This paper presents a model belonging to a theory that recently appeared in the literature dealing with accurate solutions of freely vibrating laminated plates. The present model, which is derived from a displacement-based variational approach, investigates both free edge boundary conditions and the possibility of obtaining accurate results without explicitly incorporating stress interlaminar continuity conditions where they are in principle requested. These investigations are carried out within the frame of multi-layered plates where the literature is lacking in relevant three-dimensional results.In spite of the multi-layer nature of the plate, the model is developed as if the same plate were virtually made of a single layer because a suitable set of piecewise-smooth functions is used. Once the model is theoretically introduced, natural frequencies are evaluated for the case of plates with simply supported and free edge boundaries. The evaluations are compared with those few existing values of exact or approximate three-dimensional models, new results are provided for future comparisons and, finally, the performance of the model is tested with respect to extreme cases which could also deal with interesting engineering applications without reverting to non-immediate numerical schemes.
Within the frame of industrial automation, the mechanical power related to pneumatic actuator systems involves air flows along with mechanical component, such as valves, connecting tubes, cylinder chambers and possible linkages in order to finally actuate a specific objective. Gas dynamic of the air flowing into connecting ducts plays a fundamental role in the description of the global dynamic phenomena of these systems. Several studies deal with the dynamics of such pneumatic systems but through streamlined analysis where the influence of pressure-waves propagating in ducts is neglected or poorly described. The related models are even more complex when finite volumes are placed at the ends of connecting lines. In this paper, two different mathematical models describing transient pressure-waves propagating through lines closed by finite volumes are presented. The investigation regards pressure and velocity ranges normally operating in industrial pneumatic systems. Besides the value of new system modeling of different complexity, these models are compared from an analytical and numerical point of view; advantages, disadvantages, weakness, abilities, and inabilities are highlighted and, finally, the relevant analysis is corroborated through experimental validations of wave propagating pressure at fixed positions of ducts. This study results both in the presentation of models of practical interest, as well as in an attempt to provide an elucidation on the need to resort to an accurate model rather than a streamlined one with respect to the geometric and/or operative characteristics of industrial pneumatic systems.
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