Nonlinear Dynamics

, Volume 97, Issue 4, pp 2201–2218 | Cite as

Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass

  • M. Ferretti
  • S. N. Gavrilov
  • V. A. Eremeyev
  • A. LuongoEmail author
Original paper


The planar response of horizontal massive taut strings, travelled by a heavy point-mass, either driven by an assigned force, or moving with an assigned law, is studied. A kinematically exact model is derived for the free boundary problem via a variational approach, accounting for the singularity in the slope of the deflected string. Reactive forces exchanged between the point-mass and the string are taken into account via Lagrange multipliers. The exact model is consistently simplified via asymptotic analysis, which leads to condense the horizontal displacement as a passive variable. The dynamic increment of tension, with respect the static one, is neglected in the governing equations, but evaluated a posteriori, as a higher-order quantity in a perturbation perspective. The equations are solved and rearranged in the form of an integral equation coupled with an integro-differential equation, thus extending a procedure already introduced in the literature. Numerical results, showing the importance of the horizontal reactive force on the quality of motion, are discussed, generalizing those relevant to massless strings.


Traveling mass Taut string Free boundary problem Nonlinear contact force Integral equation 



V.A.E. acknowledges the support of the Government of the Russian Federation (contract No. 14.Y26.31.0031).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest to declare.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.International Research Center on Mathematics and Mechanics of Complex SystemsUniversity of L’AquilaL’AquilaItaly
  2. 2.Department of Civil, Construction-Architectural and Environmental EngineeringUniversity of L’AquilaL’AquilaItaly
  3. 3.Institute for Problems in Mechanical Engineering RASSt. PetersburgRussia
  4. 4.Peter the Great St. Petersburg Polytechnic University (SPbPU)St. PetersburgRussia
  5. 5.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  6. 6.Research Institute for MechanicsNational Research Lobachevsky State University of Nizhni NovgorodNizhni NovgorodRussia

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