Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ

Erasmo Viola; Marco Miniaci; Nicholas Fantuzzi; Alessandro Marzani

Curved and Layered Structures (2015)

  • Volume: 2, Issue: 1
  • ISSN: 2353-7396

Abstract

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This paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.

How to cite

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Erasmo Viola, et al. "Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ." Curved and Layered Structures 2.1 (2015): null. <http://eudml.org/doc/276883>.

@article{ErasmoViola2015,
abstract = {This paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.},
author = {Erasmo Viola, Marco Miniaci, Nicholas Fantuzzi, Alessandro Marzani},
journal = {Curved and Layered Structures},
keywords = {Parabolic Arches; Generalized Differential Quadrature Method; Damage; Numerical Methods},
language = {eng},
number = {1},
pages = {null},
title = {Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ},
url = {http://eudml.org/doc/276883},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Erasmo Viola
AU - Marco Miniaci
AU - Nicholas Fantuzzi
AU - Alessandro Marzani
TI - Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ
JO - Curved and Layered Structures
PY - 2015
VL - 2
IS - 1
SP - null
AB - This paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.
LA - eng
KW - Parabolic Arches; Generalized Differential Quadrature Method; Damage; Numerical Methods
UR - http://eudml.org/doc/276883
ER -

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