12 The Dynamics of Eccentric Vibration Mechanism (Part 2)
189
dell’Isola F., Seppecher P., Madeo A. How contact interactions may depend on the shape of
Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte
Mathematik und Physik, 2012, 63(6)
Feigin M.I. Forced oscillations of systems with discontinuous nonlinearities. M.:Nauka, 1994.
–p. 288 (in Russian).
Giorgio I. Numerical identification procedure between a micro-Cauchy model and a macro-second
gradient model for planar pantographic structures. Zeitschrift für angewandte Mathematik und
Physik, 2016
Goebel, R., Sanfelice, R. G., & Teel, A. R. (2008). Invariance principles for switching systems via
hybrid systems techniques. Systems and Control Letters, 57, 980–986.
Igumnov, L. A., Metrikin, V. S., & Nikiforova, I. V. (2017). The dynamics of eccentric vibration
mechanism (Part 1). JVE Journal of Vibroengineering, 19, 4816–5656.
Ing, J., Pavlovskaia, E. E., Wiercigroch, M., & Banerjee, S. (2010). Bifurcation Analysis of Impact
Oscillator with One-Sided Elastic Constraint. Physica D: Nonlinear Phenomena, 239(3), 12–321.
Kernighan B.W., Ritchie D.M. The C programming language. Wilyams, 2016. – p.288.
Kobrinskiy A. A., Kobrinskiy A. E.Vibro-Impact Systems. Science, 1973, p. 592, (in Russian).
Leine, R. I., & Heimsch, T. F. (2012). Global uniform symptotic attractive stability of the nonautonomous bouning ball system. Journal Physica, 241, 2029–2041.
Liu, Y., Pavlovskaia, E. E., Wiercigroch, M., & Peng, Z. K. (2015). Forward and Backward Motion
Control of a Vibro-Impact Capsule System. Int. J. Non-LinearMech., 70, 30–46.
Luo, G. W., & Ma, X. H. L. (2008). Periodic – impact motions and bifurcations in dynamics of a
plastic impact oscillator with a frictional slider. Journal Mechanics a/Solids, 27, 1088–1107.
Masri, S. F., & Caughey, T. K. (1966). On the stability of the impact damper. Journal of Applied
Mechanics, 33(3), 586–592.
Nagaev R.F. Periodic modes of vibration motion. M.: Nauka, 1978. – p. 160, (in Russian).
Neimark Yu. I. The point mapping method in the theory of nonlinear oscillations. M.: LIBROKOM,
2010. – p. 472, (in Russian).
Pavloaskaia, E., & Wiercigroch, M. (2003). Periodic solution finder for an impact oscillator with a
drift. Journal of Sound and Vibration, 267(4), 893–911.
Pavlovskaia E., Hendry D.C., WiercigrochM. Modelling of high frequency vibro-impact drilling,
Int. J. Mech. Sci. 91. 2015, p. 110–119.
Placidi L., Andreaus U., Giorgio I., Identification of two-dimensional pantographic structure via a
linear D4 orthotropic second gradient elastic model. Journal of Engineering Mathematics, 2017
Placidi L., Barchiesi E., Turco E., Rizzi N.L. A review on 2D models for the description of
pantographic fabrics. Zeitschrift für angewandte Mathematik und Physik, 2016, 67(5)
Rahali Y., Giorgio I., Ganghoffer J.-F., dell’Isola F. Homogenization à la Piola produces second
gradient continuum models for linear pantographic lattices. International Journal of Engineering
Science, 2015, 97
Shilkov V. A., Savalyuk A. D., Metrikin V. S., Polyakov A. A., Shabardin A. K., Alyokhin A. I.,
OmenenkoiYaA.c. 1020479 USSR, A Vibro-ram, No. 3376593/29–33, 2005, (in Russian)
Stroustrup B. The C++ programming language. Binom, 2011. – p.1136.
Turco E., Dell’Iola F., Cazzani A., Rizzi N.L. Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Zeitschrift für angewandte
Mathematik und Physik, 2016
Tusset, A. M., Janzen, F. C., Piccirillo, V., Rocha, R. T., Balthazar, J. M. and Litak, G. (2017). On
nonlinear dynamics of a parametrically excited pendulum using both active control and passive
rotational (MR) damper. Journal of Vibration and Control, 24(9), 1587–1599,
Vagapov, I. K., Ganiev, M. M., & Shinkarev, A. S. (2007). Forced vibrations of two nonlinearly
connected solid waveguides under static load. Journal of Sound and Vibration, 302, 425–141.
((in Russian)).
Vagapov, I. K., Ganiyev, M. M., & Shinkaryov, A. S. (2008). Theoretically and experimentally
investigating the dynamics of an ultrasonic vibro-impact system with an intermediate striker.
