scholarly journals A Finite Element Formulation Of Active Constrained-Layer Functionally Graded Beam

2021 ◽  
Author(s):  
Ry Long
Keyword(s):  
Layer Structure ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Integration Scheme ◽  
Element Formulation ◽  
Constrained Layer Damping ◽  
Functionally Graded Beam ◽  
Active Constrained Layer

Active constrained-layer damping (ACLD) treatment is the combination of passive and active features in the control of structural vibrations. A three-layer structure that consists of a functionally graded (FG) host beam, with a bonded viscoelastic layer and a constraining piezoelectric fiber-reinforce composite (PFRC) laminate is modeled and analyzed. The assumptions for modeling the system are the application of Timoshenko beam theory for the host beam and PFRC laminate, and a higher-order beam theory for the viscoelastic layer. The formulation is assumed to have field variables that are expressed as polynomials through the thickness of the structure and linear interpolation across the span. The extended Hamilton's principle is utilized to determine the system equations of motion, which are then solved using the Newmark time-integration scheme. Many support conditions such as fully- and partial-clamped cantilevered, partially clamped-clamped and simply-supported are analyzed. The effects of ply angle orientaion, as well as FG properties, are also carefully examined.

scholarly journals A Finite Element Formulation Of Active Constrained-Layer Functionally Graded Beam

2021 ◽  
Author(s):  
Ry Long
Keyword(s):  
Layer Structure ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Integration Scheme ◽  
Element Formulation ◽  
Constrained Layer Damping ◽  
Functionally Graded Beam ◽  
Active Constrained Layer

Active constrained-layer damping (ACLD) treatment is the combination of passive and active features in the control of structural vibrations. A three-layer structure that consists of a functionally graded (FG) host beam, with a bonded viscoelastic layer and a constraining piezoelectric fiber-reinforce composite (PFRC) laminate is modeled and analyzed. The assumptions for modeling the system are the application of Timoshenko beam theory for the host beam and PFRC laminate, and a higher-order beam theory for the viscoelastic layer. The formulation is assumed to have field variables that are expressed as polynomials through the thickness of the structure and linear interpolation across the span. The extended Hamilton's principle is utilized to determine the system equations of motion, which are then solved using the Newmark time-integration scheme. Many support conditions such as fully- and partial-clamped cantilevered, partially clamped-clamped and simply-supported are analyzed. The effects of ply angle orientaion, as well as FG properties, are also carefully examined.

scholarly journals A quasi-2D finite element formulation of active constrained-layer functionally graded beam

2021 ◽  
Author(s):  
Elena Miroshnichenko
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Element Formulation ◽  
Constrained Layer Damping ◽  
Functionally Graded Beam ◽  
Passive Element ◽  
Fg Beam ◽  
Active Constrained Layer

A functionally graded (FG) beam with an active constrained-layer damping (ACLD) treatment is modeled and analyzed. ACLD consists of a passive element, in the form of a viscoelastic layer bonded to the host structure, and an active constraining element which is represented by a piezoelectric fiber-reinforced composite (PFRC) laminate. It is assumed in the current formulation that the field variables are expressible as polynomials through the thickness of the beam and are cubically interpolated across the span. Hamilton's principle is used in the derivation of the equations of motion, which are solved using the Newmark time-integration method. The versatility of the formulation is demonstrated using different support mechanisms in the form of analysis of cantilevered, fixed-end partially-constrained and simply-supported beam cases. The effects of ply orientation in PFRC laminate and varying elastic modulus in the FG beam are also examined.

scholarly journals A quasi-2D finite element formulation of active constrained-layer functionally graded beam

2021 ◽  
Author(s):  
Elena Miroshnichenko
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Element Formulation ◽  
Constrained Layer Damping ◽  
Functionally Graded Beam ◽  
Passive Element ◽  
Fg Beam ◽  
Active Constrained Layer

A functionally graded (FG) beam with an active constrained-layer damping (ACLD) treatment is modeled and analyzed. ACLD consists of a passive element, in the form of a viscoelastic layer bonded to the host structure, and an active constraining element which is represented by a piezoelectric fiber-reinforced composite (PFRC) laminate. It is assumed in the current formulation that the field variables are expressible as polynomials through the thickness of the beam and are cubically interpolated across the span. Hamilton's principle is used in the derivation of the equations of motion, which are solved using the Newmark time-integration method. The versatility of the formulation is demonstrated using different support mechanisms in the form of analysis of cantilevered, fixed-end partially-constrained and simply-supported beam cases. The effects of ply orientation in PFRC laminate and varying elastic modulus in the FG beam are also examined.

scholarly journals A quasi-two-dimensional finite element formulation for analysis of active-passive constrained layer beams

2021 ◽  
Author(s):  
Jean-Jacques R. Boiluea Bekuit
Keyword(s):  
Finite Element ◽  
Piezoelectric Layer ◽  
Layer Structure ◽  
Time Integration ◽  
Beam Theory ◽  
Viscoelastic Layer ◽  
Element Formulation ◽  
Transverse Displacement ◽  
Passive Damping ◽  
Dimensional Finite Element

Active-passive damping is getting more popular with designers because it combines the complementary passive and active features in the control of structural vibrations. The classical three-layer structure has a viscoelastic-layer sandwiched between the host beam and a piezoelectric-layer. The more prevalent assumptions for modeling the system are the use of Euler-Bernoulli beam theory for both the host beam and piezoelectric-layer, and Timoshenko beam theory for the viscoelastic-layer. The assumption that transverse displacement is constant through the thickness limits accuracy and applicability of the model. The current formulation expresses the through-the-thickness dependency of the field variables as polynomials while their span dependency across a finite element is cubically interpolated. The versatility of the formulation is demonstrated via static and dynamic studies of examples taken from the literature. A beam treated with active-passive damping is presented and examined. The constitutive relation of the viscoelastic layer is represented using fractional derivatives and the Grünwald approximation. The extended Hamilton's principle is used to derive the system governing equations which are integrated with the Newmark time-integration system.

