Chapter 3 - Dynamic Response of a Structure to Random Excitation

Abstract

A random excitation includes a mixture of different levels of external forces or externally imposed displacements that contain components of many different frequencies. Power spectral density (PSD) is a function that describes the energy content distribution of a quantity over the frequency range. Random input of accelerations is a very common application in the environmental testing of a structural system, and of any designed system. The system is mounted on a shaker that applies acceleration to it. The control system of the shaker is set to input a given PSD of acceleration, according to a PSD curve obtained from formal specifications or data collected in field tests. A random variable has a probability density function (PDF) that describes its distribution. This distribution can be characterized by its statistical moments. The first moment is the mean value, which in fact is the center of gravity of the PDF curve. The second moment is the mean square (MS) value, which provides information about the dispersion of the random variable population around the mean. The MS is the second moment of inertia of the PDF curve around an axis at the mean value. The third moment is called skewness, and it provides information about the symmetry of the distribution of the random variable around the mean. The main purpose of vibration laboratory tests is to discover failures in the design before a final structural design is determined.