# Basic Terminology

Free vibration is the natural response of a structure to some impact or displacement. The response is completely determined by the properties of the structure, and its vibration can be understood by examining the structure's mechanical properties. For example, when you pluck a string of a guitar, it vibrates at the tuned frequency and generates the desired sound. The frequency of the tone is a function of the tension in the string and is not related to the plucking technique.

Forced vibration is the response of a structure to a repetitive forcing function that causes the structure to vibrate at the frequency of the excitation. For example, the rear view mirror on a car will always vibrate at the frequency associated with the engine's RPMs. In forced vibration, there is a relationship between the amplitude of the forcing function and the corresponding vibration level. The relationship is dictated by the properties of the structure.

Sinusoidal vibration is a special class of vibration. The structure is excited by a forcing function that is a pure tone with a single frequency. Sinusoidal vibration is not very common in nature, but it provides an excellent engineering tool that enables us to understand complex vibrations by breaking them down into simple, one-tone vibrations. The motion of any point on the structure can be described as a sinusoidal function of time.

Random vibration is very common in nature. The vibration you feel when driving a car result from a complex combination of the rough road surface, engine vibration, wind buffeting the car's exterior, etc. Instead of trying to quantify each of these effects, they are commonly described by using statistical parameters. Random vibration quantifies the average vibration level over time across a frequency spectrum.

Time domain analysis starts by analyzing the signal as a function of time. An oscilloscope, data acquisition device, or signal analyzer can be used to acquire the signal. The plot of vibration versus time provides information that helps characterize the behavior of the structure. It behavior can be characterized by measuring the maximum vibration (or peak) level, or finding the period, (time between zero crossings), or estimating the decay rate (the amount of time for the envelope to decay to near zero). These parameters are the typical results of time domain analysis.

Frequency analysis also provides valuable information about structural vibration. Any time history signal can be transformed into the frequency domain. The most common mathematical technique for transforming time signals into the frequency domain is called the Fourier Transform, after the French Mathematician Jean Baptiste Fourier. The math is complex, but today's signal analyzers race through it automatically, in real-time. Fourier Transform theory says that any periodic signal can be represented by a series of pure sine tones. In structural analysis, usually time waveforms are measured and their Fourier Transforms computed. The Fast Fourier Transform (FFT) is a computationally optimized version of the Fourier Transform.

The Decibel dB Scale
Vibration data is often displayed in a logarithmic scale called the Decibel (dB) scale. This scale is useful because vibration levels can vary from very small to very large values. When plotting the full data range on most scales, the small signals become virtually invisible. The dB scale solves this problem because it compresses large numbers and expands small numbers. A dB value can be computed from a linear value by the equation:

where xref is a reference number that depends on the type of measurement. Comparing the motion of a mass to the motion of the base, base measurement is used as the reference in the denominator and the mass as the measurement in the numerator. In the dB scale, if the numerator and denominator are equal, the level is zero dB. A level of +6 dB means the numerator is about a factor of two times the reference value and +20 dB means the numerator is a factor of 10 times the reference.