scholarly journals Free Vibration Analysis of Fibre-Metal Laminated Beams via Hierarchical One-Dimensional Models

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
L. Hanten ◽  
G. Giunta ◽  
S. Belouettar ◽  
V. Salnikov
Keyword(s):  
Free Vibration ◽  
Displacement Field ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Field Approximation ◽  
Approximation Order ◽  
Form Solution ◽  
Fibre Metal

This paper presents a free vibration analysis of beams made of fibre-metal laminated beans. Due to its attractive properties, this class of composites has gained more and more importance in the aeronautic field. Several higher-order displacements-based theories as well as classical models (Euler-Bernoulli’s and Timoshenko’s ones) are derived, assuming Carrera’s Unified Formulation by a priori approximating the displacement field over the cross section in a compact form. The governing differential equations and the boundary conditions are derived in a general form that corresponds to a generic term in the displacement field approximation. The resulting fundamental term, named “nucleus”, does not depend upon the approximation order N, which is a free parameter of the formulation. A Navier-type, closed form solution is used. Simply supported beams are, therefore, investigated. Slender and short beams are considered. Three- and five-layer beams are studied. Bending, shear, torsional, and axial modes and frequencies are presented. Results are assessed for three-dimensional FEM solutions obtained by a commercial finite element code using three-dimensional elements showing that the proposed approach is accurate yet computationally effective.

Bending and free vibration analysis of foam-filled truss core sandwich panel

2016 ◽  
Vol 20 (5) ◽  
pp. 617-638 ◽  
Author(s):  
MP Arunkumar ◽  
Jeyaraj Pitchaimani ◽  
KV Gangadharan
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Sandwich Panel ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Form Solution ◽  
Numerical Comparison ◽  
Truss Core ◽  
Foam Filled

This paper presents the studies carried out on bending and free vibration behavior of truss core sandwich panel filled with foam typically used in aerospace applications. Equivalent stiffness properties for foam-filled truss core sandwich panel are derived by idealizing 3D foam-filled sandwich panel to an equivalent 2D orthotropic thick plate continuum. The accuracy of the derived elastic property is ensured by the numerical comparison of free vibration response of 3D and its equivalent 2D finite element model. The derived stiffness constants were used in closed form solution to evaluate the maximum deflection of the continuum. The results show that the free vibration and static behavior of the sandwich panel can be enhanced in due consideration to the space constraint by filling foam in the empty space of core. The results also reveal that triangular core foam-filled sandwich panel deflects less compared to other cores. From the free vibration analysis, effect of filling foam is effective in cellular and trapezoidal core.

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.

Free Vibration Analysis of Symmetrically Laminated Fully Clamped Skew Plates Using Extended Kantorovich Method

2011 ◽  
Vol 471-472 ◽  
pp. 739-744 ◽  
Author(s):  
Ali Fallah ◽  
Mohammad Hossein Kargarnovin ◽  
Mohammad Mohammadi Aghdam
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Power Series Solution ◽  
Order Partial Differential Equation ◽  
Kantorovich Method ◽  
Extended Kantorovich Method

In this paper, free vibration analysis of thin symmetrically laminated skew plates with fully clamped edges is investigated. The governing differential equation for skew plate which is a fourth order partial differential equation (PDE) is obtained by transforming the differential equation in Cartesian coordinates into skew coordinates. Based on the multi-term extended Kantorovich method (MTEKM) an efficient and accurate approximate closed-form solution is presented for the governing PDE. Application of the MTEKM reduces the governing PDE to a dual set of ordinary differential equations. These sets of equations are then solved with infinite power series solution, in an iterative manner until convergence was achieved. Results of this study show the fast rate of convergence of the MTEKM. Usually two or three iterations are enough to obtain reasonably accurate results. The frequency parameters of laminated composite plates are obtained for different skew angles and lay-up configuration for different composites laminates skew plates. Comparisons have been made with the available results in the literature which show the accuracy and efficiency of the method.

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