Dynamics: Glossary

Beat Phenomenon
     When a two degree-of-freedom system has two closely spaced natural frequencies, wn1 and wn2, vibration kinetic energy will transfer from one degree-of-freedom to the other in a periodic fashion. The frequency of this transfer is known as the beat frequency, given by (wn1 - wn2) / 2.
Critical Damping
     The minimum damping that results in non-periodic motion of a system under free vibration.
Damping Ratio
     The ratio of a system's actual damping to its critical damping. When less than 1, the system in underdamped and will exhibit ringing when disturbed. When larger than 1, the system is overdamped and disturbances will die out without ringing.
     In the simplest of cases, a degree-of-freedom is an independent displacement or rotation that a system may exhibit. A degree-of-freedom for a system is analogous to an independent variable for a mathematical function. All system degrees-of-freedom must be specified to fully characterize the system at any given time.
Free Body Diagram
     A schematic isolating an object (or part of an object) from its environment for the purpose of revealing all external forces and moments acting on the object. Free body diagrams are helpful in applying Newton’s 2nd Law of motion to objects.
Maxwell's Reciprocity Theorem
     For two identically-sized forces applied at the distinct points A and B on a linear structure, Maxwell’s Reciprocity Theorem states that the displacement at A caused by the force at B is the same as the displacement at B caused by the force at A. As a result, the flexibility matrix (and its inverse, the stiffness matrix) of linear systems is symmetric.
Natural Frequency
     A frequency where a system resonance exists. If excited at this frequency, the system will exhibit very large displacements (for low damping levels). If the system is undamped, then vibrations can occur at the natural frequency without any external excitation indefinitely.
     A condition where very little energy input into a structure results in a very large displacement (for low damping levels). By definition, resonances occur at the natural frequencies of a system.



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