Application of a Novel Picard-Type Time-Integration Technique to the Linear and Non-Linear Dynamics of Mechanical Structures: An Exemplary Study

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operati...

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Bibliographic Details
Published in:Applied sciences 2021-05, Vol.11 (9), p.3742
Main Authors: Oborin, Evgenii, Irschik, Hans
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Computer applications
Dynamic structural analysis
Earthquakes
Exact solutions
Free vibration
Harmonic excitation
Integration
linear and non-linear dynamics
mechanical structures
Mechanics
Methods
Nonlinear dynamics
Picard-type iteration
Seismic activity
symbolic computation
Time integration
tower-like structure
Vibrations
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Summary:Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods.
ISSN:2076-3417
2076-3417
DOI:10.3390/app11093742