Mathematical Models for Suspension Bridges

Gazzola, Filippo

doi:10.1007/978-3-319-15434-3

Cited by 95 publications

(91 citation statements)

References 133 publications

(270 reference statements)

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“…where the function y is as in (3). Let H be the dual space of H 2 ∩ H 1 0 (0, L); we denote by · H the H-norm and by ·, · the corresponding duality between…”

Section: Resultsmentioning

confidence: 99%

“…For the history and the details on the derivation of the Melan equation we also refer to the recent monograph [3].…”

Section: How To Derive the Melan Equation From A Variational Principlementioning

confidence: 99%

“…The Euler-Lagrange equation of the system is obtained by taking the critical points of the energy E. Then by recalling (3) and that the beam is hinged at its endpoints, we obtain the following boundary value problem…”

Section: How To Derive the Melan Equation From A Variational Principlementioning

confidence: 99%

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Variational formulation of the Melan equation

Gazzola

Wang

Pavani

2016

Math Methods in App Sciences

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The Melan beam equation modeling suspension bridges is considered. A slightly modified equation is derived by applying variational principles and by minimising the total energy of the bridge. The equation is nonlinear and nonlocal, while the beam is hinged at the endpoints. We show that the problem always admits at least one solution whereas the uniqueness remains open although some numerical results suggest that it should hold. We also emphasize the qualitative difference with some simplified models.

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“…where the function y is as in (3). Let H be the dual space of H 2 ∩ H 1 0 (0, L); we denote by · H the H-norm and by ·, · the corresponding duality between…”

Section: Resultsmentioning

confidence: 99%

“…For the history and the details on the derivation of the Melan equation we also refer to the recent monograph [3].…”

Section: How To Derive the Melan Equation From A Variational Principlementioning

confidence: 99%

See 1 more Smart Citation

Variational formulation of the Melan equation

Gazzola

Wang

Pavani

2016

Math Methods in App Sciences

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“…In all those cases, a common phenomenon was observed, as said in [32]: suspension bridges may suffer large oscillations that can appear suddenly.…”

Section: Conclusion On the Fluid-structure Interaction Consequencesmentioning

confidence: 94%

“…Usually noted F R , this number can be written as: 32) where U 0 is the reference flow velocity, g the gravity field and L the characteristic length.…”

Section: Froude Numbermentioning

confidence: 99%

Coupled Systems in Mechanics: Fluid Structure Interactions

FOINY¹

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Gaining Insights into the Interplay between Optical and Magnetic Properties in Photoexcited Coordination Compounds

Braun,

Powell,

Unterreiner

2024

Chemistry A European J

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We describe early and recent advances in the fascinating field of combined magnetic and optical properties of inorganic coordination compounds and in particular of 3d‐4f single molecule magnets. We cover various applied techniques which allow for the correlation of results obtained in the frequency and time domain in order to highlight the specific properties of these compounds and the future challenges towards multidimensional spectroscopic tools. An important point is to understand the details of the interplay of magnetic and optical properties through performing time‐resolved studies in the presence of external fields especially magnetic ones. This will enable further exploration of this fundamental interactions i.e. the two components of electromagnetic radiation influencing optical properties.

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Mathematical Models for Suspension Bridges

Cited by 95 publications

References 133 publications

Variational formulation of the Melan equation

Variational formulation of the Melan equation

Coupled Systems in Mechanics: Fluid Structure Interactions

Gaining Insights into the Interplay between Optical and Magnetic Properties in Photoexcited Coordination Compounds

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