4.2.1 Evaluation of a Single Degree-of-Freedom System
Dynamic response can be studied by examining a simple system — that of a single-degree-of-freedom oscillator, as shown in Figure 4-16.
The single-degree-of-freedom oscillator consists of a mass M attached to ground by a spring
with a stiffness K and a dashpot with a damping value of C. The spring pulls on the mass
with a force proportional to its extension or contraction (or the displacement of the mass);
the dashpot provides a frictional force proportional to the velocity of the mass. Any
unbalanced force accelerates the mass. The behavior of a single degree-of-freedom oscillator can then be described by the dynamic equation of motion:
This equation cannot be explicitly solved, unless the damping term, C, is zero and the
imposed load is harmonic (i.e., of the form F(t) = asinb(t+c)). Therefore, the damping value is often dropped (since it is usually small) in order to simplify the equation. The equation
can be simplified further by taking the simplest external harmonic load — a load of zero. If
there is no external load, and damping is approximately zero, the equation describes the free vibration of an undamped single-degree-of-freedom oscillator:
The system characteristics of a single degree-of-freedom oscillator can be completely
described by its natural frequency and its damping value. System response can be
determined once the Dynamic Load Factor (as a function of the natural frequency and
damping value) for the applied load is known.
Introduction to Dynamic Theory
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