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Wave Propagate Analysis in Incompressible Hyperelastic Multi-Layered Plates

Khademi, Houman | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58203 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Fallah Rajabzadeh, Famida
  7. Abstract:
  8. Elastography, or the use of wave propagation analysis in biological tissues to determine their mechanical properties, is a non-destructive method that involves emitting acoustic waves into the body and analyzing the reflected waves to diagnose and assess the progression of certain diseases. Utilizing elastography requires appropriate tissue modeling, wave propagation analysis, and derivation of dispersion relations and dispersion curves. The objective of this project is to analyze wave propagation in incompressible, multilayer hyperelastic plates with pre-stretch. For this purpose, the incrimental theory along with the equivalent single-layer theory is used for the first time to analyze wave propagation in multilayer hyperelastic plates with asymmetric layer arrangements. To this end, the displacement and pressure fields of the incompressible plate are expanded using Legendre polynomials up to order K. Then, employing Hamilton’s principle, a system of 3(K+1) governing equations for wave propagation and (K+1) incompressibility constraint equations is derived. Assuming harmonic wave propagation, the resulting equations are solved to obtain dispersion relations, which are then validated against existing solutions. Following this, parametric studies are conducted. Since wave propagation analysis in incompressible linear elastic plates has not been previously addressed, the above approach is first applied to this simpler case, and the results are validated based on available analytical solutions
  9. Keywords:
  10. Hyperelastic Materials ; Wave Propagation ; Plate Theory ; Incompressible Material ; Laminated Sheets ; Wave Propagation Analysis ; Elastography

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