Free Vibration Analysis of FGM Sandwich Beams Containing Edge Cracks

2012 ◽  
Vol 488-489 ◽  
pp. 230-235 ◽  
Author(s):  
Javad Soltani Rad ◽  
Ali Tivay ◽  
Mojtaba Sadighi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Finite Element Models ◽  
Sandwich Beams ◽  
Crack Configuration ◽  
Different Depths ◽  
Edge Cracks

This paper presents a vibration analysis of sandwich beams with functionally-graded skins containing edge cracks. Finite Element models of FGM sandwich beams are created with different depths and locations of the edge-cracks, and the first four natural frequencies of the beam are obtained for each crack configuration. The integrity of the data is validated for the FGM skins in comparison to a previously published reference. Finally, an inspection is conducted on the data to show the influences of the location and depth of cracks and material properties on the flexural vibration characteristics of cracked FGM sandwich beams.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

Nonlinear Thermo-Mechanical Vibration Analysis of Functionally Graded Beams

2011 ◽  
Author(s):  
Ali Fallah ◽  
Keikhosrow Firoozbakhsh ◽  
Abdolreza Pasharavesh
Keyword(s):  
Vibration Analysis ◽  
Vibration Amplitude ◽  
Thermal Loading ◽  
Natural Frequencies ◽  
Mechanical Vibration ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Form Solution ◽  
Functionally Graded ◽  
Material Inhomogeneity

In this paper, nonlinear thermo-mechanical free vibration analysis of functionally graded (FG) beams investigated. Euler-Bernoulli assumptions together with Von Karman’s strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He’s variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the FG beams such as the effect of vibration amplitude, material inhomogeneity and thermal loading are presented for future references.

A two-dimensional free vibration analysis of functionally graded sandwich beams under thermal environment

2012 ◽  
Vol 226 (12) ◽  
pp. 2860-2873 ◽  
Author(s):  
AR Setoodeh ◽  
M Ghorbanzadeh ◽  
P Malekzadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Thermal Environment ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Sandwich Beams ◽  
Two Dimensional

In this article, free vibration analysis of elastically supported sandwich beams with functionally graded face sheets subjected to thermal environment is presented. In order to accurately include the transverse shear deformation and the inertia effects, two-dimensional elasticity theory is used to formulate the problem. The layerwise theory in conjunction with the differential quadrature method is employed to discretize the governing equations in the thickness and axial directions, respectively. The material properties of functionally graded face sheets are assumed to be temperature-dependent and graded in the thickness direction according to a power-law distribution. For the purpose of comparison, the problem under consideration is also solved using two-dimensional finite element method and the first-order shear deformation theory. The accuracy, convergence, and versatility of the method are demonstrated by comparing the results with those of the two aforementioned approaches and also with the existing solutions in literature. Eventually, some new numerical results are presented which depict the effects of different material and geometrical parameters on natural frequencies and mode shapes of the beam.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

Radial vibration analysis of heterogeneous and non-uniform disks via complementary functions method

2018 ◽  
Vol 53 (5) ◽  
pp. 332-337 ◽  
Author(s):  
Sefa Yildirim ◽  
Naki Tutuncu
Keyword(s):  
Vibration Analysis ◽  
Solution Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Closed Form Solutions ◽  
Novel Approach ◽  
Spatially Varying ◽  
Uniform Disk

Free vibration analysis of heterogeneous (functionally graded) and non-uniform (variable thickness) disks using plane elasticity results in a two-point boundary value problem. Spatially varying mechanical and thickness properties yield variable coefficient governing differential equations where obtaining closed-form solutions are not possible except for certain simple grading and thickness functions. This article uses complementary functions method as a novel approach to determine natural frequencies of functionally graded non-uniform disks. The validation and observation of converges are done using analytical and ANSYS results for a simple power law model uniform disk. The proposed solution method can be applied for disks with any continuous thickness and material grading functions.

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