On application of Newton’s law to mechanical systems with motion constraints

Paraskevopoulos, Elias; Natsiavas, S.

doi:10.1007/s11071-012-0727-1

Cited by 32 publications

(58 citation statements)

References 19 publications

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“…When inertial Cartesian coordinates are used, the metric of this space involves only constant diagonal elements, while all the affinities vanish [19]. Furthermore, even when general curvilinear coordinates are used, the geometric properties of this manifold may depend on the position on the manifold but they do not depend on time explicitly.…”

Section: Geometric Properties Of Event Manifold -Application Of Newtomentioning

confidence: 99%

“…(19). Such bases will be referred to as separable bases of p T M (or M , for simplicity) in the sequel.…”

Section: Nmentioning

confidence: 99%

“…where the n m × matrix N and the n -vector υ are determined in terms of the elements of the k n × matrix A and the k -vector a [12,19]. To overcome the loss of linearity, due to the presence of the term υ , the last equation is put in the form of a linear transformation between the tangent spaces …”

Section: Application Of a Special Coordinate Transformation On The Evmentioning

confidence: 99%

“…Finally, another advantage of the present approach is that the affinities are independent and not derived from the metric components (i.e., the connection is not necessarily metric compatible). This allows for the most general and consistent derivation of the equations of motion [19].…”

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: 97%

See 4 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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Section: Geometric Properties Of Event Manifold -Application Of Newtomentioning

confidence: 99%

“…(19). Such bases will be referred to as separable bases of p T M (or M , for simplicity) in the sequel.…”

Section: Nmentioning

confidence: 99%

Section: Application Of a Special Coordinate Transformation On The Evmentioning

confidence: 99%

Section: Equations Of Motion On the Configuration Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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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Extended Modified Bridge System (EMBS) method for decoupling seismic vehicle‐bridge interaction

Homaei,

Stoura,

Dimitrakopoulos

2024

Earthq Engng Struct Dyn

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Seismic vehicle‐bridge interaction (SVBI) is the study of vehicle‐bridge interaction (VBI) in the presence of earthquake excitation. SVBI is an interdisciplinary problem of increasing importance to the design and safety of railways. This study deploys a consistent methodology to decouple the vehicle‐bridge system and solve independently the bridge and vehicle subsystems, bypassing multiple challenges the seismic response analysis of a coupled vehicle‐bridge system entails. The proposed approach builds upon the previously established Extended Modified Bridge System (EMBS) method for decoupling vehicle‐bridge systems (in the absence of earthquake excitation). Its premise is to first characterize and then assess the relative importance of the VBI effect on the bridge and vehicle responses and replicate it by modifying the pertinent uncoupled equations of motion (EOMs). The formulation deployed accommodates multi‐degree of freedom models for both the vehicle and bridge and can thus tackle complex systems. The analysis examines the ability of the proposed decoupling approach to predict the response of a realistic system vehicle‐bridge system under a suit of historical earthquake records. The decoupled results are in excellent agreement with the coupled solutions for all earthquake records and scenarios (i.e., earthquake excitation solely in the transverse direction of the bridge, as well as in both the transverse and vertical directions simultaneously).

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On application of Newton’s law to mechanical systems with motion constraints

Cited by 32 publications

References 19 publications

Equations of Motion for Mechanical Systems Subject to Acatastatic Constraints

Equations of Motion for Mechanical Systems Subject to Acatastatic Constraints

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

Extended Modified Bridge System (EMBS) method for decoupling seismic vehicle‐bridge interaction

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