Lagrangian Formalism for the Analysis of Acoustic Properties of Two-Phase Composite Materials with Damaged Interfaces

New macroscopic mechanical model of a two-phase composite based on the Lagrange function and principle least action was developed. The key advantage is direct consideration phase interaction defects (discontinuities) at interphase boundaries. As distinct from classical models, equations developed are solved in terms velocities elastic waves composite. effective (macroscopic) moduli calculated using derived velocities. On example an analytical solution for 1D case, qualitatively new possibilities demonstrated, provided by evaluating acoustic characteristics composites analyzing effect volume content phases damage It theoretically shown first time that, addition to with parameters estimated good accuracy framework traditional “slow” can originated steadily propagate materials interfaces. Analytical relations obtained allow one solve both problem determining “fast” imperfect boundaries, inverse estimating known values wave