On the Coupled Flap-Lag Bending Vibration of Propeller Blades: An Exact Dynamic Finite Element Formulation

2000 ◽  
Author(s):  
S. M. Hashemi ◽  
M. J. Richard
Keyword(s):  
Finite Element ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Form Solution ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Weighted Residual Method ◽  
Bending Vibration ◽  
Dynamic Finite Element ◽  
Propeller Blades

Abstract An exact Dynamic Finite Element (DFE) approach for the coupled Flap-Lag vibration of blades is presented. DFE can be considered as a combination of the Finite Element Method (FEM) and the Dynamic Stiffness Matrix (DSM) formulations. The weighted residual method is used and the weighting and shape functions are chosen referring to the appropriate closed form solution of the non-coupled member equations. Based on the DFE approach, the natural frequencies for a scaled propeller blade are calculated and they are compared to the experimental data and other existing results.

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

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.

Study of Combined Heat and Mass Transfer From Fins Using Non-Dimensional Finite Element Formulation

2013 ◽  
Author(s):  
Sulaman Pashah ◽  
Syed M. Zubair ◽  
Abul Fazal M. Arif
Keyword(s):  
Mass Transfer ◽  
Finite Element ◽  
Closed Form ◽  
Heat And Mass Transfer ◽  
Closed Form Solution ◽  
Base Material ◽  
Form Solution ◽  
Element Formulation ◽  
Dimensionless Parameters ◽  
Dimensional Finite Element

The use of dimensional analysis and dimensionless parameters is very common in the field of heat transfer. The paper presents a non-dimensional finite element capable of modeling combined heat and mass transfer from fins. The aim of the formulation is to get solution of the fin problems that do not have a closed form solution. The performance of a fin is described through its efficiency and numerous closed form solutions for fin efficiency under combined heat and mass transfer are available in the literature. Deriving a closed form solution for geometric or material complexities is somewhat a difficult task. An example is variable profile composite fin. A composite fin is composed of base material or substrate with a coating layer. Finite element approach can handle such complexity with relatively ease, Therefore the main objective is to developed formulation for mass transfer problems. The formulation is derived in dimensionless form to extend the applicability of finite element results to a class of problems with same governing dimensionless parameters. The derived formulation is then applied to study the combined heat and mass transfer for variable profile composite fins under fully wet condition.

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.

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MATLAB® software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

Non-Dimensional Finite Element Formulation for Thermal Problems

2012 ◽  
Author(s):  
Sulaman Pashah ◽  
Abul Fazal M. Arif ◽  
Syed M. Zubair
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Finite Element Approach ◽  
Fin Efficiency ◽  
Dimensional Finite Element ◽  
Element Approach

The use of dimensional analysis and dimensionless parameters is very common in the field of heat transfer; nevertheless the concept of non-dimensional finite element formulation has been applied to a limited type of thermo-fluid problems. The non-dimensional finite element method should provide the dimensionless solution for a given problem. The aim of present work is to develop a non-dimensional thermal finite element for getting dimensionless solution of the problems that do not have a closed form solution. An example is a fin (or extended surface) design. Fin efficiency is a performance characteristic that can be used as design criterion; thus closed form dimensionless solutions for fin efficiency are available in the literature. The results are for different geometry, single material fins. In case, if the fin problem has some geometric and/or material complexities then closed form solutions are not available and finite element approach can be used. However, the obtained finite element solution would not be in dimensionless form. For example, no closed form solutions are available for variable thickness composite fins (i.e. a fin having a base material with a coating over its surface), and the literature shows that finite element solution has been used to study thermal performance of the variable thickness composite fins. Therefore, non-dimensional finite element approach can be applied to directly obtain the dimensionless solution for the problem. The current work consists of presenting a non-dimensional finite element formulation for thermal problems. The element formulation is first validated by solving a test case study that has known closed form solution. The objective is to demonstrate the usefulness of the non-dimensional finite element approach by obtaining dimensionless finite element solutions for some applied problems that do not have a closed form solution.

scholarly journals Triply Coupled Bending-Bending-Torsion Vibrational Analysis of Rotating Beams Using Fem and Dynamic Finite Element Formulation

2021 ◽  
Author(s):  
Mohammad Shavezipur
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Convergence Rates ◽  
Equations Of Motion ◽  
Vibrational Analysis ◽  
Element Formulation ◽  
Shape Functions ◽  
Weighted Residual Method ◽  
Torsion Beam ◽  
Dynamic Finite Element

This research presents the numerical analysis of the triply coupled flap-wise, cord-wise and torsional vibrations of flexible rotating blades. Euler-Bernoulli bending and St. Venant torsion beam theories are considered to derive the governing differential equations of motion. Based on Finite Element Methodology (FEM), the cubic "Hermite" shape functions are implemented where the solution of the equations results in a linear engine problem. Then, the Dynamic (frequency dependent) Trigonometric Shape Functions (DISF's) for beam's uncoupled displacements are derived. The application of the Dynamic Finite Element (DFE) approach to the solution of the governing equations is then presented. The DFE formulation, based on the weighted residual method and the DTSF's results in a nonlinear engine problem representing eigenvalues and engine modes of the system. The applicability of the DFE method is then demonstrated by illustrative examples, where a Wittrick-Williams root counting technique is used to find the system's natural frequencies. The DFE approach, an intermediate method between FEM and "Exact" formulation, is characterized by higher convergence rates, and can be advantageously used when multiple natural frequencies and/or higher modes of beam-like structures are to be evaluated.

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.

A new approach for closed-form analytical solution of two-dimensional symmetric double contacts and the comparison with finite element method

2017 ◽  
Vol 232 (8) ◽  
pp. 1025-1035 ◽  
Author(s):  
Parisa Ghanati ◽  
Saeed Adibnazari ◽  
Mohammad Alrefai ◽  
Azadeh Sheidaei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Closed Form ◽  
Flat Surface ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Contact Zones ◽  
Element Method

In this paper, a new procedure is developed for the solution of a general two-dimensional uncoupled symmetric double contact problem with smooth contact zones in which the indenter geometry is described by a piecewise biquadratic function. This procedure gives an approximate closed-form solution for any smooth indenter profile. In order to evaluate the accuracy of this approach, it is applied to the symmetric indentation of a flat surface by two rigidly interconnected parabolic indenters and results are compared with the exact unclosed-form solution. Moreover, this procedure is applied to the symmetric indentation of a flat surface by two rigidly interconnected cylinders to compare the results with the finite element solution obtained by the finite element method software, ABAQUS. The results showed that in comparison with the finite element method, this procedure is a fast and highly accurate method with low complexity that makes feasible the possibility of determining approximate closed-form solution for a wide range of indenter geometries with a concavity between two symmetric contact zones; hence it can be useful in practical issues.

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