scholarly journals Dynamic Finite Element Modelling And Free Vibration Analysis Of Two Dimensional Elements

2021 ◽  
Author(s):  
Mohammad Moeid Elahikahooker
Keyword(s):  
Vibration Analysis ◽  
Finite Element Modelling ◽  
Systematic Approach ◽  
Free Vibration Analysis ◽  
Future Research ◽  
Plate Bending ◽  
Dynamic Finite Element ◽  
Structural Problems ◽  
Great Performance ◽  
Reference Equation

DFE is proven to be a powerful tool for analysis of structural problems involving vibration of beams, by introducing frequency dependence in element matrices. This method is extended here to thin plate vibration cases. Lack of previous systematic approach and great performance of beam DFEs were particular drives of the present work. Kirchhoff’s plate bending theory is derived and used as the reference equation describing element behaviour. DFE is implemented in MATLAB® software and evaluated for different conditions. FEM plates are developed for similar geometry using MATLAB® as well and their performance is compared against DFE formulation. Convergence studies are performed and comparisons between FEM and DFE elements are shown. Moreover, critical review of previous works on plate vibrational modelling is made which highlighted the difficulty involved in solving the partial differential equation of plates. Finally comments about the current element and the potential direction of future research are given.

scholarly journals Dynamic Finite Element Modelling And Free Vibration Analysis Of Two Dimensional Elements

2021 ◽  
Author(s):  
Mohammad Moeid Elahikahooker
Keyword(s):  
Vibration Analysis ◽  
Finite Element Modelling ◽  
Systematic Approach ◽  
Free Vibration Analysis ◽  
Future Research ◽  
Plate Bending ◽  
Dynamic Finite Element ◽  
Structural Problems ◽  
Great Performance ◽  
Reference Equation

DFE is proven to be a powerful tool for analysis of structural problems involving vibration of beams, by introducing frequency dependence in element matrices. This method is extended here to thin plate vibration cases. Lack of previous systematic approach and great performance of beam DFEs were particular drives of the present work. Kirchhoff’s plate bending theory is derived and used as the reference equation describing element behaviour. DFE is implemented in MATLAB® software and evaluated for different conditions. FEM plates are developed for similar geometry using MATLAB® as well and their performance is compared against DFE formulation. Convergence studies are performed and comparisons between FEM and DFE elements are shown. Moreover, critical review of previous works on plate vibrational modelling is made which highlighted the difficulty involved in solving the partial differential equation of plates. Finally comments about the current element and the potential direction of future research are given.

scholarly journals Free Vibration Analysis of Laminated Composites by a Nine Node Isoparametric Plate Bending Element

2016 ◽  
Vol 25 (5) ◽  
pp. 096369351602500 ◽  
Author(s):  
Kanak Kalita ◽  
M. Ramachandran ◽  
Pramod Raichurkar ◽  
Sneha D. Mokal ◽  
Salil Haldar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Laminated Composites ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Engineering Industry ◽  
Plate Bending ◽  
Skew Angle ◽  
Laminated Structures

Composite laminates are being widely used in engineering industry primarily due to their high strength-to-weight ratio. Considerable research has been carried out to understand the static and dynamic behaviour of laminated composite plates. There is much demand for developing efficient finite element codes which can predict the dynamic responses of laminated structures at affordable computational cost. In this paper a nine node isoparametric plate bending element has been used for free vibration analysis of laminated composite plate. The first-order shear deformation theory (FSDT) has been incorporated in the element formulation. Composite plates with different side-to-thickness ratio (a/h), ply orientations and number of layers have been analysed. Based on comparison with literature data, we propose that the present formulation is capable of yielding highly accurate results. Laminated composites with central cut-outs are also studied. Novel data is reported for skew laminated composites. It is found that the natural frequency increases with the increase in skew angle (a) and decreases with increase in aspect ratio (b/a) and thickness (h).

scholarly journals Dynamic Finite Element Modelling and Vibration Analysis of Prestressed Layered Bending–Torsion Coupled Beams

2022 ◽  
Vol 3 (1) ◽  
pp. 103-120
Author(s):  
MirTahmaseb Kashani ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Nonlinear Eigenvalue Problem ◽  
Free Vibration Analysis ◽  
Rates Of Convergence ◽  
Homogenization Method ◽  
Unidirectional Composite ◽  
Dynamic Finite Element ◽  
Fundamental Frequencies ◽  
Fiber Metal

Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those obtained from the conventional FEM (ANSYS, Canonsburg, PA, USA) as well as the Homogenization Method (HM). Unlike the FEM, the application of the DFE formulation leads to a nonlinear eigenvalue problem, which is solved to determine the system’s natural frequencies and modes. The governing differential equations of coupled flexural–torsional vibrations, resulting from the end moment, are developed using Euler–Bernoulli bending and St. Venant torsion beam theories and assuming linear harmonic motion and linearly elastic materials. Illustrative examples of prestressed layered, FML, and unidirectional composite beam configurations, exhibiting geometric bending-torsion coupling, are studied. The presented DFE and FEM results show excellent agreement with the homogenization method and ANSYS modeling results, with the DFE’s rates of convergence surpassing all. An investigation is also carried out to examine the effects of various combined axial loads and end moments on the stiffness and fundamental frequencies of the structure. An illustrative example, demonstrating the application of the presented methods to the buckling analysis of layered beams is also presented.

scholarly journals Framework for Dynamic-Stiffness-Based Free Vibration Analysis of Plate-Like Structures

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Miroslav Marjanović ◽  
Marija Nefovska-Danilović ◽  
Emilija Damnjanović
Keyword(s):  
Free Vibration ◽  
Software Design ◽  
Vibration Analysis ◽  
Orthotropic Material ◽  
Dynamic Stiffness ◽  
Object Oriented ◽  
Free Vibration Analysis ◽  
Plate Structures ◽  
Structural Problems ◽  
Wide Range

A framework for free vibration analysis of plate-like structures is presented in the paper. Based on the previously formulated dynamic stiffness elements, FREEVIB object-oriented software in Python environment has been created. Software design and structure as well as a wide range of possible structural problems that could be analyzed using the FREEVIB are presented. Through several illustrative examples including free vibration analysis of stepped, stiffened and folded plate structures, implying isotropic or orthotropic material formulations, the efficiency and accuracy of the FREEVIB is demonstrated. The possibilities of further extensions and improvements of the software are discussed.

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