Single side damage simulations and detection in beam-like structures

The vibrational effect is one of the primary considerations during construction due to the ambient excitation from the surrounding environment. Thus, it is necessary to find the most dependable Finite Element (FE) model for the actual structure to improve its quality and life span on site. In this context, the study included a 3-story building model that was analyzed using finite element analysis to determine its dynamic properties such as natural frequency and mode shape to avoid the resonance effect. It is due to the importance of obtaining a reliable and accurate model by verifying with the results of the Operational Modal Analysis (OMA). In general, the goal of this study is to update the FE model so that it is close to the actual scaled model based on the previous OMA study. As a result, an initial linear FE model of the 3-story building scaled model was created using CAD software based on actual geometry to describe the structure's physical properties. The FE model was then imported into CAE software, where the boundary condition and estimated material properties were assigned to determine the effect of random vibration. Through the pairing of Finite Element Analysis results and previous studies, 9 natural frequencies and 9 mode shapes were extracted. The Modal Assurance Criterion (MAC) was used to compare the mode shape of FE results against the OMA to determine the degree of consistency between paired mode shapes. A model updating process was carried out to reduce the discrepancy between the methods. The uncertainties arising from the initial conditions have been discussed in terms of the stiffness of the material used. The updated model allows for an evaluation of the structure's current actions as well as the development of models for a wide range of potential future research scenarios.

Comparison of rubbing induced vibration responses using varying-thickness-twisted shell and solid-element blade models

The primary objective of this numerical study is to provide a finite element (FE) analysis approach for segmental structures. The study was conducted using a hollow circular segmental structure model capable of adequately imitating real structural behavior and deals with the effect of varying number of segments on structural performance. In order to verify the FE procedure conducted by DIANA software, comparisons are made with the acquired numerical results and the results taken from previous experimental studies for 1 reinforced concrete (RC) beam, 2 post-tensioned (PT) beam, and 3 segmental post-tensioned beams (SPT). For the considered cases, 1D line, 2D shell, and 3D solid FE models are made, and it is found out that the 3D solid model with interface elements yields the most plausible results. Further, the FE model was constructed to accurately predict segment joint behavior concerning the relationship between the number of segments, concrete compressive strength, and the width of the openings at the segment joints up to collapse. In this study, a hollow circular segmental structure model is utilized to mimic real structural behavior, presenting a novel perspective on internal force transfer mechanisms within segmental structures. Moreover, the FE model is tailored to accurately predict segment joint behavior, elucidating the intricate relationship between the number of segments, concrete compressive strength, and the width of openings at segment joints up to collapse. In addition to presenting a robust numerical analysis framework, this study contributes novel insights into the complex interplay between segmental geometry, material properties, and structural behavior, thus advancing the state-of-the-art in segmental structural design. Thus, a modular construction methodology is proposed for segmental beam type structures ensuring safety, efficiency, and flexibility in challenging load conditions.

Fatigue failures at fastener holes in structures are undesirable as they can lead to catastrophic mechanical failures. Interference pins create interference fits with joined components to reduce stresses around fastener holes and extend the fatigue life of a structure. In this research, a novel method for finite element (FE) modeling of interference pin connections in a wind turbine lattice tower component was developed. The installation of interference pins was modeled using a two-stage process that causes local stiffness changes in joined members of the component. The local stiffness changes were accounted for in the FE model by using cylinders to represent the interference pins. An experimental setup, including a three-dimensional (3D) scanning laser Doppler vibrometer (SLDV) and a mirror, was used to measure out-of-plane and in-plane natural frequencies and mode shapes of the component. Ten out-of-plane modes and one in-plane mode from the FE model are compared with the experimental results to validate the accuracy of the FE modeling approach. The maximum percent difference between the theoretical and experimental natural frequencies of the component is 3.21%, and the modal assurance criterion (MAC) values between the theoretical and experimental mode shapes are 0.92 or greater, showing good agreement between the theoretical and experimental modal parameters of the component.

Damage detection and structural health monitoring have always been of great importance to civil engineers and researchers. Vibration-based damage detection has several advantages compared to traditional methods of non-destructive evaluation, such as ground penetrating radar (GPR) or ultrasonic testing, since they give a global response and are feasible for large structures. Damage detection requires a comparison between two systems states, the baseline or “healthy state”, i.e., the initial modal parameters, and the damaged state. In this study, system identification (SI) was carried out on a pedestrian bridge by measuring the dynamic response using six low-cost triaxial accelerometers. These low-cost accelerometers use a micro-electro-mechanical system (MEMS), which is cheaper compared to a piezoelectric sensor. The frequency domain decomposition algorithm, which is an output-only method of modal analysis, was used to obtain the modal properties, i.e., natural frequencies and mode shapes. Three mode shapes and frequencies were found out using system identification and were compared with the finite element model (FEM) of the bridge, developed using the commercial finite element software, Abaqus. A good comparison was found between the FEM and SI results. The frequency difference was nearly 10%, and the modal assurance criterion (MAC) of experimental and analytical mode shapes was greater than 0.80, which proved to be a good comparison despite the small number of accelerometers available and the simplifications and idealizations in FEM.

