PSI - Issue 24

L. Beretta, E. Marotta,P. Salvini / Structur l Integrity Procedia 00 (

Lorenzo Beretta et al. / Procedia Structural Integrity 24 (2019) 267–278 ) 000 000

271 5

Fig. 4. Net mechanical scheme.

An analytic approach for the circular net does not exist in the literature; therefore, it was thought to apply the same analogy given for rectangular membranes, to obtain a non-exact, but right-minded, trend for the frequency of vibration of a circular net, when two orthogonal loads are present. ( ) , , 2 x y m n m n a T T r      +  = (5) Again, for the first natural frequency ( ) , ≅ 2,404 . The present study focusses on transverse vibrations since it is a hard task to deal with the in-plane vibrations, even if studying these latter ones would have been much better for our goal. In fact, transverse vibrations extend up to the edges, thus being strongly influenced by the boundary conditions (the type of restraints and perimeter shape). The measurements here done refer to a hinged circular perimeter, but changing the boundary conditions means altering the frequency dependence from loads. On the other hand, in-plane vibrations affect a much smaller area of the mesh and are virtually independent of the type of boundary (if the dimensions of the disturbed areas are reasonably small compared to those of the mesh, which was our case). Therefore, in-plane vibrations offer the possibility to get a broader universal formula, independent of the particular boundary conditions. Unfortunately, in-plane vibrations present the inconvenience of being much faster than the transverse ones, thus resulting in difficult to catch with the available photographic equipment. This is why in-plane vibrations have been omitted in this study. 4. Experimental results Because of the strong anisotropy and deformability of the metal mesh, it was necessary to design and implement a machine that can guarantee a two-dimensional tensioning. This equipment has been called T.A.S.T.I., which stands for Two Axial Stretch Test Instrument. On the device, it is possible to mount a sample of the mesh, up to 400x400 mm, which is grasped and pulled by adjustable hooks, anchored to sliding supports along very low friction guides. The machine can impose independent displacements along with two orthogonal directions while measuring the reaction forces. Through a PID control, it is also possible to apply loads on a given sequence. The displacement is applied through a system of cables and pulleys connected to two stepper motors, able to rotate at small step angles, while the reaction forces are measured through extensimetric load cells, Marotta et al. (2016). Fig. 5 and Fig. 6 show the whole device and the load system, respectively. 4.1. Testing Machine