Author

# Marco Amabili

Other affiliations: University of Parma

Bio: Marco Amabili is an academic researcher from McGill University. The author has contributed to research in topics: Nonlinear system & Equations of motion. The author has an hindex of 61, co-authored 314 publications receiving 11779 citations. Previous affiliations of Marco Amabili include University of Parma.

##### Papers published on a yearly basis

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01 Aug 2014

TL;DR: In this article, a comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells is presented. But the authors do not consider the effect of boundary conditions on the large-amplitude vibrations of circular cylinders.

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

862 citations

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374 citations

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TL;DR: In this article, the nonlinear forced vibrations of a microbeam are investigated by employing the strain gradient elasticity theory, and the geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach.

Abstract: The nonlinear forced vibrations of a microbeam are investigated in this paper, employing the strain gradient elasticity theory. The geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach. Specifically, Hamilton’s principle is used to derive the nonlinear partial differential equation governing the motion of the system which is then discretized into a set of second-order nonlinear ordinary differential equations (ODEs) by means of the Galerkin technique. A change of variables is then introduced to this set of second-order ODEs, and a new set of ODEs is obtained consisting of first-order nonlinear ordinary differential equations. This new set is solved numerically employing the pseudo-arclength continuation technique which results in the frequency–response curves of the system. The advantage of this method lies in its capability of continuing both stable and unstable solution branches.

253 citations

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TL;DR: In this paper, the nonlinear resonant dynamics of a microscale beam is studied numerically by means of the pseudo-arclength continuation technique, which is capable of continuing both the stable and unstable solution branches as well as determining different types of bifurcations.

Abstract: In the present study, the nonlinear resonant dynamics of a microscale beam is studied numerically. The nonlinear partial differential equation governing the motion of the system is derived based on the modified couple stress theory, employing Hamilton’s principle. In order to take advantage of the available numerical techniques, the Galerkin method along with appropriate eigenfunctions are used to discretize the nonlinear partial differential equation of motion into a set of nonlinear ordinary differential equations with coupled terms. This set of equations is solved numerically by means of the pseudo-arclength continuation technique, which is capable of continuing both the stable and unstable solution branches as well as determining different types of bifurcations. The frequency–response curves of the system are constructed. Moreover, the effect of different system parameters on the resonant dynamic response of the system is investigated.

247 citations

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TL;DR: In this paper, the authors investigated the nonlinear size-dependent behavior of an electrically actuated MEMS resonator based on the modified couple stress theory; the microbeam is excited by an AC voltage which is superimposed on a DC voltage.

Abstract: The present study investigates the nonlinear size-dependent behaviour of an electrically actuated MEMS resonator based on the modified couple stress theory; the microbeam is excited by an AC voltage which is superimposed on a DC voltage. A high-dimensional reduced order model of the continuous system is obtained by applying the Galerkin scheme to the nonlinear partial differential equation of motion. The pseudo-arclength continuation technique is employed to examine the nonlinear static and dynamic behaviour of the system. Specifically, the nonlinear static behaviour of the system is investigated when the microbeam is excited by the electrostatic excitation (DC voltage); this analysis yields the static deflected configuration of the system and the value of the DC voltage corresponding to the static pull-in instability. The size-dependent dynamic behaviour of the system is examined under primary and superharmonic excitations; the frequency- and force-response curves of the system as well as time histories and phase-plane portraits are constructed. Moreover, the effect of taking into account the length-scale parameter on the static and dynamic behaviour of the system is examined by comparing the results obtained by means of the classical and modified couple stress theories.

246 citations

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01 Mar 1995

TL;DR: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series and results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages.

Abstract: : This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

1,545 citations

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1,524 citations

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TL;DR: 5. M. Green, J. Schwarz, and E. Witten, Superstring theory, and An interpretation of classical Yang-Mills theory, Cambridge Univ.

Abstract: 5. M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987. 6. J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464. 7. B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometric Methods in Mathematicas Physics, Lecture Notes in Math., vol. 570, SpringerVerlag, Berlin and New York, 1977. 8. C. LeBrun, Thickenings and gauge fields, Class. Quantum Grav. 3 (1986), 1039-1059. 9. , Thickenings and conformai gravity, preprint, 1989. 10. C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Commun. Math. Phys. 117(1988), 159-176. 11. Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245. 12. R. Penrose and W. Rindler, Spinors and space-time, V.2, spinor and twistor methods in space-time geometry, Cambridge Univ. Press, 1986. 13. R. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. 14. E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398. 15. , Twistor-like transform in ten dimensions, Nucl. Phys. B266 (1986), 245-264. 16. , Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267302, Amer. Math. Soc, Providence, R.I., 1987.

1,252 citations

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1,191 citations

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TL;DR: In this article, a review of the past and recent developments in system identification of nonlinear dynamical structures is presented, highlighting their assets and limitations and identifying future directions in this research area.

Abstract: This survey paper contains a review of the past and recent developments in system identification of nonlinear dynamical structures. The objective is to present some of the popular approaches that have been proposed in the technical literature, to illustrate them using numerical and experimental applications, to highlight their assets and limitations and to identify future directions in this research area. The fundamental differences between linear and nonlinear oscillations are also detailed in a tutorial.

1,000 citations