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Mechanical Vibrations Lecture 13

Mechanical Vibrations Lecture 13. Multi-Degree of Freedom Force Vibration The Eigen -Value Problem Modal Analysis Solution. Mass Normalisation of Mode Shapes. Properties in Eigen Vector Matrices. Modal Analysis. Scale the mode shapes so that

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Mechanical Vibrations Lecture 13

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  1. Mechanical VibrationsLecture 13 Multi-Degree of Freedom Force Vibration The Eigen-Value Problem Modal Analysis Solution

  2. Mass Normalisation of Mode Shapes

  3. Properties in Eigen Vector Matrices

  4. Modal Analysis • Scale the mode shapes so that • Where is a matrix of the mass normalised mode shapes • This gives

  5. Calculation of Mass Normalised mode shapes

  6. Inverting the spatial matrix

  7. Inverting the spatial matrix No Matrix Inversion

  8. Summary of Process • Find mass and stiffness matrix • Find roots of characteristic equation • Find mode shapes • Mass normalise mode shapes • Use summing solution to find inverse of system matrix

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