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.

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.

Damage Modes Detection of Composite Laminates Using Improved Modal Strain Energy Method

2011 ◽  
Vol 338 ◽  
pp. 375-379
Author(s):  
Jia Hui ◽  
Xiao Peng Wan ◽  
Mei Ying Zhao
Keyword(s):  
Composite Laminates ◽  
Strain Energy ◽  
Composite Laminate ◽  
Dynamic Properties ◽  
Structural Parameters ◽  
Damage Index ◽  
Qualitative Description ◽  
Mode Shapes ◽  
Modal Strain Energy ◽  
Damage Level

Damage causes changes in structural parameters, which in turn, modify dynamic properties, such as natural frequencies and mode shapes. Based on this assumption, this paper presents a new approach to detect different damage modes of composite laminates. Finite element modal analysis is performed on the composite laminate to obtain the modal mode shapes used to compute the modal strain energy. Consequently, an improved damage index is defined by using the ratio of modal strain energies of composite laminates before and after damage. The proposed method is validated using a numerical simulation of a composite laminate with damages in some elements, which are simulated by reducing elements’ material stiffness properties under a combined material properties degradation rule. The result shows that six kinds of damage modes of composite laminates can be detected by this method preferably and give a qualitative description for the damage level.

Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) With a Gap in Mindlin Plates or Panels

2007 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Lap Joint ◽  
Bending Vibrations ◽  
Joint System ◽  
Adhesive Layers ◽  
Bonded Joint ◽  
Free Bending

In this present study, the “Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap in Mindlin Plates or Panels” are theoretically analyzed and are numerically solved in some detail. The “plate adherends” and the upper and lower “doubler plates” of the “Bonded Joint” system are considered as dissimilar, orthotropic “Mindlin Plates” joined through the dissimilar upper and lower very thin adhesive layers. There is a symmetrically and centrally located “Gap” between the “plate adherends” of the joint system. In the “adherends” and the “doublers” of the “Bonded Joint” assembly, the transverse shear deformations and the transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers are assumed to be linearly elastic continua with transverse normal and shear stresses. The “damping effects” in the entire “Bonded Joint” system are neglected. The sets of the dynamic “Mindlin Plate” equations of the “plate adherends”, the “double doubler plates” and the thin adhesive layers are combined together with the orthotropic stress resultant-displacement expressions in a “special form”. This system of equations, after some further manipulations, is eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in terms of the “state vectors” of the problem. Hence, the final set of the aforementioned “Governing Systems of Equations” together with the “Continuity Conditions” and the “Boundary conditions” facilitate the present solution procedure. This is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials). The present theoretical formulation and the method of solution are applied to a typical “Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap”. The effects of the relatively stiff (or “hard”) and the relatively flexible (or “soft”) adhesive properties, on the natural frequencies and mode shapes are considered in detail. The very interesting mode shapes with their dimensionless natural frequencies are presented for various sets of boundary conditions. Also, several parametric studies of the dimensionless natural frequencies of the entire system are graphically presented. From the numerical results obtained, some important conclusions are drawn for the “Bonded Joint System” studied here.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

scholarly journals Looseness localization for bolted joints using Bayesian operational modal analysis and modal strain energy

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880869 ◽  
Author(s):  
Yu-Jia Hu ◽  
Wei-Gong Guo ◽  
Cheng Jiang ◽  
Yun-Lai Zhou ◽  
Weidong Zhu
Keyword(s):  
Modal Analysis ◽  
Strain Energy ◽  
Damage Index ◽  
Operational Modal Analysis ◽  
Modal Identification ◽  
Bolted Joints ◽  
Mode Shapes ◽  
Bolted Connections ◽  
Modal Strain Energy ◽  
Beam Structures

Bayesian operational modal analysis and modal strain energy are employed for determining the damage and looseness of bolted joints in beam structures under ambient excitation. With this ambient modal identification technique, mode shapes of a damaged beam structure with loosened bolted connections are obtained based on Bayesian theory. Then, the corresponding modal strain energy can be calculated based on the mode shapes. The modal strain energy of the structure with loosened bolted connections is compared with the theoretical one without bolted joints to define a damage index. This approach uses vibration-based nondestructive testing of locations and looseness of bolted joints in beam structures with different boundary conditions by first obtaining modal parameters from ambient vibration data. The damage index is then used to identify locations and looseness of bolted joints in beam structures with single or multiple bolted joints. Furthermore, the comparison between damage indexes due to different looseness levels of bolted connections demonstrates a qualitatively proportional relationship.

