A set of ordinary differential equations of motion for constrained mechanical systems

Natsiavas, S.; Paraskevopoulos, Elias

doi:10.1007/s11071-014-1783-5

Cited by 32 publications

(46 citation statements)

References 24 publications

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“…This presents certain advantages when compared to classical approaches leading to a set of differential algebraic equations, instead. It also exhibits better characteristics than previous methods leading to sets of ordinary differential equations through elimination of motion constraints or Lagrange multipliers [2,15]. Finally, for the special case of scleronomic systems, the equations of motion derived are shown to become identical with a similar set of equations obtained earlier [15].…”

Section: Introductionmentioning

confidence: 74%

“…The derivation of the equations of motion is based on a consistent application of Newton's law of motion, similar to that performed in an earlier study [15]. One of the basic ideas in that study was to consider the configuration manifold M as the total space of a fiber bundle with base space A M and fibers consisting of the Cartesian product manifold …”

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

“…Following the analysis presented in [15], by incorporating the above modifications into the constraint equations and omitting the details, the equations of motion can be put in the form…”

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

“…The additional information needed for a complete mathematical formulation is obtained by incorporating an appropriate form of the k equations of the constraints. In particular, proceeding in a manner similar to that followed in previous work [15], a second order ordinary differential equation (ODE) is obtained for each holonomic constraint, with form…”

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

“…The present study is an extension of recent work of the authors on scleronomic systems [15,19]. Again, the emphasis is put on explaining several demanding theoretical aspects, which are of keen interest to the engineering community.…”

Section: Introductionmentioning

confidence: 96%

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Equations of Motion for Mechanical Systems Subject to Acatastatic Constraints

Paraskevopoulos¹,

Natsiavas²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Section: Introductionmentioning

confidence: 74%

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

“…Following the analysis presented in [15], by incorporating the above modifications into the constraint equations and omitting the details, the equations of motion can be put in the form…”

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 3 more Smart Citations

Equations of Motion for Mechanical Systems Subject to Acatastatic Constraints

Paraskevopoulos¹,

Natsiavas²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Seismic fragility analysis of railway reinforced concrete bridges considering real‐time vehicle‐bridge interaction with the aid of co‐simulation techniques

Paraskevopoulos

2022

Earthq Engng Struct Dyn

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Based on past earthquake events, bridges are the most critical and most vulnerable component of road and rail transport systems, while bridge damage is related to substantial direct and indirect losses. For the case of railway bridges, the estimation of seismic fragility is a rather complex and computationally demanding procedure given the real-time interaction of the train movement and the bridge and the different failure modes of subsystems. Considering vehicle-bridge interaction (VBI) in the frame of railway bridge fragility analysis is rather challenging, requiring analysis of the bridge and the vehicle at every time step. Partitioning of the coupled VBI problem proposing a weak formulation scheme and a set of second-order ordinary differential equations (ODEs) is performed in a way that allows for independent subsystem (vehicle and bridge) analysis. Several methodologies are available in the literature to estimate the seismic fragility of train-bridge systems that ignore the nonlinear behavior of the bridge during earthquake loading, the step-by-step VBI, and the different failure modes of critical components. The scope of this research paper is to propose a real-time component-based methodology for estimating bridge fragility curves, considering all critical components and failure modes of subsystems. The two subsystems are incorporated in a uniform software platform using the co-simulation approach and a Gauss-Seidel communication pattern. The vehicle-rail system is solved using a C++ tailor-made code, including a mathematical formulation that is based on the description of the constrained problem with a set of pure ODEs, avoiding issues related to differential-algebraic equations, constraint violation, drifts, energy loss, stability, and convergence. The vehicle subsystem is solved using multibody dynamics (MBD), while the bridge subsystem is modeled and solved using OpenSees.py. An ad-hoc software for the implementation of the probabilistic framework and the derivation of fragility curves is developed in Python. A novel methodological procedure is proposed, dully tailored to the demanding estimation of fragility curves of the coupled vehicle-bridge problem.The step-by-step solution of subsystems is performed using the co-simulation technique. Real-time interaction is allowed, considering a rational transfer of

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