I.II Equation of motion i- Characteristics of a SDOF Why SDOF?

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Presentation transcript:

I.II Equation of motion i- Characteristics of a SDOF Why SDOF? 1- Simple starting point 2- Many multi-degree of freedom structures can be approximated by a SDOF system i- Characteristics of a SDOF 1- Rigid girder of mass m () 2- Weightless columns of stiffness k 3- Weightless a damper with a damping coefficient c

ii- Newton’s second law FI = rate of change of momentum of any mass is equal to the force acting on it (for constant m) iii- D’Alembert principle (dynamic equilibrium)

Where

Example 1[Ref 1 ] Weight = w lb Length = 10’ E = 29,000 ksi and The weight contribution !!

Example 1 (cont’d)

Example 2 [Ref 1 ]