Canadian Journal of Pure & Applied Sciences

Abstract: This short theoretical work discusses some problems of finding of the suitable eigenvalues and eigenvectors. The eigenvalues and eigenvectors represent the solutions of the coupled equations of motion written in the well-known tensor form. These coupled equations of motion describe shear-horizontal (SH) wave propagation in the transversely isotropic piezoelectromagnetic materials of class 6mm when the SH-wave propagation is coupled with both the electrical and magnetic potentials. It is stated that as many as six eigenvalues can be soundly found for the problem. The problem is that some eigenvalues result in the corresponding certain eigenvectors and some eigenvalues allow existence of uncertain eigenvectors that can be chosen by a researcher. This uncertainty allows researchers to choose several certain forms for the uncertain eigenvectors. It is discussed that the author of this report has used the certain forms for the uncertain eigenvectors that are naturally coupled with the certain eigenvectors. However, some researchers suggest to use the following forms for the uncertain eigenvectors: (0,1,0) and (0,0,1). It is stated that the simplest and perhaps convenient eigenvectors in the forms of (0,1,0) and (0,0,1) are actually unsuitable because they are independent from the certain eigenvectors and the CMEMC coupling mechanisms. It is very important to use suitable eigenvectors because different forms of them can result in different final expressions for the velocities of the SH-waves. The SH-wave velocity is a very important wave characteristic and evaluation of its value can help for creation and optimization of novel technical devices based on surface, interfacial, and plate SH-waves