Changes In Mode Shapes Research Articles

The impact of adsorbate mass on a nanomechanical resonator

We present a theoretical investigation on the dynamic characteristics of a nanomechanical resonator attached with an adsorbate at an arbitrary position. Cantilevered and bridged configurations are both considered for the resonators. Closed-form expressions relating the exact mode shape and the resonant frequency of the loaded resonator are obtained analytically using the Rayleigh–Ritz theorem, from which the relationship between the adsorbate mass and changes in the dynamic characteristics can be obtained. The results indicate that the mode shape change due to adsorption of a relatively large particle can influence the performance of the nanomechanical resonator considerably.

Stability analysis of deepwater compliant vertical access riser about parametric excitation

If heave motion in the platform causes horizontal parametric vibration of a Compliant Vertical Access Riser (CVAR), the riser may become unstable. A combination of riser parameters lies in the unstable region aggravates vibrational damage to the riser. Change of axial tensile stress in the riser combined with its natural frequency and mode shape change results in mode coupling. In accordance with the state transition matrices of the riser in the coupled and uncoupled states, the stable and unstable regions were obtained by Floquet theory, and the vibration response under different conditions was obtained. The parametric excitation of the CVAR is shown to occur mainly in first-order unstable regions. Mode coupling may cause parametric excitation in the least stable regions. Damping reduces the extent of unstable regions to a certain extent.

Influence of seasonal freezing on dynamic bridge characteristics using in-situ monitoring data

This paper uses the results of experimental and finite element analyses of the Campbell Creek Bridge in Alaska to highlight the effect of seasonal freezing on bridge dynamic response and the structural and geotechnical parameters controlling the changes in response. The experimental modal characteristics of the bridge were defined using dynamic monitoring data collected over 1 year by means of several frequency and time domain system identification techniques. Good agreement was shown across the range of techniques and clear modal characteristics were defined, suggesting a significant increase in natural frequency and change in mode shape of the bridge due to seasonal freezing effects. Elastic finite element models of the bridge, utilizing a Winkler spring approach, were able to effectively capture the experimental dynamic response, with the natural frequencies and mode shapes of the bridge in the transverse direction shown to be controlled by the changes in the stiffness of the foundation soil and the bearings. The significant shift in bridge dynamic characteristics and change in boundary conditions due to seasonal freezing demonstrates the need for seismic assessment of the bridge stock across potential temperature ranges in seismically active regions that experience seasonal freezing.

Modelization of boundary friction damping induced by second-order bending strain

Damping induced by frictional slipping in assembled structures is always a difficulty in vibration mechanics. Sometimes the cycling movement in riveted or bolted joint is generated by in-plane force field which is directly related to transverse deflection. Since this phenomenon cannot be described by classical plate theory, a general formulation based on von-Kármán plate theory is proposed in this study. The response estimation involving damping is conducted with the Krylov-Bogoliubov linearization method (HBM). The notion of non-linear mode is introduced in the context of single mode method and multi-mode method. The influence of mode shape change on forced response is also analyzed.

Structural damage detection based on improved frequency change ratio

Frequency Change Ratio (FCR) based damage detection methodology for structural health monitoring (SHM) is analyzed in detail. The effectiveness of damage localization using FCR for some slight damage cases and worse ones are studied on an asymmetric planar truss numerically. Disadvantages of damage detection using FCR in practical application are found and the reasons for the cases are discussed. To conquer the disadvantages of FCR, an Improved Frequency Change Ratio (IFCR) based damage detection method which takes the changes of mode shapes into account is proposed. Verification is done in some damage cases and the results reveal that IFCR can identify the damage more efficiently. Noisy cases are considered to assess the robustness of IFCR and results indicate that the proposed method can work well when the noise is not severe.

Vibration‐Based Damage Assessment in Gravity‐Based Wind Turbine Tower under Various Waves

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.

