Energy and Nonlinear Dynamics of Hybrid Systems

Katica, R. (Stevanović) Hedrih

doi:10.1007/978-1-4614-0454-5_2

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…In References [30][31][32][33][34][35] series of mass particle motion along smooth or rough curvilinear line are studied and result presented.…”

Section: Vibro-impact Dynamics Of Multiple Collisions Of Two Difmentioning

confidence: 99%

“…For that reason expression of the momentary angular velocity of rolling ball is necessary to express by generalized coordinate 1  in the following form: (35) and for next impact angular velocity of each of the rolling balls depends of the outgoing angular velocity in previous collision of the balls…”

Section: Iii1 Kinetc Parameters Of a Rolling Heavy Ball Motion Alonmentioning

confidence: 99%

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Central collision of two rolling balls: theory and examples

Hedrih¹

2017

atam

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Paper is focused to central collision of two rolling rigid and heavy smooth balls and using elements of mathematical phenomenology and phenomenological mapping obtain corresponding post collision and outgoing angular velocities of the balls and applied these results for investigation vibro-impact dynamics of two rolling balls along circle trace. This task is fully solved and obtained results are original and new! Original plans of component impact velocities and angular velocity of each of two different rolling balls in central collision and corresponding outgoing angular velocities are presented. Use Petroviċ's elements of mathematical phenomenology, especially mathematical analogy between kinetic parameters of collision of two bodies in translator motion and collision of two rolling different size balls, new original expressions of two outgoing angular velocities for each of rolling balls after collision are defined. Using this new and original result vibro-impact dynamics of two rolling different heavy balls on the circle trace in vertical plane in period of series collisions is investigated. Use series of the elliptic integrals, new nonlinear equations for obtaining angles of balls positions at positions of collisions are defined. Branches of phase trajectories of the balls in vibro-impact dynamics are theoretically presented.

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“…In References [30][31][32][33][34][35] series of mass particle motion along smooth or rough curvilinear line are studied and result presented.…”

Section: Vibro-impact Dynamics Of Multiple Collisions Of Two Difmentioning

confidence: 99%

Section: Iii1 Kinetc Parameters Of a Rolling Heavy Ball Motion Alonmentioning

confidence: 99%

Central collision of two rolling balls: theory and examples

Hedrih¹

2017

atam

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“…by Hedrih (Stevanovi c) K.R., the contributions of author to linear and nonlinear dynamics of deformable bodies (rods, beams, plates, axially moving strips), systems of coupled subsystems and deformable bodies, especially stand out and can be classifies as a single scientific area of Elastodynamics and the newly established area of hybrid system dynamics (see Refereces 1,8,[23][24][25][26][27][28][29][30][31] Five theorems on characteristic equations of hybrid system dynamics with complex structure, obtained by coupling deformable bodies and discrete systems with finite number of degrees of freedom, free or forced dynamic or combined couples have been defined and proven. 24,28,29,[31][32][33][34][35][36][37][38] A number of results are on the energy analysis of complex hybrid system dynamics. 12,13,20,24,27,31,33,35,[39][40][41] In Hedrih (Stevanovi c) and Simonovi c [42][43][44][45][46][47][48][49][50][51] published in period in 2008-2013, and late publi...…”

Section: Introductionmentioning

confidence: 99%

“…24,28,29,[31][32][33][34][35][36][37][38] A number of results are on the energy analysis of complex hybrid system dynamics. 12,13,20,24,27,31,33,35,[39][40][41] In Hedrih (Stevanovi c) and Simonovi c [42][43][44][45][46][47][48][49][50][51] published in period in 2008-2013, and late published Simonovi c [52][53][54] as well as in monographs published by Kluwer and Springer and other contributions of author and coauthors to linear and nonlinear dynamics of deformable bodies (rods, beams, plates, moving strips) can be classified as systems of coupled subsystems and deformable bodies. [55][56][57][58][59][60][61][62][63][64][65][66][6...…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear dynamics of hybrid systems

Hedrih

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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Discrete continuum method for investigation of linear and nonlinear dynamics of hybrid systems containing coupled multi deformable bodies is presented. By use coupled rods, beams, strings, plates and membranes by discrete continuum mass less layers as well as layers with translator and rotator inertia properties into series of hybrid system dynamics are investigated and phenomenological mappings in dynamics of these different real systems are identified. Expressions of generalized forces of subsystem interactions in hybrid system are presented by component mechanical energies and functions of energy dissipations. A model of dynamical dislocations with inertia properties in plate is presented. Transfer energy between subsystems is investigated. Constitutive relation of standard elements of discrete continuum coupling layers with translator and rolling inertia properties, nonlinear elastic and fractional order properties are presented. Interaction between two coupled linear and nonlinear system, each with one degree of freedom as well as dynamics of discrete no homogeneous chain are considered in the light of mathematical analogy for obtaining eigen time functions of solutions of component deformable body displacements in hybrid system dynamics. For pointing out the major contributions outlined in the manuscript it is necessary to add: The manuscript contains reviews on results obtained of a few scientific problems of nonlinear dynamics, namely, for stochastic stability of vibration modes of a parametrically excited sandwich beam, transversal vibrations of axially moving double belt system, multi deformable bodies coupled by standard light fractional type discrete continuum layers. New model of dynamical dislocation in continuum is proposed and analyzed Series of the original results of author’s doctorates supervised is listed.

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Nonlinear Phenomena in the Dynamics of a Class of Rolling Pendulums: A Trigger of Coupled Singularities

(Stevanović) Hedrih

2022

Springer Proceedings in Complexity

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Energy and Nonlinear Dynamics of Hybrid Systems

Cited by 6 publications

References 26 publications

Central collision of two rolling balls: theory and examples

Central collision of two rolling balls: theory and examples

Linear and nonlinear dynamics of hybrid systems

Nonlinear Phenomena in the Dynamics of a Class of Rolling Pendulums: A Trigger of Coupled Singularities

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