Theory of Composites Modeled by Interpenetrating Solid Continua |
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a₁ A₂ amplitude ratios an² antisymmetric arbitrary assumed b₁ b₂ body forces boundary conditions chain rule constituents composite material constitutive equations denote derived determinant differential equations displacement dt dt dt² dw² elastic equations of motion exx3 Fiber Reinforced Composite function integral forms interaction invariant isotropic composite material JELM linear homogeneous equations mass density matrix and fibers matrix material obtain Piola-Kirchhoff Piola-Kirchhoff stress tensor plane waves problem Pw² Section solving static stress equations Substituting 7.45 surface of discontinuity surface waves tensor theory thermodynamic thickness vibration three continua tions transversely isotropic composites U₁ U₂ vanish vector W₁ wave equations WAVE NUMBER wavenumber Waves Propagating Wj,m written x-axis x-direction x₁ x₂ XM,i yields nontrivial solutions