Governing Equations



This chapter develops the governing equations of motion for a homogeneous isotropic elastic solid, using the linear three-dimensional theory of elasticity in cylindrical coordinates. At first, classical relationships between stress, strain, and displacement are reviewed and implemented into the dynamic equilibrium equations. The mathematical representations of the linear theory of elasticity derived in this chapter will set the stage for the development of the required governing equations for the possible modes of vibrations in cylindrical structures with any thickness.


Shear Stress Shear Modulus Shear Strain Volumetric Strain Direct Stress 


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Copyright information

© Springer-Verlag US 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTennessee State UniversityNashvilleUSA
  2. 2.Department of Mechanical and Automotive Engineering School of Aerospace, Mechanical and Manufacturing EngineeringRMIT UniversityMelbourneAustralia

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