In this paper, we discuss the dynamics of beams with multiple delaminations. The objective of the study is to use the dynamic response of the delaminated beams in health monitoring of composite structures. As a first step, we present experimental results on the vibrations of a cantilever beam with multiple delaminations. These experiments are conducted by exciting the beam with piezoelectric actuators. The response is detected by using a high-speed video camera to study the existence of delamination opening modes in a beam with multiple delaminations. Then, an analysis of natural frequencies and mode shapes, for a delaminated beam, is presented by using analytical techniques. The measured dynamic responses of the beam with multiple delaminations are also presented. The experimentally detected nonlinear response is discussed. Introduction Delaminations or interlayer cracks and impact damages are typical defects observed in composite structures. The presence of these defects changes the dynamic characteristics of the structure . Some of the specific changes in the observed dynamic characteristics include changes in natural frequencies, changes in the mode shapes and changes in damping ratios. These changes can be used to identify the existence, location and magnitude of a delamination or an impact damage, before they can grow to their critical sizes. Studies, to date, are concerned with the dynamics of beams and plates with a single delamination. In this paper, we specifically discuss the structural dynamics of a beam with multiple delaminations. This information can be used to develop health-monitoring techniques for composite beams with multiple delaminations. In an earlier paper, Luo and Hanagud studied the effects of defects, like saw-cuts, impact damage and delamination, on the structural dynamic characteristics of composite beams. They have shown that perturbations in natural frequencies and modes of a beam, due to defects, can be used for health monitoring of structures. In particular, it has been shown that an integral equation that considers perturbations in curvature modes and natural frequencies can be very effectively used to detect local defects. To distinguish delaminations from other types of monitored (identified) defects Luo and Hanagud have discussed nonlinear effects like superharmonic response in the dynamic response of a harmonically excited delaminated beam. They considered only a single delamination. In this paper we study beams with multiple delaminations. More specifically, we discuss dynamic response and the changes in natural frequencies, mode shapes due to multiple delaminations in a composite beam. One of the earliest models for vibration analysis of composite beams with delaminations was proposed by Ramkumar et al. This model simply used four Timoshenko beams connected at the delamination edges to model a composite beam with one throughwidth delamination. The predicted frequencies, based on this model, were consistently lower than the results of experimental measurements. Wang et al. improved the analytical solution by including coupling between flexural and axial vibrations of the delaminated sublaminates. Using an isotropic beam with splits and the classical beam model, they found that the calculated natural frequencies were closer to experimental results. With similar considerations, Nagesh Gummadi and Hanagud formulated a finite element solution for arbitrary composite beams. In the finite element models, they considered a classical composite beam model as well as the beam model with high order shear deformations. Mujumdar and Suryanarayan have proposed a model which imposed a constraint between the delaminated sublaminates to force them to have the same flexural displacement. This model was unable to * Ph.D. Student, School of Aerospace Engineering † Professor, School of Aerospace Engineering, AIAA Member Copyright © 1999 The American Institute of Aeronautics and Astronautics Inc. All rights reserved

Finite element analysis of wind turbine blades subjected to torsional loads: Shell vs solid elements

The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation of the results from experimental and numerical tests with hollow section cantilevers containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional rectangular shell elements and one rectangular shell element with a transverse, internal, open crack. The analytical results from the numerical models are compared with data obtained from experimental tests. The numerical models give good agreements with the experimental data. The beam model takes into account only the first mode of the crack evaluation. In the shell model all three modes of the crack growth are taken into account. Nevertheless, the results obtained for both models are satisfactory because the beam is subjected to bending. It can be concluded that it is sufficient to use crack models for calculating natural frequencies in bending, taking into account the first mode of the crack extension only.

Finite element model updating from full-field vibration measurement using digital image correlation

Recently, many structural damage detection (SDD) methods have been proposed to monitor the safety of structures. As an important modal parameter, mode shape has been widely used in SDD, and the difference of vectors was adopted based on sensitivity analysis and mode shapes in the existing studies. However, amplitudes of mode shapes in different measured points are relative values. Therefore, the difference of mode shapes will be influenced by their amplitudes, and the SDD results may be inaccurate. Focus on this deficiency, a multi-strategy SDD method is proposed based on the included angle of vectors and sparse regularization in this study. Firstly, inspired by modal assurance criterion (MAC), a relationship between mode shapes and changes in damage coefficients is established based on the included angle of vectors. Then, frequencies are introduced for multi-strategy SDD by a weighted coefficient. Meanwhile, sparse regularization is applied to improve the ill-posedness of the SDD problem. As a result, a novel convex optimization problem is proposed for effective SDD. To evaluate the effectiveness of the proposed method, numerical simulations in a planar truss and experimental studies in a six-story aluminum alloy frame in laboratory are conducted. The identified results indicate that the proposed method can effectively reduce the influence of noises, and it has good ability in locating structural damages and quantifying damage degrees.

