Fundamentals of nonlinear acoustical techniques and sideband peak count

This chapter gives readers fundamental understandings of various nonlinear acoustical techniques. It briefly describes the nonlinear techniques that are popular today such as higher harmonic generation, subharmonic generation, nonlinear resonant acoustic spectroscopy, vibro-acoustics, wave modulation between two wave frequencies-pumping and probing frequencies-and sideband generation. Some examples are provided showing the applications of these techniques in nondestructive evaluation (NDE) of materials and structures. The difficulties associated with various nonlinear techniques and current challenges encountered by the scientists and engineers in implementing nonlinear guided wave-based techniques are discussed. Recent development (within last 5 years) of a new promising nonlinear technique called sideband peak count (or SPC) for NDE is also discussed. SPC overcomes many shortcomings of the existing frequency modulation techniques. The objective of this chapter is to present the readers, in simple words, a broad overview of nonlinear acoustical techniques starting with the fundamental equations of mechanics. This presentation does not go into great depth of every available technique but provides sufficient basic knowledge and exposure to the new developments in this field, such as SPC. SPC is described in detail in Sect. 1.10.2. Interested readers can read this section without going through the detailed derivations of the earlier sections and can still understand this new technique. Other techniques are discussed in greater detail in the subsequent chapters.