Buckling and free vibrations of rectangular plates with symmetrically varying mechanical properties – Analytical and FEM studies

2019 ◽  
Vol 220 ◽  
pp. 355-361 ◽  
Author(s):  
Krzysztof Magnucki ◽  
Dawid Witkowski ◽  
Ewa Magnucka-Blandzi
Keyword(s):  
Mechanical Properties ◽  
Free Vibrations ◽  
Rectangular Plates

Numerical analysis of free vibrations of rectangular plates based on different approaches

2019 ◽  
pp. 33-41
Author(s):  
Oleksandr Grigorenko ◽  
◽  
Maksym Borysenko ◽  
Olena Boychuk ◽  
Volodymyr Novytskyi ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Free Vibrations ◽  
Rectangular Plates

Free vibrations of periodically point-supported rectangular plates

1989 ◽  
Vol 132 (3) ◽  
pp. 491-509 ◽  
Author(s):  
A.V. Bapat ◽  
S. Suryanarayan
Keyword(s):  
Free Vibrations ◽  
Rectangular Plates

scholarly journals Free Vibrations of Sandwich Plates with Damaged Soft-Core and Non-Uniform Mechanical Properties: Modeling and Finite Element Analysis

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2444 ◽  
Author(s):  
Michele Bacciocchi ◽  
Raimondo Luciano ◽  
Carmelo Majorana ◽  
Angelo Marcello Tarantino
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Thickness Distribution ◽  
Free Vibrations ◽  
Soft Core ◽  
Sandwich Plates ◽  
Element Analysis ◽  
Three Phase ◽  
Reinforcing Fibers ◽  
Parametric Analyses

The paper aims to investigate the natural frequencies of sandwich plates by means of a Finite Element (FE) formulation based on the Reissner-Mindlin Zig-zag (RMZ) theory. The structures are made of a damaged isotropic soft-core and two external stiffer orthotropic face-sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. A non-uniform distribution of the reinforcing fibers is assumed along the thickness of the skin and is modeled analytically by means of peculiar expressions given as a function of the thickness coordinate. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution of the straight fibers, stacking sequence, and mass fraction of the constituents. Some final remarks are presented to provide useful observations and design criteria.

scholarly journals Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates

2002 ◽  
Vol 9 (4-5) ◽  
pp. 193-201 ◽  
Author(s):  
Sergio Ferreira Bastos ◽  
Lavinia Borges ◽  
Fernando A. Rochinha
Keyword(s):  
Experimental Approach ◽  
Natural Frequencies ◽  
Free Edge ◽  
Free Vibrations ◽  
Elastic Parameter ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Elastic Parameters ◽  
Non Destructive ◽  
Parameter Problem

This article deals with the identification of elastic parameters (engineering constants) in sandwich honeycomb orthotropic rectangular plates. A non-destructive method is introduced to identify the elastic parameters through the experimental measurements of natural frequencies of a plate undergoing free vibrations. Four elastic constant are identified. The estimation of the elastic parameter problem is solved by minimizing the differences between the measured and the calculated natural frequencies. The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. The analysis of the results indicates the efficiency of the method.

Comments on “New exact solutions for free vibrations of thin orthotropic rectangular plates”

2014 ◽  
Vol 107 ◽  
pp. 745-746 ◽  
Author(s):  
Arian Bahrami ◽  
Mansour Nikkhah Bahrami ◽  
Mohammad Reza Ilkhani
Keyword(s):  
Exact Solutions ◽  
Free Vibrations ◽  
Rectangular Plates ◽  
New Exact Solutions

scholarly journals Nonlinear calculation of a system of rectangular plates with due regard to changes in the mechanical properties of the material

2016 ◽  
Author(s):  
Margarita Moiseenko ◽  
Anatoly Malinovskiy ◽  
Oleg Popov ◽  
Tatiana Treputneva
Keyword(s):  
Mechanical Properties ◽  
Rectangular Plates

VIBRATION AND BUCKLING OF SS-F-SS-F RECTANGULAR PLATES LOADED BY IN-PLANE MOMENTS

2001 ◽  
Vol 01 (04) ◽  
pp. 527-543 ◽  
Author(s):  
JAE-HOON KANG ◽  
ARTHUR W. LEISSA
Keyword(s):  
Beam Theory ◽  
Free Edge ◽  
Free Vibrations ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
One Dimensional ◽  
Simply Supported ◽  
Free Vibration Frequency ◽  
Edge Conditions

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon the Poisson's ratio (ν), results are shown for 0≤ν≤0.5, valid for isotropic materials.

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