Complete semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation with non-homogeneous initial conditions

2018 ◽  
Vol 144 ◽  
pp. 283-311 ◽  
Author(s):  
Zuzana Dimitrovová
Keyword(s):  
Analytical Solution ◽  
Elastic Foundation ◽  
Initial Conditions ◽  
Moving Mass ◽  
Two Parameter

scholarly journals Moving mass problem: Complete solution with the effect of initial conditions

2018 ◽  
Vol 148 ◽  
pp. 05001 ◽  
Author(s):  
Zuzana Dimitrovová
Keyword(s):  
Analytical Solution ◽  
Initial Conditions ◽  
Complete Solution ◽  
Harmonic Component ◽  
Moving Mass ◽  
Vertical Force ◽  
Mass Problem ◽  
Harmonic Vibrations ◽  
Full Solution ◽  
Two Parameter

In this contribution, recently published new semi-analytical solution for the moving mass problem [1] is extended to account for the transient terms that adapt the initial part of the complete solution in a way to match the initial conditions. It is assumed that a mass and a vertical force with harmonic component move by constant velocity along a horizontal infinite beam posted on a two-parameter visco-elastic foundation. The new semi-analytical solution is presented as a sum of truly steady-state terms, harmonic terms induced by the moving mass and transient terms adapting the initial conditions. Closed-form formula is given for the first two types of vibrations. It is concluded that transient terms have in most cases almost negligible effect on the full solution and that the initial conditions can significantly affect the amplitudes of the induced harmonic vibrations, but the induced frequencies are kept without any changes.

scholarly journals Snap-through buckling of a shallow arch resting on a two-parameter elastic foundation

2013 ◽  
Vol 37 (16-17) ◽  
pp. 7953-7963 ◽  
Author(s):  
Adel Abdelgawad ◽  
Ahmed Anwar ◽  
Mohamed Nassar
Keyword(s):  
Elastic Foundation ◽  
Shallow Arch ◽  
Two Parameter

A study of mixed-mode composite delamination using enriched interface elements

2013 ◽  
Vol 117 (1195) ◽  
pp. 959-967
Author(s):  
I. Guiamatsia ◽  
J. K. Ankersen ◽  
L. Iannucci
Keyword(s):  
Finite Elements ◽  
Analytical Solution ◽  
Elastic Foundation ◽  
Displacement Field ◽  
Mixed Mode ◽  
Crack Tip ◽  
Shape Functions ◽  
Interface Elements ◽  
Minimum Element ◽  
Element Size

Abstract This paper examines the performance of enriching the shape functions of interface finite elements in the prediction of mixed-mode delamination. Enriching second-order interface and solid elements with the analytical solution of a beam on elastic foundation problem yields the correct displacement field ahead of the crack tip. Despite the enrichment being fixed at elements nodes, resulting in non-traceability of the crack tip location, the strategy is shown to perform consistently well, increasing the minimum element size from the typical 0·5mm to 5mm, for a range of classical mixed-mode bending (MMB) specimens.

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