Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment

An enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained la...

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Main Authors: Zhicheng Huang, Huanyou Peng, Xingguo Wang, Fulei Chu
Format: Article
Language:English
Published: MDPI AG 2023-02-01
Series:Materials
Subjects:
Online Access:https://www.mdpi.com/1996-1944/16/4/1652
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author Zhicheng Huang
Huanyou Peng
Xingguo Wang
Fulei Chu
author_facet Zhicheng Huang
Huanyou Peng
Xingguo Wang
Fulei Chu
author_sort Zhicheng Huang
collection DOAJ
description An enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained layer damping (ACLD) thin plate structure is taken as the research object to study vibration control. Based on the FEM method, energy method, and Hamilton principle, the dynamic model of an ACLD thin plate structure is derived, in which the Golla–Hughes–McTavish (GHM) model is used to characterize the damping characteristics of the viscoelastic layer, and the equivalent Rayleigh damping is used to characterize the damping characteristics of the base layer. The order of the model is reduced based on the high-precision physical condensation method and balance reduction method, and the model has good controllability and observability. An LQR controller is designed to actively control the ACLD sheet, and the controller parameters and piezoelectric sheet parameters are optimized. The results show that the finite element model established in this paper is accurate under different boundary conditions, and the model can still accurately and reliably describe the dynamic characteristics of the original system in the time and frequency domain after using the joint reduction method. Under different excitation and boundary conditions, LQR control can effectively suppress structural vibration. Considering the performance and cost balance, the most suitable control parameter for the system is: Q-matrix coefficient is between 1 × 10<sup>4</sup> and 1 × 10<sup>5</sup>, the R-matrix coefficient is between 1 and 10, and the thickness of the piezoelectric plate is 0.5 mm.
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spelling doaj.art-e059c624fdcc468d9aa3d9c9b4ae37bc2023-11-16T21:52:38ZengMDPI AGMaterials1996-19442023-02-01164165210.3390/ma16041652Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping TreatmentZhicheng Huang0Huanyou Peng1Xingguo Wang2Fulei Chu3College of Mechanical and Electrical Engineering, Jingdezhen Ceramic University, Jingdezhen 333001, ChinaCollege of Mechanical and Electrical Engineering, Jingdezhen Ceramic University, Jingdezhen 333001, ChinaCollege of Mechanical and Electrical Engineering, Jingdezhen Ceramic University, Jingdezhen 333001, ChinaDepartment of Mechanical Engineering, Tsinghua University, Beijing 100084, ChinaAn enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained layer damping (ACLD) thin plate structure is taken as the research object to study vibration control. Based on the FEM method, energy method, and Hamilton principle, the dynamic model of an ACLD thin plate structure is derived, in which the Golla–Hughes–McTavish (GHM) model is used to characterize the damping characteristics of the viscoelastic layer, and the equivalent Rayleigh damping is used to characterize the damping characteristics of the base layer. The order of the model is reduced based on the high-precision physical condensation method and balance reduction method, and the model has good controllability and observability. An LQR controller is designed to actively control the ACLD sheet, and the controller parameters and piezoelectric sheet parameters are optimized. The results show that the finite element model established in this paper is accurate under different boundary conditions, and the model can still accurately and reliably describe the dynamic characteristics of the original system in the time and frequency domain after using the joint reduction method. Under different excitation and boundary conditions, LQR control can effectively suppress structural vibration. Considering the performance and cost balance, the most suitable control parameter for the system is: Q-matrix coefficient is between 1 × 10<sup>4</sup> and 1 × 10<sup>5</sup>, the R-matrix coefficient is between 1 and 10, and the thickness of the piezoelectric plate is 0.5 mm.https://www.mdpi.com/1996-1944/16/4/1652active constrained layer dampingfinite element modelingmodel order reductionactive controlviscoelastic material
spellingShingle Zhicheng Huang
Huanyou Peng
Xingguo Wang
Fulei Chu
Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment
Materials
active constrained layer damping
finite element modeling
model order reduction
active control
viscoelastic material
title Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment
title_full Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment
title_fullStr Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment
title_full_unstemmed Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment
title_short Finite Element Modeling and Vibration Control of Plates with Active Constrained Layer Damping Treatment
title_sort finite element modeling and vibration control of plates with active constrained layer damping treatment
topic active constrained layer damping
finite element modeling
model order reduction
active control
viscoelastic material
url https://www.mdpi.com/1996-1944/16/4/1652
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AT huanyoupeng finiteelementmodelingandvibrationcontrolofplateswithactiveconstrainedlayerdampingtreatment
AT xingguowang finiteelementmodelingandvibrationcontrolofplateswithactiveconstrainedlayerdampingtreatment
AT fuleichu finiteelementmodelingandvibrationcontrolofplateswithactiveconstrainedlayerdampingtreatment