................... 47 Implementating Modifications ....................................... 48 Case Story: Application of Synthesized FRFs .....….. 49 Further Reading .............................................................. 51 Symbols and Notation .................................................... 52

March 1988

Preface to Part 2
The study of structural dynamics is essential for understandingand evaluating the performance of any engineering product. Whether we are concerned with printed-circuit boards or suspension bridges, high-speed printer mechanisms or satellite launchers, dynamic response is fundamental to sustained and satisfactory operation. Modal analysis of the data obtained from structural testing, provides us with a definitive description of the response of a structure, whichcan be evaluated against design specifications. It also enables us to construct a powerful tool, the modal model, with which we can investigate the effects of structural modifications, or predict how the structure will perform under changed operating conditions. A simplified definition of modal analysis can be made by comparing it to frequency analysis. In frequency analysis, a complex signal isresolved into a set of simple sine waves with individual frequency and amplitude parameters. In modal analysis a complex deflection pattern (of a vibrating structure) is resolved into a set of simple mode shapes with individual frequency and damping parameters. A rigorous mathematical approach to the subject is outside the scope of this primer. Where necessary we simply quote the mathematics!...