Vibration and damping of carbon fiber reinforced polymer orthogonal lattice truss sandwich panels manufactured by a new manufacturing process

A homogenization method for the vibration analysis of periodic sandwich panels is presented. Periodic boundary conditions are applied to a representative volume element (RVE) of the structures. The complex responses of the RVE under eight sinusoidal excitations are calculated and the complex stiffness matrix of the sandwich panels is obtained by the direct-solution steady-state dynamic analysis (DSDA) using the finite element method (FEM) in the frequency domain. Based on equivalent single-layer (ESL) theory and finite element-modal strain energy (FE-MSE) method, the natural frequencies, the mode shapes and the loss factors of the structures are obtained by shell models. The effectiveness of the homogenization method is validated by using pyramidal lattice truss sandwich panels made of carbon fiber reinforced plastics (CFRP). The results obtained by the homogenization method are compared with those obtained by experiments and solid models. The effects of the number of cells and damping layers are discussed.

Modal analysis is an approach to determine the dynamic behavior of a structure through numerical analysis or experimental approach. Nowadays, numerical analysis has been preferred by most researchers and engineers compared to experimental analysis to analyze the structure due to expenditure and time consuming factors of the research. Recently, numerical analysis is done computationally or well known as Finite Element Analysis (FEA) by using finite element (FE) model to replicate the real test structure. Instead of advantage of FE analysis, the trustworthiness of FE model has been questioned since simplification has been made during design stage for complex structure and inaccurate of geometry input of the model. Hence, this paper is carried out to reduce the discrepancies between numerical prediction results with measured test data on FE model of exhaust structure by implementing FE model updating using SOL200 algorithm. Initially, the FE model is running on normal mode analysis SOL103 to extract the modal parameters such as natural frequency and mode shape. Then, the numerical pre-diction result has been correlated and validated with measured test data obtained through Experimental Modal Analysis (EMA). Due to disagreement between numerical result and experimental data in correlation process, the FE model has been updated using SOL200 algorithm. The percentage error between numerical prediction result and measured test data is minimized from 5.67 to 3.23% after been updated. It’s shown the capability SOL200 algorithm in preparing the reliable FE model before been used for further analysis such as structural dynamic modification.KeywordsDynamic studyJoints strategyFinite element analysisExperimental modal analysisFE model updating

Tree risk assessment requires mechanical response studies, but simplification of the shape, material, or boundary conditions is necessary when dealing with such complex structures. To observe overall tree response, sub-structuring to several levels of detail can be used, enabled by recent developments in numerical methods and three-dimensional laser scanning (3D scan). This study aimed to determine an appropriate level of geometry and loading simplification allowed for high-order branches at the crown border, which is useful for the mechanical analysis of structured tree models. Four higher-order branches were pruned and experimentally tested by single-point loading. Beam and solid finite-element models (FEMs) were created based on measured geometric parameters and detailed 3D scans, respectively. The FEMs were used to analyze seven loading scenarios with force applied at (a) the center of gravity, (b) the top of side branches, (c) key discrete points, and (d) uniformly to the whole volume (to each finite element). Force was distributed by ratios weighted according to the mass, area, and diameter of side branches; or according to the mass of each finite element. The results showed no significant difference between the beam model and 3D scan-based model. The scenarios with finite elements’ mass-based force distribution deviated significantly from those of the other scenarios. The most simplified single-point loading caused a deviation in the deflection curve. The deviation of single-point loading in the case of the bending moment was related to force distribution ratios given by the branches architecture. Therefore, such loading simplification is not considered always appropriate. Consistency between the bending moment and branch deflection provided a representative mechanical response, recommended for further modeling of trees by sub-structuring.

While doing vibration analysis in terms of the dynamic response of a beam, the end conditions, in most of the cases, are assumed to be fixed, simply supported, free or sliding imposing an ideal condition of end support displacement. But, in real engineering structures, the end supports are non-ideal (for example welded, riveted etc.) and allow certain degree of translational or rotational motion of the support ends. To simulate the effect of real engineering boundary states, a combination of linear and torsional springs has been considered at the two boundaries of the beam structure. The theoretical analysis of free undamped beam structure with elastically restrained end conditions has been undertaken using approximation of the modal displacement as a Fourier cosine series to generate natural frequencies and corresponding mode shape equations. The effect of variation in stiffness values of the boundary springs on the vibration characteristics (natural frequency, mode shapes and dynamic response) has been presented for vibration conditions for the free undamped beam structure. Thereafter, forced undamped and damped (taking combined effects of both viscous and structural damping) beam structures have been theoretically analysed to generate response equation. Finally, numerical assessment has been undertaken to present the effect of damping ratio, forcing frequency and force magnitude on the response of a nearly clamped beam and has been compared with the response of an undamped beam under similar forcing and boundary condition. The results indicate considerable effects of real boundary condition, on the vibration characteristics and dynamic response of beam structures thus cannot be ignored in design of real engineering structures. Further, the presence of damping does not change the vibration characteristics beam structures, but is useful in achieving steady-state condition of response for a harmonic force input. The technique presented provides a simplified and convenient tool for obtaining vibration response for real engineering boundary supports. Further, the beam model can be extended for analysis of plate structures considering non-ideal boundary conditions.