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Matakuliah : Dinamika Struktur & Teknik Gempa Tahun : S0774

MULTI DEGREE OF FREEDOM SYSTEM Equation of Motion, Problem Statement & Solution Methods Pertemuan 16. Matakuliah : Dinamika Struktur & Teknik Gempa Tahun : S0774. MDOF Systems. Topics: Introduction to Multi DOF Systems Close Coupled Systems Far Coupled Systems

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Matakuliah : Dinamika Struktur & Teknik Gempa Tahun : S0774

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  1. MULTI DEGREE OF FREEDOM SYSTEM Equation of Motion, Problem Statement & Solution MethodsPertemuan 16 Matakuliah : Dinamika Struktur & Teknik Gempa Tahun : S0774

  2. MDOF Systems Topics: Introduction to Multi DOF Systems Close Coupled Systems Far Coupled Systems Orthogonality of Mode Shapes Modal Analysis Undamped Analysis Damped Analysis Forced Vibration

  3. Introduction Continuous Systems • Any Mechanical System is Continuous in Mass and Stiffness Properties • Some Systems e.g. Turbine Blade Better Modeled as Distributed then Lumped • Partial Differential Equations • Solutions are Simpler and Accurate compared to MDOF System • Strings, Bars, Rods & Beams

  4. Introduction Continuous Systems Radial Drilling machine Modeled as MDOF System

  5. MDOF Systems Topics: Introduction to Multi DOF Systems Close Coupled Systems Far Coupled Systems Orthogonality of Mode Shapes Modal Analysis Undamped Analysis Damped Analysis Forced Vibration

  6. Close Coupled Systems Mass Matrix

  7. Close Coupled Systems Free Vibrations

  8. Close Coupled Systems Eigen Value Problem Natural Frequencies Mode Shapes

  9. Close Coupled Systems

  10. MDOF Systems Topics: Introduction to Multi DOF Systems Close Coupled Systems Far Coupled Systems Orthogonality of Mode Shapes Modal Analysis Undamped Analysis Damped Analysis Forced Vibration

  11. Far Coupled Systems Influence Coefficient Method

  12. Far Coupled Systems

  13. MDOF Systems Topics: Introduction to Multi DOF Systems Close Coupled Systems Far Coupled Systems Orthogonality of Mode Shapes Modal Analysis Undamped Analysis Damped Analysis Forced Vibration

  14. Orthogonality of Mode Shapes Mode r Mode s [U] is Orthonormal Modal Matrix

  15. MDOF Systems Topics: Introduction to Multi DOF Systems Close Coupled Systems Far Coupled Systems Orthogonality of Mode Shapes Modal Analysis Undamped Analysis Damped Analysis Forced Vibration

  16. Modal Analysis Modal Analysis is a Powerful Tool to Determine the Free and Forced Vibrations of MDOF systems We can Consider Physical MDOF system to be replaced by several SDOF Systems, each SDOF system representing one Specific Natural Mode This process of determining the modal masses and stiffness in each mode Of Vibration of a MDOF and determine the response in each of the modes to Determine the Total Behavior is Modal Analysis General Response can be written as:

  17. Modal Analysis Undamped Analysis

  18. Modal Analysis Undamped Analysis

  19. Modal Analysis Damped Analysis Proportional Damping Decoupled Governing Equations

  20. Modal Analysis Damped Analysis For Non Rigid Body Modes Rigid Body mode

  21. Modal Analysis Damped Analysis

  22. Modal Analysis Forced Vibration For Harmonic Excitation Steady State Solution

  23. Assignment 1

  24. Assignment 2

  25. Assignment An automobile has an instrument of mass 200kg mounted on its chassis using an isolator of stiffness 580kN/m. The chassis has a mass of 1200kg and is sprung on the wheel axle through suspension of total stiffness 80kN/m. The axle has a mass of 220kg and tyre stiffness is 1000kN/m. Model the automobile as a three mass system with instrument, chassis and axle mass. For the sake of quick assessment of vibratory response of the automobile, remodel the above system as a two mass system and then using a modal analysis approach, find the response of the instrument mounted on the chassis after the automobile encountered a step bump of 5cm. 3

  26. Assignment 4 Mc = 1200 kg Kc1 = 35kN/m

  27. Thank You

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