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A semi-analytic method for dynamic response analysis based on Gurtin’s variational principle. (English) Zbl 0821.73033

Summary: A semi-analytic approach for solving dynamic response problems is developed which is based on Gurtin’s convolution-type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantage for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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