Mechanical Engineering, 5, 3–24. ((in Russian)).
189
dell’Isola F., Seppecher P., Madeo A. How contact interactions may depend on the shape of
Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte
Mathematik und Physik, 2012, 63(6)
Feigin M.I. Forced oscillations of systems with discontinuous nonlinearities. M.:Nauka, 1994.
–p. 288 (in Russian).
Giorgio I. Numerical identification procedure between a micro-Cauchy model and a macro-second
gradient model for planar pantographic structures. Zeitschrift für angewandte Mathematik und
Physik, 2016
Goebel, R., Sanfelice, R. G., & Teel, A. R. (2008). Invariance principles for switching systems via
hybrid systems techniques. Systems and Control Letters, 57, 980–986.
Igumnov, L. A., Metrikin, V. S., & Nikiforova, I. V. (2017). The dynamics of eccentric vibration
mechanism (Part 1). JVE Journal of Vibroengineering, 19, 4816–5656.
Ing, J., Pavlovskaia, E. E., Wiercigroch, M., & Banerjee, S. (2010). Bifurcation Analysis of Impact
Oscillator with One-Sided Elastic Constraint. Physica D: Nonlinear Phenomena, 239(3), 12–321.
Kernighan B.W., Ritchie D.M. The C programming language. Wilyams, 2016. – p.288.
Kobrinskiy A. A., Kobrinskiy A. E.Vibro-Impact Systems. Science, 1973, p. 592, (in Russian).
Leine, R. I., & Heimsch, T. F. (2012). Global uniform symptotic attractive stability of the nonautonomous bouning ball system. Journal Physica, 241, 2029–2041.
Liu, Y., Pavlovskaia, E. E., Wiercigroch, M., & Peng, Z. K. (2015). Forward and Backward Motion
Control of a Vibro-Impact Capsule System. Int. J. Non-LinearMech., 70, 30–46.
Luo, G. W., & Ma, X. H. L. (2008). Periodic – impact motions and bifurcations in dynamics of a
plastic impact oscillator with a frictional slider. Journal Mechanics a/Solids, 27, 1088–1107.
Masri, S. F., & Caughey, T. K. (1966). On the stability of the impact damper. Journal of Applied
Mechanics, 33(3), 586–592.
Nagaev R.F. Periodic modes of vibration motion. M.: Nauka, 1978. – p. 160, (in Russian).
Neimark Yu. I. The point mapping method in the theory of nonlinear oscillations. M.: LIBROKOM,
2010. – p. 472, (in Russian).
Pavloaskaia, E., & Wiercigroch, M. (2003). Periodic solution finder for an impact oscillator with a
drift. Journal of Sound and Vibration, 267(4), 893–911.
Pavlovskaia E., Hendry D.C., WiercigrochM. Modelling of high frequency vibro-impact drilling,
Int. J. Mech. Sci. 91. 2015, p. 110–119.
Placidi L., Andreaus U., Giorgio I., Identification of two-dimensional pantographic structure via a
linear D4 orthotropic second gradient elastic model. Journal of Engineering Mathematics, 2017
Placidi L., Barchiesi E., Turco E., Rizzi N.L. A review on 2D models for the description of
pantographic fabrics. Zeitschrift für angewandte Mathematik und Physik, 2016, 67(5)
Rahali Y., Giorgio I., Ganghoffer J.-F., dell’Isola F. Homogenization à la Piola produces second
gradient continuum models for linear pantographic lattices. International Journal of Engineering
Science, 2015, 97
Shilkov V. A., Savalyuk A. D., Metrikin V. S., Polyakov A. A., Shabardin A. K., Alyokhin A. I.,
OmenenkoiYaA.c. 1020479 USSR, A Vibro-ram, No. 3376593/29–33, 2005, (in Russian)
Stroustrup B. The C++ programming language. Binom, 2011. – p.1136.
Turco E., Dell’Iola F., Cazzani A., Rizzi N.L. Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Zeitschrift für angewandte
Mathematik und Physik, 2016
Tusset, A. M., Janzen, F. C., Piccirillo, V., Rocha, R. T., Balthazar, J. M. and Litak, G. (2017). On
nonlinear dynamics of a parametrically excited pendulum using both active control and passive
rotational (MR) damper. Journal of Vibration and Control, 24(9), 1587–1599,
Vagapov, I. K., Ganiev, M. M., & Shinkarev, A. S. (2007). Forced vibrations of two nonlinearly
connected solid waveguides under static load. Journal of Sound and Vibration, 302, 425–141.
((in Russian)).
Vagapov, I. K., Ganiyev, M. M., & Shinkaryov, A. S. (2008). Theoretically and experimentally
investigating the dynamics of an ultrasonic vibro-impact system with an intermediate striker.
Mechanical Engineering, 5, 3–24. ((in Russian)).