3_Chapter_2.pptx - MECHANICAL VIBRATION SINGLE DEGREE OF FREEDOM SYSTEMS Free Undamped Vibration Equation of Motion Newton's Law Energy Method 1 Free

3_Chapter_2.pptx - MECHANICAL VIBRATION SINGLE DEGREE OF...

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MECHANICAL VIBRATION SINGLE DEGREE OF FREEDOM SYSTEMS Free Undamped Vibration Equation of Motion Newton's Law Energy Method 1
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Free undamped vibration single DoF Recall: Free vibrations system given initial disturbance and oscillates free of external forces. Undamped: no decay of vibration amplitude Single DoF: mass treated as rigid, limped (particle) Elasticity idealised by single spring only one natural frequency. The equation of motion can be derived using Newton’s second law of motion D’Alembert’s Principle, The principle of virtual displacements and, The principle of conservation of energy.
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Free undamped vibration single DoF Using Newton’s second law of motion to develop the equation of motion. 1. Select suitable coordinates 2. Establish (static) equilibrium position 3. Draw free-body-diagram of mass 4. Use FBD to apply Newton’s second law of motion: Rate of change of momentum = applied force” As m is constant For rotational motion For the free, undamped single DoF system d dx( t ) F( t ) m dt dt 2 2
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  • Fall '16
  • MR BIJU CV
  • Energy, Force, undamped vibration, Free undamped vibration

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