**Theoretical and Numerical Investigations of Acoustic Waves**

**1** 

Zi-Gui Huang

*Taiwan* 

**Analysis of Acoustic Wave in** 

**Using Finite Element Method** 

**Homogeneous and Inhomogeneous Media** 

*Department of Mechanical Design Engineering, National Formosa University* 

Even though the propagation of elastic/acoustic waves in inhomogeneous and layered media has been an active research topic for many decades already, new problems and challenges continue to be posed even up to now. In fact, during the last few years, renewed interests have been witnessed by researchers in the various fields of acoustics, such as acoustic mirrors, filters, resonators, waveguides, and other kinds of acoustic devices, in relation to wave propagation in periodic elastic media. In acoustics and applied mechanics, these developments have been triggered by the need for new acoustic devices in order to

What sort of material can allow us to have complete control over the elastic/acoustic wave's propagation? We would like to discuss and answer this question in this chapter. It is well known that the successful applications of photonic band-gap materials have hastened the related researches on phononic band-gap materials. *Analysis of Acoustic Wave in Homogeneous and Inhomogeneous Media Using Finite Element Method* explores the theoretical road leading to the possible applications of phononic band gaps. It should quickly bring the elastic/acoustic professionals and engineers up to speed in this field of study where elastic/acoustic waves and solid-state physics meet. It will also provide an excellent overview to any course in

Previous research on photonic crystals (Johnson & Joannopoulos, 2001, 2003; Joannopoulos et al., 1995; Leung & Liu, 1990) has sparked rapidly growing interest in the analogous acoustic effects of phononic crystals and periodic elastic structures. The various techniques for band structure calculations were introduced (Hussein, 2009). There are many wellknown methods of calculating the band structures of photonic and phononic crystals in addition to the reduced Bloch mode expansion method: the plane-wave expansion (PWE) method (Huang & Wu, 2005; Kushwaha et al., 1993; Laude et al., 2005; Tanaka & Tamura, 1998; Wu et al., 2004 ; Wu & Huang, 2004), the multiple-scattering theory (MST) (Leung & Qiu, 1993; Kafesaki & Economou, 1999; Psarobas & Stefanou, 2000; Wang et al., 1993), the finite-difference (FD) method (Garica-Pabloset et al., 2000; Sun & Wu, 2005; Yang, 1996), the transfer matrix method (Pendry & MacKinnon, 1992), the meshless method (Jun et al., 2003), the multiple multipole method (Moreno et al., 2002), the wavelet method (Checoury & Lourtioz, 2006; Yan & Wang, 2006), the pseudospectral method (Chiang et al., 2007), the finite element method (FEM) (Axmann & Kuchment, 1999; Dobson, 1999; Huang & Chen,

**1. Introduction** 

elastic/acoustic media.

obtain quality control of elastic/acoustic waves.
