Parachute System with elastic top cords forced vibrations

Theoretical mechanics


Churkin V. M.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The paper considers parachute system with elastic top cords forced vibrations in a vertical plane. While setting the equations of motion the parachute canopy is considered as a symmetrical solid body. The top cords are modeled as two linear weightless springs, and the weight — as a point mass. Disturbing action causing these vibrations is presented as an additional component of the parachute canopy pressure center velocity vector directed horizontally and changed according to harmonic law.

The parachute system with elastic top cords forced vibrations is analyzed with methodology, implemented earlier for studies of forced vibrations of a parachute system model with unchangeable geometry and a model with pivotally suspended weight. The parachute system vibrations are considered in frequency range of the fundamental resonance. It is assumed that the parachute canopy is made of the cloth with low permeability, and, hence, the parachute canopy aerodynamic force normal component is described by highly nonlinear dependence from parachute canopy angle of incidence. While generation of equations of parachute system disturbed motion, harmonic linearization of this non-linear dependence is performed. The equations obtained are separated into two systems: with constant and varying components of desired solutions. We obtain the values of vibrations shift, while the system with varying components is used to obtain amplitude and phase, corresponding to the specified frequency of the desired vibrations. The results obtained allow plotting the amplitude-phase-frequency characteristic of a parachute system.


parachute system, elastic straps, forced vibrations, harmonic linearization , parameters of the vibrational modes


  1. Churkin V.M. Dinamika parashyutnykh sistem na etape spuska (Dynamics of parachute systems during descent), Moscow, Izd-vo MAI-PRINT, 2008, 184 p.

  2. Popov E.P., Pal’tov I.P. Priblizhennye metody issledovaniya nelineinykh atomaticheskikh system (Approximate methods for the study of nonlinear atumatic systems), Moscow, Fizmatgiz, 1960, 792 p.

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