Abstract
The examples of the calculations of the selected engineering problems given in this Chapter demonstrate the practice of numerical solutions. In real structures we always ask questions as to what geometry and what values of the material data are appropriate to pass from the physical model of the structure to the numerical one. Real shapes are usually complex and we try to simplify them, replacing curves with straight lines, non-uniformly distributed material parameters with homogeneous material, material damping with a numerical decay of the amplitude. Let us consider, as a first example, a track subjected to a moving vehicle. We can build a detailed three-dimensional model using cubes or tetrahedra with many degrees of freedom describing the foundation, ballast, track elements, rails, wheels, and the remaining part of the vehicle. We can include contact phenomena, friction, material nonlinearities, thermo-mechanical coupling, etc. However, such a model nowadays would be a challenge even for a static problem.Calculating the solution can last even a quarter of an hour. That is relatively long considering the computational power of multi-core processors. In a dynamic analysis, such a computation must be repeated thousands of times. The duration of the task exceeds any reasonable length of time. That is why we must still simplify our numerical models and improve the computational tools. Fortunately, a coarse discretization and a simplified mesh does not influence the frequencies significantly. The amplitudes are worse.
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© 2012 Springer-Verlag Berlin Heidelberg
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Bajer, C.I., Dyniewicz, B. (2012). Examples of Applications. In: Numerical Analysis of Vibrations of Structures under Moving Inertial Load. Lecture Notes in Applied and Computational Mechanics, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29548-5_10
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DOI: https://doi.org/10.1007/978-3-642-29548-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29547-8
Online ISBN: 978-3-642-29548-5
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