Evaluation of a Strain Energy Equivalence Principle (SEEP)-Based Continuum Damage Model

2007 ◽  
Vol 353-358 ◽  
pp. 1199-1202
Author(s):  
Usik Lee ◽  
Deokki Youn ◽  
Sang Kwon Lee
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Damage Model ◽  
Elastic Stiffness ◽  
Constitutive Law ◽  
Mode Shapes ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Square Plate

A new continuum damage theory (CDT) has been proposed by Lee et al. (1997) based on the SEEP. The CDT has the apparent advantage over the other related theories because the complete constitutive law can be readily derived by simply replacing the virgin elastic stiffness with the effective orthotropic elastic stiffness obtained by using the proposed continuum damage theory. In this paper, the CDT is evaluated by comparing the mode shapes and natural frequencies of a square plate containing a small line-through crack with those of the same plate with a damaged site replaced with the effective orthotropic elastic stiffness computed by using the CDT.

A Theory of Continuum Damage Mechanics for Anisotropic Solids

1999 ◽  
Vol 66 (1) ◽  
pp. 264-268 ◽  
Author(s):  
U. Lee
Keyword(s):  
Elastic Properties ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Anisotropic Elastic ◽  
Isotropic Solids ◽  
Line Crack

This paper develops a fracture mechanics based continuum damage theory for initially anisotropic solids by extending the author’s previous damage theory for isotropic solids. The concepts of strain energy equivalence principle (SEEP) and equivalent line-crack modeling are used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged anisotropic elastic properties and a scalar damage variable.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1993 ◽  
Author(s):  
Mohan D. Rao ◽  
Krishna M. Gorrepati
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

Abstract This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

Analysis of Modal Parameters of Adhesively Bonded Double-Strap Joints by the Modal Strain Energy Method

1996 ◽  
Vol 118 (1) ◽  
pp. 28-35 ◽  
Author(s):  
K. M. Gorrepati ◽  
M. D. Rao
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Structural Parameters ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Adhesively Bonded ◽  
Modal Strain Energy ◽  
Joint System ◽  
Damping Material

This paper presents the analysis of modal parameters (natural frequencies, damping and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joints with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

Quantitative Vibration Amplitude Measurement Using Stroboscopic Phase Shifting ESPI

2006 ◽  
Vol 321-323 ◽  
pp. 95-98 ◽  
Author(s):  
Hyun Chul Jung ◽  
Koung Suk Kim
Keyword(s):  
Vibration Amplitude ◽  
Natural Frequencies ◽  
Measurement Techniques ◽  
Phase Shifting ◽  
Mode Shapes ◽  
Ansys Analysis ◽  
Amplitude Measurement ◽  
Stroboscopic Illumination ◽  
Square Plate ◽  
Optical Vibration

The stroboscopic phase shifting ESPI (SPS-ESPI), one of the optical vibration amplitude measurement techniques, is presented. Although the general PS-ESPI can be used for quantitative deformation measurement of the object, this technique cannot measure the vibration amplitude with itself only. The phase change due to the vibration of the object cannot be calculated with general PS-ESPI correctly. Therefore, in order to solve this problem, the stroboscopic illumination must be introduced to the general PS-ESPI. This can be done by using a device called as AOM (Acousto-Optic Modulator). In this paper, SPS-ESPI is applied to measure the vibration amplitude of the square plate whose all edges were fixed. The natural frequencies and mode shapes are analyzed by using ANSYS. And the results obtained by using SPS-ESPI technique are compared with that of the ANSYS analysis. The vibration amplitude is measured by using SPS-ESPI quantitatively.

Use of a Continuum Damage Model Based on Energy Equivalence to Predict the Response of a Single-Crystal Superalloy

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
P. Grammenoudis ◽  
D. Reckwerth ◽  
Ch. Tsakmakis
Keyword(s):  
Equivalence Principle ◽  
Evolution Equations ◽  
Dynamic Recovery ◽  
Damage Model ◽  
Yield Function ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Deformation Processes ◽  
Multiple Holes

Anisotropic viscoplasticity coupled with anisotropic damage has been modeled in previous works by using the energy equivalence principle appropriately adjusted. Isotropic and kinematic hardenings are present in the viscoplastic part of the model and the evolution equations for the hardening variables incorporate both static and dynamic recovery terms. The main difference to other approaches consists in the formulation of the energy equivalence principle for the plastic stress power and the rate of hardening energy stored in the material. As a practical consequence, a yield function has been established, which depends, besides effective stress variables, on specific functions of damage. The present paper addresses the capabilities of the model in predicting responses of deformation processes with complex specimen geometry. In particular, multiple notched circular specimens and plates with multiple holes under cyclic loading conditions are considered. Comparison of predicted responses with experimental results confirms the convenience of the proposed theory for describing anisotropic damage effects.

scholarly journals Vibration Analysis of Circular Arch Element Using Curvature

2008 ◽  
Vol 15 (5) ◽  
pp. 481-492 ◽  
Author(s):  
H. Saffari ◽  
R. Tabatabaei ◽  
S.H. Mansouri
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Axial Strain ◽  
Mode Shapes ◽  
Element Formulation ◽  
Equilibrium Equations ◽  
Lagrangian Equation ◽  
Circular Arch ◽  
Nodal Displacements ◽  
Element Technique

In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.

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