A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Nonlinear Vibrations of Orthotropic Viscoelastic Plates with a Concentrated Mass
The article considers the nonlinear vibrations of orthotropic viscoelastic rectangular plates with a concentrated mass. In the calculations, the mass is considered rigidly fixed and concentrated at points. The classical Kirchhoff-Love theory is used to derive the equations describing the stress-strain state of the plates. When composing the equations for the equilibrium of the plate, the effect of a concentrated mass is taken into account using the Dirac delta function. With the Bubnov-Galerkin method, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations of Volterra type with a Koltunov-Rzhanitsyn singular kernel. To solve the resulting system, a numerical method based on the use of quadrature formulas is applied. The amplitude-frequency response of vibrations was investigated for various values of geometrical and physical-mechanical parameters of the plate. The calculation of nonlinear vibrations of orthotropic viscoelastic rectangular plates with concentrated masses showed that an increase in the concentrated mass leads to a more intense decrease in the vibration amplitude as compared to the elastic plate.
Nonlinear Vibrations of Orthotropic Viscoelastic Plates with a Concentrated Mass
The article considers the nonlinear vibrations of orthotropic viscoelastic rectangular plates with a concentrated mass. In the calculations, the mass is considered rigidly fixed and concentrated at points. The classical Kirchhoff-Love theory is used to derive the equations describing the stress-strain state of the plates. When composing the equations for the equilibrium of the plate, the effect of a concentrated mass is taken into account using the Dirac delta function. With the Bubnov-Galerkin method, the problem is reduced to solving a system of ordinary nonlinear integro-differential equations of Volterra type with a Koltunov-Rzhanitsyn singular kernel. To solve the resulting system, a numerical method based on the use of quadrature formulas is applied. The amplitude-frequency response of vibrations was investigated for various values of geometrical and physical-mechanical parameters of the plate. The calculation of nonlinear vibrations of orthotropic viscoelastic rectangular plates with concentrated masses showed that an increase in the concentrated mass leads to a more intense decrease in the vibration amplitude as compared to the elastic plate.
Nonlinear Vibrations of Orthotropic Viscoelastic Plates with a Concentrated Mass
Lecture Notes in Civil Engineering
Vatin, Nikolai (editor) / Borodinecs, Anatolijs (editor) / Teltayev, Bagdat (editor) / Vatin, Nikolai (author) / Abdikarimov, Rustamkhan (author) / Khodzhaev, Dadakhan (author)
International Scientific Conference on Energy, Environmental and Construction Engineering ; 2020 ; St. Petersburg, Russia
2021-03-27
8 pages
Article/Chapter (Book)
Electronic Resource
English
Parametric Vibrations of Viscoelastic Rectangular Plates with Concentrated Masses
| Springer Verlag | 2021
Nonlinear Vibrations of an Orthotropic Viscoelastic Rectangular Plate Under Periodic Loads
| Springer Verlag | 2022
| British Library Online Contents | 1999