Vibration of Continuous Systems.pjjjjjjjjptx

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1. Vibration of Continuous Systems:

2. Discrete lumped mass: § Discrete model the governing equations are ordinary differential equations, relatively easy to solve. § In many cases, known as distributed or continuous systems, it is not possible to identify discrete masses, dampers. § A continuous distribution of the mass, damping, and elasticity each of the infinite number of points of the system can vibrate. ♾ degrees of freedom. § Continuous model, the governing equations are partial differential equations, more difficult to solve.

3. Continuous Systems: § Examples are: A string A shaft (torsional) A beam (longitudinal and transverse) A membrane (plate-transverse) § infinite degrees of freedom = infinite modes of vibration!!! § 1-n 1 st , 2 nd , 3 rd ,……..n th § Each with a characteristic frequency and mode shape. § Can ‘all’ be occurring simultaneously- lower order ones tend to dominate

4. Continuous Systems: An added (essential!!!) factor is that the modes of vibration also depend on how the system is fixed in space- Simply supported Clamped Free Any external forces or moments

5. Effects of boundary conditions:

6. Solutions:

7. Transverse (Lateral) vibration of simple beams: