A high-precisioyumerical time step integratio'method is proposedfor a linear time-invariant structural dynamic system. Its numerical results are almost identical to the precise solution and are almost independentqf the time step size for a wide range of step sizes. Numerical examples illustrate this high precision.
Based on the analogy between structural mechanics and optimal control theory, the eigensolutions of a symplectic matrix, the adjoint symplectic ortho-normalization relation and the eigenuector expansion method are introduced into the wave propagation theory for sub-structural chain-type structures, such as space structures, composite material and turbine blades. The positive and reverse algebraic Riccati equations are derived,Jor which the solution matricrs are closely related to the power.flow along the sub-structural chain. The power Jlow orthogonality relation for various eigenvectors is proved, and the energy conservation result is also proved for wave scattering problems.
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