Reflection of plane waves at the stress-free/rigid surface of a micro-mechanically modeled Piezo-electro-magnetic fiber-reinforced half-space

Abstract

The development of fiber-reinforced composites (FRCs) is ever-increasing for better vibrational energy absorption within a material, reducing transmission of noise/vibration to neighboring structures, etc. The integrity of these structural components is tackled using Non-destructive testing (NDT)/Non-destructive evaluation (NDE) methods based on wave reflection through transducers. Owing to such factors, the present work has two primary objectives-firstly, to develop the micro-mechanics model of an orthotropic Piezo-Electro-Magnetic Fiber-Reinforced Composite (PEMFRC), which consists of BaTiO as fiber constituent and CoFeO as matrix constituent. Secondly, to analyze plane wave (qP/qSV) reflection at stress-free/rigid surface of a solid PEMFRC half-space. For an incident plane wave, four waves, namely quasi-longitudinal (qP), quasi-transverse (qSV), electroacoustic (EA), and magnetoacoustic (MA) waves, get reflected. The propagation directions of all reflected waves for incident qP/qSV wave are graphically demonstrated. Electrically Open Magnetically Open (EOMO), Electrically Short Magnetically Short (ESMS), Electrically Open Magnetically Short(EOMS), and Electrically Short Magnetically Open (ESMO) boundaries, for both Stress-free and Rigid surfaces, are considered. Using secular equations along with suitable boundary conditions, the amplitude ratios are derived using Cramer's rule. Furthermore, using the energy flux relation and expressions of amplitude ratios, the energy ratios of all reflected waves, interaction energy, and net energy are derived, which exhibit the influence of the existing parameters. Some special cases of the problem are discussed, and the Law of Conservation of Energy is validated.