LIANG Xiqiang, GAO Qiang, YAO Weian. An Efficient Algorithm Based on Dynamic System Properties and Group Theory for Transient Responses of 1D Periodic Structures[J]. Applied Mathematics and Mechanics, 2018, 39(2): 170-182. doi: 10.21656/1000-0887.380129
Citation: LIANG Xiqiang, GAO Qiang, YAO Weian. An Efficient Algorithm Based on Dynamic System Properties and Group Theory for Transient Responses of 1D Periodic Structures[J]. Applied Mathematics and Mechanics, 2018, 39(2): 170-182. doi: 10.21656/1000-0887.380129

An Efficient Algorithm Based on Dynamic System Properties and Group Theory for Transient Responses of 1D Periodic Structures

doi: 10.21656/1000-0887.380129
Funds:  The National Natural Science Foundation of China(11572076);The National Basic Research Program of China(973 Program)(2014CB049000)
  • Received Date: 2017-05-09
  • Rev Recd Date: 2017-11-01
  • Publish Date: 2018-02-15
  • Based on the condensation technology, the dynamic periodic structure properties and the group theory, an efficient numerical method for computing the transient responses of 1D periodic structures was proposed. Efficiently solving linear equations is an issue for computing the dynamic responses. Based on the periodic properties of the structure and with the condensation technology, the scale of the linear equation corresponding to the structure was reduced. By means of the properties of linear equations for dynamic periodic systems, it was proved that the force on any chosen unit cell can only influence a finite number of adjacent unit cells within a time step. Then, the dynamic response computation of 1D periodic structures was converted into the computation of a series of small-scale substructures. Subsequently, the dynamic response computation of the substructures can be converted into the computation of the cyclic-periodic structures. Then, the cyclic-periodic structures were solved efficiently in light of the group theory. Numerical examples illustrate the high efficiency and memory saving of the proposed method.
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