Nonlinear Multiple Degrees of Freedom Model for Tuned Liquid Damper


This paper investigates new nonlinear mechanical model for sloshing liquid in liquid damper to mitigate vibrations. The proposed nonlinear model consists of successive multiple liquid damped masses, which are connected in series. Governing differential equations are derived and are solved using the Fourier expansion-based differential quadrature method. Verification is carried out with a single degree of freedom, traditional model, also the verification with experimental dynamic responses is carried out. Studying model accuracy is executed considering different filling ratios and different liquids’ physical properties. The new model shows a good agreement with experimental results, where the results become more close to experimental results than earlier model. The efficiency of the new proposed model raises as the filling ratio increases, also as the liquid viscosity increases the results of the new proposed model become closer to the experimental results than the earlier double degrees of freedom model.

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c P :

Damping coefficient for platform

c d, c di :

Damping coefficients for sloshing mass

k d, k di :

Equivalent stiffness of tuned masses damper

k P :

Equivalent stiffness of platform

m d, m di :

Active liquid masses

m S :

Stationary liquid mass

m P :

Mass of structure (platform and empty tank mass)

N :

The number of used grid points

n :

The number of used damped masses

t m :


\(W_{ij}^{n}\) :

The weighting coefficients

x :

Displacement of platform

x 1 :

Displacement of active mass of liquid (m)


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Correspondence to Ahmad Salah Edeen Nassef.

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Nassef, A.S.E., Abdelhamid, A. Nonlinear Multiple Degrees of Freedom Model for Tuned Liquid Damper. Iran J Sci Technol Trans Mech Eng (2021).

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  • Sloshing
  • Differential quadrature
  • Tuned liquid damper
  • Dynamic response
  • Multiple degrees of freedom