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 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

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 On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature

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.

scholarly journals On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature

scholarly journals On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through-width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature.

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.

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.

Large Amplitude Thermo-Mechanical Vibration Analysis of Asymmetrically Laminated Composite Beams

2011 ◽  
Vol 471-472 ◽  
pp. 745-750 ◽  
Author(s):  
Ali Fallah ◽  
Hamid Shahsavari Alavijeh ◽  
Abdoreza Pasharavesh ◽  
Mohammad Mohammadi Aghdam
Keyword(s):  
Large Amplitude ◽  
Vibration Analysis ◽  
Thermal Loading ◽  
Closed Form Solution ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Form Solution ◽  
Simple Analytical Expression ◽  
Laminated Composite Beams

In this paper, simple analytical expression is presented for large amplitude thermo-mechanical free vibration analysis of asymmetrically laminated composite beams. 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 laminated beams such as the effect of vibration amplitude, lay-up configuration and thermal loading are presented for future references.

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