scholarly journals A quasi-two-dimensional finite element formulation for analysis of active-passive constrained layer beams

2021 ◽  
Author(s):  
Jean-Jacques R. Boiluea Bekuit
Keyword(s):  
Finite Element ◽  
Piezoelectric Layer ◽  
Layer Structure ◽  
Time Integration ◽  
Beam Theory ◽  
Viscoelastic Layer ◽  
Element Formulation ◽  
Transverse Displacement ◽  
Passive Damping ◽  
Dimensional Finite Element

Active-passive damping is getting more popular with designers because it combines the complementary passive and active features in the control of structural vibrations. The classical three-layer structure has a viscoelastic-layer sandwiched between the host beam and a piezoelectric-layer. The more prevalent assumptions for modeling the system are the use of Euler-Bernoulli beam theory for both the host beam and piezoelectric-layer, and Timoshenko beam theory for the viscoelastic-layer. The assumption that transverse displacement is constant through the thickness limits accuracy and applicability of the model. The current formulation expresses the through-the-thickness dependency of the field variables as polynomials while their span dependency across a finite element is cubically interpolated. The versatility of the formulation is demonstrated via static and dynamic studies of examples taken from the literature. A beam treated with active-passive damping is presented and examined. The constitutive relation of the viscoelastic layer is represented using fractional derivatives and the Grünwald approximation. The extended Hamilton's principle is used to derive the system governing equations which are integrated with the Newmark time-integration system.

Numerical analysis of nonlinear functionally graded piezoelectric energy harvester subjected to multi moving oscillators

2021 ◽  
pp. 095440622110036
Author(s):  
P Fatehi ◽  
M Mahzoon ◽  
M Farid
Keyword(s):  
Energy Harvesting ◽  
Nonlinear Vibration ◽  
Electromechanical Coupling ◽  
Damping Ratio ◽  
Beam Theory ◽  
Functionally Graded ◽  
Integration Scheme ◽  
Functionally Graded Beam ◽  
Piezoelectric Patch ◽  
Piezoelectric Energy

In this paper, energy harvesting from nonlinear vibration of a functionally graded beam covered by a piezoelectric patch under multi-moving oscillators is studied. The material of both the substructure and the piezoelectric patch is assumed to be functionally graded in the thickness direction. A coupled system of equations considering Euler-Bernoulli beam theory and von-Karman nonlinearity as well as electromechanical coupling are derived using the generalized Hamilton’s principle. Finite element method as well as Newmark time integration scheme are used to solve the coupled nonlinear time dependent problem. The effects of different parameters including material distribution, velocity of the moving oscillators, piezoelectric patch thickness and load resistance on the output voltage and harvested power are investigated. Moreover, the effects of oscillator characteristics such as damping ratio and stiffness on the nonlinear behavior of the beam and harvested power are also studied. Results indicate that the aforementioned parameters have considerable effects on the harvested power. It is also shown that ignoring nonlinear effects may lead to erroneous and unacceptable results. To the best of authors’ knowledge, there is no study about energy harvesting from nonlinear vibration of beams under moving oscillators.

Modal Loss Factor Predication in Flexible Mechanism Systems With Constrain Viscoelastic Layers

1998 ◽  
Author(s):  
Zhang Xianmin ◽  
Liu Jike
Keyword(s):  
Equations Of Motion ◽  
Sandwich Beam ◽  
Viscoelastic Layer ◽  
Treatment Technique ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Frame Element ◽  
Modal Damping ◽  
Flexible Mechanism ◽  
Viscoelastic Layers

Abstract Control of dynamic vibration is critical to the operational success of many flexible mechanism systems. This paper addresses the problem of vibration control of such mechanisms through passive damping, using constrained layer damping treatment technique. A new type of shape function for three layer frame element containing a viscoelastic layer is developed. The equations of motion of the damped flexible mechanism are derived. Modal loss factors of this kind mechanisms are predicated from undamped normal mode by means of the modal strain energy method. Comparisons between the results obtained by this paper and the results obtained by exact solution of the governing equations for a well known sandwich beam demonstrate that the method presented in this paper is correct and reliable. Application of this method in predication of modal damping ratios for damped mechanisms is discussed. It is believed that the method of this paper hold the greatest potential for optimal design of damped flexible mechanism systems.

Dynamic analysis of three-layer cylindrical shells with fractional viscoelastic core and functionally graded face layers

2020 ◽  
pp. 107754632096622
Author(s):  
Meisam Shakouri ◽  
Mohammad Reza Permoon ◽  
Abdolreza Askarian ◽  
Hassan Haddadpour
Keyword(s):  
Natural Frequency ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Core Layer ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Viscoelastic Core ◽  
Graded Layers

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz method. The obtained results are validated with those in the literature, and finally, the effects of some geometrical and material parameters such as length-to-radius ratio, functionally graded properties, radius and thickness of viscoelastic layer on the natural frequency, and loss factor of the system are considered, and some conclusions are drawn.

scholarly journals An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2198 ◽  
Author(s):  
Hoang Nam Nguyen ◽  
Tran Thi Hong ◽  
Pham Van Vinh ◽  
Do Van Thom
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Beam Theory ◽  
Beam Element ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Beam ◽  
Transverse Shear Stresses ◽  
Power Law Index ◽  
Transverse Shear Strains

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

Sign in / Sign up

Export Citation Format

Share Document