Introduction

Ultrasonic vibrations have often been used in the past on various structures without any real understanding of the impact of a loading function on structural resonances or resulting vibrational patterns at different frequencies. The method was used to obtain an ultrasonic signal signature of a part being inspected, most often in quality control after manufacture. A purpose of this chapter is therefore to establish an understanding of the ultrasonic vibration as a superposition of guided wave modes traveling in a structure and ways to optimize sensitivity to certain defects by way of loading function choice. In more traditional low-frequency modal analysis, the loading function choice is not so critical; results depend primarily on excitation frequency. With ultrasonic vibration, we will see that the choice of a loading function plays a major role in the design of an inspection system for developing various quality control and in-service inspection solutions.

This chapter now examines the subject of ultrasonic vibrations, the topic of which is a logical extension to ultrasonic guided waves. A few applications are considered.

Let’s consider the long time solution to a wave propagation problem. In the bulk wave case, because waves are traveling in infinite space, there is no vibration aspect of the problem to be considered as there are no wave reflection and transmission factors. On the other hand, for guided wave propagation, the long time solution in many cases leads to a vibrations problem. This may not occur if no boundary exists in a particular direction as the wave is transmitted to infinity. In examining a closed structure, such as a finite plate or tube, the reflection and transmission factors for each entry of a wave onto a boundary leads to a variety of constructive and destructive interference phenomena. The long time solution therefore leads to a vibrations or modal analysis problem. There will be specific resonant frequency values for a structure as well as specific vibrational patterns at on and off resonance. Researchers are carrying out work examining the transition from the initial transient response to a long time vibrations solution. As a consequence, ultrasonic nondestructive evaluation (NDE) and structural health monitoring (SHM) is being developed by considering many aspects of ultrasonic bulk wave analysis, ultrasonic guided wave analysis, and modal vibration analysis.