- April 2021
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- In this paper, different standard and non-standard continualization methods are applied to a one-dimensional beam system, consisting of a chain of masses and linear rotational springs. The purpose of the study is to check the reliability of new non-classical continuum models when capturing the dispersive behaviour of the discrete system, considered as a reference. Low order continuous equations are pursued since they avoid the need to involve extra boundary conditions. Besides, the presence of physical inconsistencies in these new equations is examined. Comparisons between discrete and continuum models are carried out through vibration analyses, for solids considered to be infinite (dispersion analysis), as well as for bounded solids (natural frequencies), assessing also the treatment of edge conditions. Among all the models presented, there are three novel ones that show the best performance.
- Mechanical Engineering
- beam lattice; continualization; dispersive behaviour; natural frequencies; pseudo-differential operator