Effect of the boundary conditions on the vibrations of functionally graded shells

In this paper, the effect of the boundary conditions on the nonlinear vibration of functionally graded circular cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load; different geometries and material distributions are considered. A convergence analysis is carried out in order to determine the correct number of the modes to be used; the role of the axisymmetric and asymmetric modes is carefully analyzed. The effect of the geometry on the nonlinear response is investigated; i.e. thickness and radius are varied; simply supported, clamped-clamped and free-free shells are considered. The effect of the constituent volume fractions and the configurations of the constituent materials on the natural frequencies and nonlinear response are studied

Nonlinear vibrations of functionally graded cylindrical shells: effect of the companion mode participation

In this paper, the effect of the companion mode participation on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load. A convergence analysis is carried out by considering a different number of axisymmetric and asymmetric modes. The present study is focused on modelling the nonlinear travelling-wave response of the shell in the circumferential direction with the companion mode participation

Virtual Prototyping of a Compliant Spindle for Robotic Deburring

At the current state-of-the-art, Robotic Deburring (RD) has been successfully adopted in many industrial applications, but it still needs improvements in terms of final quality. In fact, the effectiveness of a RD process is highly influenced by the limited accuracyof the robot motions and by the unpredictable variety of burr size/shape. Tool compliance partially solves the problem, although dedicated engineering design tools are strictly needed, in order to identify those optimized parameters and RD strategies that allow achieving the best quality and cost-effectiveness. In this context, the present paper proposes a CAD-based Virtual Prototype (VP) of a pneumatic compliant spindle, suitable to assess the process efficiency in different case scenarios. The proposed VP is created by integrating a 3D multi-body model of the spindle mechanical structure with the behavioural model of the process forces, as adapted from previous literature. Numerical simulations are provided, concerning the prediction of both cutting forces and surface finishing accuracy

Nonlinear vibrations and energy distribution of carbon nanotubes

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter thin shell theory is applied in order to obtain the elastic strain and kinetic energy. The carbon nanotube deformation is described in terms of axial, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is then considered to obtain a set of nonlinear ordinary differential equations. The total energy distribution of the shell is studied by considering combinations of different vibration modes. The effect of the conjugate modes is analysed

Nonlinear oscillations and energy localization in carbon nanotubes

In this paper, the low-frequency nonlinear oscillations and energy localizations of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied within the framework of the Sanders-Koiter thin shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported boundary conditions are investigated. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion which are solved using the multiple scales analytical method. The natural frequencies obtained by considering the two approaches are compared in linear field. The effect of the aspect ratio on the analytic and numerical values of the localization threshold is investigated in nonlinear field

APPLICAZIONE DELLA NORMA ISO 16792:2006 PER LA SPECIFICAZIONE GEOMETRICA DI PRODOTTO 3D IN AMBITO AUTOMOTIVE

Accanto alla documentazione tecnica di prodotto mediante disegni ed annotazioni 2D, nella pratica industriale è fortemente sentita l’esigenza di gestire le informazioni tecniche di prodotto direttamente nell’ambiente di modellazione CAD 3D. Con l’obiettivo di migliorare la gestione del ciclo di vita di prodotto tramite modelli 3D, i produttori di software CAD 3D commerciali e l’industria stessa, soprattutto in ambito automotive ed aerospace, hanno generato molteplici soluzioni che tuttavia risultano individualizzate e non univoche. La normativa tecnica ISO definisce linee guida per la specificazione geometrica di prodotto 3D, che tuttavia risultano solamente in parte accolte da un punto di vista industriale e commerciale. In questo scenario, il presente studio vuole verificare l’implementazione dei contenuti della norma ISO 16792:2006 in alcuni CAD 3D commerciali selezionati. Mediante un benchmark industriale opportunamente identificato, i CAD 3D sono comparati sulla base di criteri redatti secondo la norma ISO 16792:2006 stessa. I risultati ottenuti permettono di individuare, per ogni CAD 3D analizzato, eventuali gap operativi ed i relativi interventi volti a garantire il raggiungimento di un livello comune di applicabilità della norma e di leggibilità della documentazione tecnica 3D generata

Design and Virtual Prototyping of a Variable Stiffness Joint via Shape Optimization in a CAD/CAE Environment

During the latest decade, collaborative robots, namely machines specifically designed for the physical interaction with humans, have been gradually making their transition from laboratories to real-world applications [1]. Naturally, whenever the envisaged task would benefit form physical human-machine interaction, safety and dependability become issues of paramount importance [2]. Nonetheless, especially when dealing with collaborative operations in the manufacturing industry, safety regulations may lead the plant designer to face opposite goals. On one hand, robots should indeed be designed so as to never cause harm to people (both during regular functioning or in case of failure). On the other hand, the wide-spread use of industrial manipulators traditionally leverages on their capabilities to carry rather high payloads, while achieving a very fast and precise positioning of the end-effector. These requirements are usually pursued by coupling powerful actuation systems with extremely rigid mechanical structures, which hardly comply with safety needs whenever the workers are supposed to enter the robot workspace. Therefore, the engineering challenge when designing collaborative robotics systems, which have to be safe and efficient at the same time, is usually tackled via the following strategies: i) by enhancing the robot sensory apparatus; ii) by adopting active control strategies; iii) by reducing the inertia of any moving part employing lightweight materials whenever possible. In parallel, as previously proven by several researchers [3], another way to actually implement safe machines for collaborative tasks is to increase (rather than minimize) the inherent compliance of their mechanical structure [4], simultaneously introducing the possibility to actively vary such compliance during the robot movements. This capability can be implemented, for instance, by means of Variable Stiffness Joints (VSJ), namely particular actuation systems which allow to independently control the position of an output link along with the transmission stiffness. In light of this consideration, the present talk describes the design of a novel VSJ architecture, depicted in Fig. 1a. The VSJ can achieve stiffness modulation via the use of a pair of compliant mechanisms with distributed compliance, which act as nonlinear springs with proper torque-deflection characteristic. These elastic elements are composed of slender beams whose neutral axis is described by a spline curve with non-trivial shape. The beam geometry is determined by leveraging on a CAD/CAE framework that allows for the shape optimization of complex flexures. In particular, the design method makes use of the modeling and simulation capabilities of a parametric CAD seamlessly connected to a FEM tool. For validation purposes, proof-concept 3D printed prototypes of both elastic elements (Fig. 1a) and overall VSJ (Fig. 1b) are finally produced and tested (Fig. 1c). Experimental results fully confirm that the VSJ behaves as expected. BIBLIOGRAFY [1] Heyer, C., 2010. \u201cHuman-robot interaction and future industrial robotics applications\u201d. Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4749\u20134754. [2] Fryman, J., and Matthias, B., 2012. \u201cSafety of industrial robots: From conventional to collaborative applications\u201d. Proceeding of ROBOTIK, 7th German Conference on Robotics, May, pp. 1\u20135. [3] Bicchi, A., and Tonietti, G., 2004. \u201cFast and soft arm tactics: Dealing with the safety-performance trade-off in robot arms design and control\u201d. IEEE Robotics and Automation Magazine, 11(2), pp. 22\u201333. [4] Berselli, G., Guerra, A., Vassura, G., and Andrisano, A. O., 2014. \u201cAn engineering method for comparing selectively compliant joints in robotic structures\u201d. IEEE/ASME Transactions on Mechatronics, 19(6), pp. 1882\u20131895