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.

Effects of Variable Non-Central Locations of Bonded Double Doubler Joint System on Free Flexural Vibrations of Orthotropic Composite Mindlin Plate or Panel Adherents

2012 ◽  
Author(s):  
U. Yuceoglu ◽  
Ö. Güvendik
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Central Position ◽  
Joint Region ◽  
Joint System ◽  
Adhesive Layers ◽  
Governing System ◽  
Plate Elements ◽  
Interpolation Polynomials

This study investigates the “Effects of Variable Non-Central Locations of Bonded Double Doubler Joint System on Free Flexural Vibrations of Orthotropic Composite Mindlin Plate or Panel Adherents”. The problem is theoretically analyzed and is numerically solved in terms of the natural frequencies and the corresponding mode shapes of the entire “System”. The “Bonded Double Doubler Joint System” and the “Plate of Panel Adherents” are considered as dissimilar “Orthotropic Mindlin Plates”. In all plate elements, the transverse shear deformations and the transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers in the “Bounded Joint Region” are assumed to be linearly elastic continua with transverse normal and shear deformations. The “damping effects” in the adhesive layers and in all plate elements of the “System” are neglected. The sets of the “Dynamic Mindlin Equations” of both upper and lower “Doubler Plates” and the “Plate or Panel Adherents” and the adhesive layer equations are combined together with the orthotropic stress resultant-displacement expressions resulting in a set of “Governing System of PDE’s” in a “special form”. By making use of the “Classical Levy’s Solutions”, in aforementioned “Governing PDE’s” and following some algebraic manipulations and combinations, the “Governing System of the First Order Ordinary Differential Equations” are obtained in compact “state vector” forms. Thus, the “Initial and Boundary Value Problem” at the beginning is finally converted into a “Multi-Point Boundary Value Problem” of Mechanics (and Physics). These analytical results developed facilitate the present method of solution that is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. The final set of the “Governing System of ODE’s” is numerically integrated by means of the “MTMM with Interpolation Polynomials”. In this way, the natural frequencies and the mode shapes of the “Bonded System”, depending on the variable non-central location of the “Bonded Double Doubler Joint System” are computed for several sets of the far left and the far right “Boundary Conditions” of the “Orthotropic Plate or Panel Adherents”. It was observed that, based on the numerical results, the mode shapes and their natural frequencies are very much affected by the variable position (or location) of the “Bonded Double Doubler Joint” in the “System”. It was also found that as the “Bonded Double Doubler Joint” moves from the central position in the “System” towards the increasingly non-central position, the natural frequencies (in comparison with those of the central position) changes, respectively. The highly-stiff “Bonded Double Doubler Joint Region” becomes “almost stationary” in all modes in “Hard” Adhesive cases.

scholarly journals UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

scholarly journals Vibration-Based Damage Assessment in Gravity-Based Wind Turbine Tower under Various Waves

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Cong-Uy Nguyen ◽  
So-Young Lee ◽  
Heon-Tae Kim ◽  
Jeong-Tae Kim
Keyword(s):  
Wind Turbine ◽  
Damage Assessment ◽  
Natural Frequencies ◽  
Modal Identification ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Damage Scenarios ◽  
Wind Turbine Tower ◽  
Induced Variation ◽  
Wave Induced

In this study, the feasibility of vibration-based damage assessment in a wind turbine tower (WTT) with gravity-based foundation (GBF) under various waves is numerically investigated. Firstly, a finite element model is constructed for the GBF WTT which consists of a tower, caisson, and foundation bed. Eigenvalue analysis is performed to identify a few vibration modes of interest, which represent complex behaviors of a flexible tower, rigid caisson, and deformable foundation. Secondly, wave-induced dynamic pressures are analyzed for a few selected wave conditions and damage scenarios are also designed to simulate the main components of the target GBF WTT. Thirdly, forced vibration responses of the GBF WTT are analyzed for the wave-induced excitation. Then modal parameters (i.e., natural frequencies and mode shapes) are extracted by using a combined use of time-domain and frequency-domain modal identification methods. Finally, the variation of modal parameters is estimated by measuring relative changes in natural frequencies and mode shapes in order to quantify the damage-induced effects. Also, the wave-induced variation of modal parameters is estimated to relatively assess the effect of various wave actions on the damage-induced variation of modal parameters.

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.

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