Analytical Formulation and Damping Analysis of Beams With Enhanced Active Constrained Layer Treatments Under Various Boundary Conditions

2005 ◽  
Author(s):  
J. X. Gao ◽  
W. H. Liao
Keyword(s):  
Boundary Conditions ◽  
Analytical Formulation ◽  
Edge Elements ◽  
Various Boundary Conditions ◽  
Damping Characteristics ◽  
Damping Treatments ◽  
Active Constrained Layer ◽  
Loss Factors

In this paper, an energy-based approach is developed to investigate damping characteristics of beams partially covered with enhanced self-sensing active constrained layer (ESACL) damping treatments. Analytical formulations for the active, passive, and total hybrid modal loss factors of partially covered beams with ESACL under various boundary conditions are derived. The results show that the edge elements in the ESACL can significantly improve the system damping performance as compared to the active constrained layer treatment. The effects of other key parameters and the boundary conditions have also been investigated.

Damping Characteristics of Beams with Enhanced Self-Sensing Active Constrained Layer Treatments Under Various Boundary Conditions

2004 ◽  
Vol 127 (2) ◽  
pp. 173-187 ◽  
Author(s):  
J. X. Gao ◽  
W. H. Liao
Keyword(s):  
Boundary Conditions ◽  
Careful Analysis ◽  
Constrained Layer Damping ◽  
Various Boundary Conditions ◽  
Damping Characteristics ◽  
Control Gain ◽  
Active Constrained Layer Damping ◽  
Damping Treatments ◽  
Active Constrained Layer ◽  
Loss Factors

In this paper, an energy-based approach is developed to investigate damping characteristics of beams with enhanced self-sensing active constrained layer (ESACL) damping treatments. Analytical formulations for the active, passive, and total hybrid modal loss factors of the cantilever and simply-supported beams partially covered with the ESACL are derived. The analytical formulations are validated with the results in the literature and experimental data for the cantilever beam. Beams with other boundary conditions can also be solved and discussed using the presented approach. The results show that the edge elements in the ESACL can significantly improve the system damping performance as compared to the active constrained layer damping treatment. The effects of key parameters, such as control gain, edge element stiffness, location, and coverage of the ESACL patch on the system loss factors, have been investigated. It has also been shown that the boundary conditions play an important role on the damping characteristics of the beam structure with the ESACL treatment. With careful analysis on the location and coverage of the partially covered ESACL treatment, effective vibration control for beams under various boundary conditions for specific modes of interest would be achieved.

A Modified Fourier Solution for Free Damped Vibration Analysis of Sandwich Viscoelastic-Core Conical Shells and Annular Plates with Arbitrary Restraints

2016 ◽  
Vol 08 (08) ◽  
pp. 1650094 ◽  
Author(s):  
Chuanmeng Yang ◽  
Guoyong Jin ◽  
Weijian Xu ◽  
Zhigang Liu
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Current Method ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Annular Plates ◽  
Damping Characteristics ◽  
Loss Factors

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

Frequency and Loss Factors of Sandwich Beams under Various Boundary Conditions

1978 ◽  
Vol 20 (5) ◽  
pp. 271-282 ◽  
Author(s):  
D. K. Rao
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Energy Approach ◽  
Sandwich Beams ◽  
Exact Results ◽  
Various Boundary Conditions ◽  
Complete Set ◽  
Loss Factors

A complete set of equations of motion and boundary conditions governing the vibration of sandwich beams are derived by using the energy approach. They are solved exactly for important boundary conditions. The computational difficulties that were encountered in previous attempts at the exact solution of these equations have been overcome by careful programming. These exact results are presented in the form of design graphs and formulae, and their usage is illustrated by examples.

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

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