Exact free vibration analysis of Lévy FGM plates with higher-order shear and normal deformation theories

2014 ◽  
Vol 111 ◽  
pp. 415-425 ◽  
Author(s):  
Lorenzo Dozio
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Normal Deformation

Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One-Dimensional Analysis

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Alberto Varello ◽  
Erasmo Carrera
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Plane Deformation ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Variable Order ◽  
Vibrational Modes ◽  
One Dimensional

The free vibration analysis of thin- and thick-walled layered structures via a refined one-dimensional (1D) approach is addressed in this paper. Carrera unified formulation (CUF) is employed to introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the cross section. Classical Euler–Bernoulli (EBBM) and Timoshenko (TBM) beam theories are obtained as particular cases. Different kinds of vibrational modes with increasing half-wave numbers are investigated for short and relatively short cylindrical shells with different cross section geometries and laminations. Numerical results of natural frequencies and modal shapes are provided by using the finite element method (FEM), which permits various boundary conditions to be handled with ease. The analyses highlight that the refinement of the displacement field by means of higher-order terms is fundamental especially to capture vibrational modes that require warping and in-plane deformation to be detected. Classical beam models are not able to predict the realistic dynamic behavior of shells. Comparisons with three-dimensional elasticity solutions and solid finite element solutions prove that CUF provides accuracy in the free vibration analysis of even short, nonhomogeneous thin- and thick-walled shell structures, despite its 1D approach. The results clearly show that bending, radial, axial, and also shell lobe-type modes can be accurately evaluated by variable kinematic 1D CUF models with a remarkably lower computational effort compared to solid FE models.

scholarly journals Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
G. Giunta ◽  
S. Belouettar
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Approximation Order ◽  
Higher Order ◽  
Geometrical Parameters ◽  
Thin Walled ◽  
Three Dimensional Finite Element

This paper addresses a free vibration analysis of thin-walled isotropic beams via higher-order refined theories. The unknown kinematic variables are approximated along the beam cross section as aN-order polynomial expansion, whereNis a free parameter of the formulation. The governing equations are derived via the dynamic version of the Principle of Virtual Displacements and are written in a unified form in terms of a “fundamental nucleus.” This latter does not depend upon order of expansion of the theory over the cross section. Analyses are carried out through a closed form, Navier-type solution. Simply supported, slender, and short beams are investigated. Besides “classical” modes (such as bending and torsion), several higher modes are investigated. Results are assessed toward three-dimensional finite element solutions. The numerical investigation shows that the proposed Unified Formulation yields accurate results as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam.

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