  Phononic crystals have been widely employed in many engineering fields, which
is due to their unique feature of frequency band gaps. For example, their
capability to filter out the incoming elastic waves, which include seismic
waves, will have a significant impact on the seismic safety of nuclear
infrastructure. In order to accurately design the desired frequency band gaps,
one must pay attention on how the input parameters and the interaction of the
parameters can affect the frequency band gaps. Global sensitivity analysis can
decompose the dispersion relationship of the phononic crystals and screen the
variance attributed to each of the parameters and the interaction between them.
Prior to the application in one-dimensional (1D) phononic crystals, this paper
will first review the theory of global sensitivity analysis using variance
decomposition (Sobol sensitivity analysis). Afterwards, the sensitivity
analysis is applied to study a simple mathematical model with three input
variables for better understanding of the concept. Then, the sensitivity
analysis is utilized to study the characteristic of the first frequency band
gap in 1D phononic crystals with respect to the input parameters. This study
reveals the quantified influence of the parameters and their correlation in
determining the first frequency band gap. In addition, simple straight-forward
design equations based on reduced Sobol functions are proposed to easily
estimate the first frequency band gap. Finally, the error associated with the
proposed design equations is also addressed.
