1. Mechanical Vibrations Introduction to 2DOF Vibrations 2. LESSON OUTCOMES 1. Define & describe what it means by VIBRATION and the importance of studying it 2. Describe different types of vibrations and the main elements within a vibrating system 3. Describe basic steps and procedure in analyzing vibration of a body 4. Derive a mathematical model of a 2DOF system 3. What does it mean? 4. Defined as oscillatory motion of bodies in response to a disturbance Occur due to presence of a restoring force Can be found everywhere: Human Body ear drums, vocal chords, walking, running Vehicles residual imbalance in engines, suspension vibrations, locomotive wheels Musical instruments guitar strings, speakers Rotating Machines turbines, pumps, fans, 5. Excessive vibrations: Noise Loosening fasteners Fatigue failure Discomfort When vibration frequency coincides with natural frequency of system Resonance occurs Collapse of Bridge Tacoma, USA 6. Technically, vibration process involves the transfer of potential energy to kinetic energy and vice versa in alternating fashion In general, a vibratory system consists of: A mean to store potential energy (spring, gravity) A mean to store kinetic energy (mass, inertial component) A mean to absorb/dissipate vibrational energy (damper) 7. Classification of vibrations Free and Forced vibrations Free Vibrations: Initial disturbance, system left to vibrate without external influence Forced Vibrations: Vibrating body stimulated by external forces Damped and Undamped vibrations Damped Vibrations: Dissipation of energy occurs, vibration amplitude decays Undamped Vibrations: No dissipation of energy, 8. Analysis of Vibrational System STAGE I: Device Mathematical or Physical Model of structure to be analyzed STAGE II: From model, derive equation of motions STAGE III: Evaluate the structure response 9. 2 DOF System 10. 2 DOF System STAGE I: Device physical model for system. 11. STAGE II: Derive Equation of Motions 12. STAGE II: Derive Equation of Motions 13. STAGE III: Evaluate Structure Response 14. STAGE III: Evaluate Structure Response 15. Recheck Outcomes 1. Define & describe what it means by VIBRATION and the importance of studying it 2. Describe different types of vibrations and the main elements within a vibrating system 3. Describe basic steps and procedure in analyzing vibration of a body 4. Derive a mathematical model of a 2DOF system