Stress Strain Modeling by Transformed Equations of Ultrasonic wave

Abstract:- The equations of ultrasonic wave propagation in Cartesian coordinates are functions of 27 partial displacement derivatives, which first derived and then transformed into cylindrical coordinates. The new obtained functions are functions of 27 partial displacements of first and second order derivatives in cylindrical coordinates too and they will be linearized using a perturbation method based on the Taylor series expansion. A displacement wave, which propagates in a body, composed of two general part; static displacement part, and also small dynamic displacement part. Happening of the small dynamic displacement of a particle around its static situation, Taylor series expansion can be written around this point. Using this determined static situation and considering only the two first components of Taylor series expansion, the equations of motion will be linearized. Tremendously lengthy algebraic operations involved in the derivation and linearization process, all of the mathematical manipulations are performed using Mathematica. Key-Words: perturbation- acoustoelasticity- strained cylindrical solids- ultrasonic- wave propagation- Mathematic