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Vibration of
Continuous Systems:
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
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 1st, 2nd, 3rd,……..nth
§ Each with a characteristic frequency and mode
shape.
§Can ‘all’ be occurring simultaneously- lower order
ones tend to dominate
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
Effects of boundary
conditions:
Solutions:
Transverse (Lateral) vibration
of simple beams:
Vibration of Continuous Systems.pjjjjjjjjptx

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Vibration of Continuous Systems.pjjjjjjjjptx

  • 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
  • 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 1st, 2nd, 3rd,……..nth § 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