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 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.

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.

Effectiveness of Active Constrained Layer Damping Treatments in Attenuating Resonant Oscillations

2002 ◽  
Vol 8 (6) ◽  
pp. 747-775 ◽  
Author(s):  
Farhan Gandhi ◽  
Brian Munsky
Keyword(s):  
Excitation Level ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Velocity Feedback ◽  
Vibration Attenuation ◽  
Position Feedback ◽  
Active Constrained Layer Damping ◽  
Excitation Force ◽  
Viscoelastic Layers ◽  
Active Constrained Layer

This paper highlights the importance of considering the piezoelectric constraining layer voltage (or electric field) limits when evaluating the effectiveness of an active constrained layer damping treatment in attenuating resonant vibration. It is seen that, when position feedback is used, intermediate viscoelastic layer stiffness values are always optimal, and maximum allowable control gains and possible vibration attenuation progressively decrease with increasing excitation force levels. On the other hand, with velocity feedback, the optimal viscoelastic layer stiffness is dependent on the excitation level. For low excitation force amplitudes, stiff viscoelastic layers are most effective, with large velocity feedback gains producing substantial vibration attenuation without exceeding piezoelectric layer voltage limits. However, for higher excitation force levels, stiff viscoelastic layers result in excess voltages even at very small velocity feedback gains, and are unable to provide any vibration attenuation. In such a case, intermediate viscoelastic layer stiffness values are preferable, and maximum velocity feedback gains and possible vibration attenuation progressively decrease with increasing excitation level, as in the case of position feedback. For both position and velocity feedback, when excitation forces are beyond a certain level the allowable control gains are so limited that no additional damping is obtained beyond that already available through the passive treatment.

Characteristics of Enhanced Active Constrained Layer Damping Treatments With Edge Elements, Part 1: Finite Element Model Development and Validation

1998 ◽  
Vol 120 (4) ◽  
pp. 886-893 ◽  
Author(s):  
W. H. Liao ◽  
K. W. Wang
Keyword(s):  
Finite Element ◽  
Model Development ◽  
Element Model ◽  
System Model ◽  
Viscoelastic Layer ◽  
Constrained Layer Damping ◽  
Active System ◽  
Edge Elements ◽  
Active Constrained Layer Damping ◽  
Active Constrained Layer

This paper is concerned with the enhanced active constrained layer (EACL) damping treatment with edge elements. A finite element time-domain-based model (FEM) is developed for the beam structure with partially covered EACL. The edge elements are modeled as equivalent springs mounted at the boundaries of the piezoelectric layer. The Golla-Hughes-McTavish (GHM) method is used to model the viscoelastic layer. The GHM dissipation coordinates can describe the frequency-dependent viscoelastic material properties. This model becomes the current active constrained layer (ACL) system model as the stiffness of the edge elements approaches zero. Without the edge elements and viscoelastic materials, the purely active system model can also be obtained from the EACL model as a special case. Lab tests are conducted to validate the models. The frequency responses of the EACL, current ACL, and purely active systems predicted by the FEM match the test results closely. Utilizing these models, analysis results are illustrated and discussed in Part (2) of this paper.

scholarly journals Vibration and Damping Analysis of Pipeline System Based on Partially Piezoelectric Active Constrained Layer Damping Treatment

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1209
Author(s):  
Yuanlin Zhang ◽  
Xuefeng Liu ◽  
Weichong Rong ◽  
Peixin Gao ◽  
Tao Yu ◽  
...  
Keyword(s):  
Vibration Control ◽  
Piezoelectric Materials ◽  
Active Vibration Control ◽  
Control Technique ◽  
Viscoelastic Layer ◽  
Pipeline System ◽  
Constrained Layer Damping ◽  
Damping Effect ◽  
Active Constrained Layer Damping ◽  
Active Constrained Layer

Pipelines work in serious vibration environments caused by mechanical-based excitation, and it is thus challenging to put forward effective methods to reduce the vibration of pipelines. The common vibration control technique mainly uses the installation of dampers, constrained layer damping materials, and an optimized layout to control the vibration of pipelines. However, the passive damping treatment has little influence on the low frequency range of a pipeline system. Active control technology can obtain a remarkable damping effect. An active constrained layer damping (ACLD) system with piezoelectric materials is proposed in this paper. This paper aims to investigate the vibration and damping effect of ACLD pipeline under fixed support. The finite element method is employed to establish the motion equations of the ACLD pipeline. The effect of the thickness and elastic modulus of the viscoelastic layer, the laying position, and the coverage of ACLD patch, and the voltage of the piezoelectric material are all considered. The results show that the best damping performance can be obtained by selecting appropriate control parameters, and it can provide effective design guidance for active vibration control of a pipeline system.

scholarly journals Finite Element Model of Vibration Control for an Exponential Functionally Graded Timoshenko Beam with Distributed Piezoelectric Sensor/Actuator

Actuators ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 19 ◽  
Author(s):  
Khalid El Harti ◽  
Mohammed Rahmoune ◽  
Mustapha Sanbi ◽  
Rachid Saadani ◽  
Mouhcine Bentaleb ◽  
...  
Keyword(s):  
Finite Element ◽  
Active Control ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Piezoelectric Sensor ◽  
Functionally Graded ◽  
Flexible Beam ◽  
Linear Quadratic ◽  
Sensors And Actuators ◽  
Functionally Graded Beam

This paper presents a dynamic study of sandwich functionally graded beam with piezoelectric layers that are used as sensors and actuators. This study is exploited later in the formulation of the active control laws, while using the optimal control Linear Quadratic Gaussian (LQG), accompanied by the Kalman filter. The mathematical formulation is based on Timoshenko’s assumptions and the finite element method, which is applied to a flexible beam divided into a finite number of elements. By applying the Hamilton principle, the equations of motion are obtained. The vibration frequencies are found by solving the eigenvalue problem. The structure is analytically then numerically modeled and the results of the simulations are presented in order to visualize the states of their dynamics without and with active control.

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