Eigensolutions of joined/hermetic shell structures using the state space method

Abstract A substructure synthesis method based on state space mathematics is proposed for the eigensolution of axisymmetric joined/hermetic thin shell structures. In the state space method (SSM), a system of eight coupled first order differential equations is solved for each shell substructure using the Pade approximation for matrix exponentiation. The substructures are then joined by matching all of the displacement and force boundary variables. The Pade method allows a space-invariant substructure (e.g., uniform cylinder) to be treated as a continuum. Further, a space-variant substructure (e.g., cone) is assumed to be a piecewise continuum which allows one to still use the Pade method. SSM is validated by applying it to structural elements such as a cylinder, a cone, a sphere, and a toroidal segment, and comparing the predicted natural frequencies with well-known theoretical solutions. The strength of SSM from the substructure synthesis viewpoint is demonstrated by analyzing several shell structures including a hermetic capsule and a refrigeration compressor shell. In all examples, finite element method (FEM) predictions are used to support SSM results. For the compressor shell, SSM results compare well with the limited experimental data.

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