Hierarchical neural network for damage detection using modal parameters

This study develops a damage detection method based on neural networks. The performance of the method is numerically and experimentally verified using a three-story shear building model. The framework is mainly composed of two hierarchical stages to identify damage location and extent using artificial neural network (ANN). The normalized damage signature index, that is a normalized ratio of the changes in the natural frequency and mode shape caused by the damage, is used to identify the damage location. The modal parameters extracted from the numerically developed structure for multiple damage scenarios are used to train the ANN. The positive alarm from the first stage of damage detection activates the second stage of ANN to assess the damage extent. The difference in mode shape vectors between the intact and damaged structures is used to determine the extent of the related damage. The entire procedure is verified using laboratory experiments. The damage is artificially modeled by replacing the column element with a narrow section, and a stochastic subspace identification method is used to identify the modal parameters. The results verify that the proposed method can accurately detect the damage location and extent.

Influence of Geometric Design Parameters Onto Vibratory Response and High-Cycle Fatigue Safety for Turbine Blades With Friction Damper

Among the major concerns for high aspect-ratio, turbine blades are forced and self-excited (flutter) vibrations, which can cause failure by high-cycle fatigue (HCF). The introduction of friction damping in turbine blades, such as by coupling of adjacent blades via under platform dampers, can lead to a significant reduction of resonance amplitudes at critical operational conditions. In this paper, the influence of basic geometric blade design parameters onto the damped system response will be investigated to link design parameters with functional parameters like damper normal load, frequently used in nonlinear dynamic analysis. The shape of a simplified turbine blade is parameterized along with the under platform damper configuration. The airfoil is explicitly included into the parameterization in order to account for changes in blade mode shapes. For evaluation of the damped system response, a reduced-order model for nonlinear friction damping is included into an automated three-dimensional (3D) finite element analysis (FEA) tool-chain. Based on a design of experiments approach, the design space will be sampled and surrogate models will be trained on the received dataset. Subsequently, the mean and interaction effects of the geometric design parameters onto the resonance amplitude and safety against HCF will be outlined. The HCF safety is found to be affected by strong secondary effects onto static and resonant vibratory stress levels. Applying an evolutionary optimization algorithm, it is shown that the optimum blade design with respect to minimum vibratory response can differ significantly from a blade designed toward maximum HCF safety.

Implementation of Kriging Surrogate Models for Delamination Detection in Composite Structures

Composite structures are prone to impact and fatigue loads in service which in turn causes defects such as de-lamination. This affects the dynamic characteristics of the composite laminates such as its Natural frequency, Mode shapes and its damping characteristics. Hence it can be used as a prominent indicator for structural health monitoring. This paper focusses on the use of Kriging based surrogate model for the prediction of delamination in Carbon fibre reinforced epoxy composite panels with an edge constraint. The change in natural frequency and mode shapes of the damaged and undamaged model has been taken as the primary damage indicator for the present analysis. The size and location of the damage were predicted from the developed surrogate models. The performance of the proposed approach has been studied experimentally and compared it with numerical simulation and has been found satisfactory. The surrogate approach reduces the computational time considerably without compromising the accuracy.

Enhanced sparse component analysis for operational modal identification of real-life bridge structures

Abstract Blind source separation receives increasing attention as an alternative tool for operational modal analysis in civil applications. However, the implementations on real-life structures in literature are rare, especially in the case of using limited sensors. In this study, an enhanced version of sparse component analysis is proposed for output-only modal identification with less user involvement compared with the existing work. The method is validated on ambient and non-stationary vibration signals collected from two bridge structures with the working performance evaluated by the classic operational modal analysis methods, stochastic subspace identification and natural excitation technique combined with the eigensystem realisation algorithm (NExT/ERA). Analysis results indicate that the method is capable of providing comparative results about modal parameters as the NExT/ERA for ambient vibration data. The method is also effective in analysing non-stationary signals due to heavy truck loads or human excitations and capturing small changes in mode shapes and modal frequencies of bridges. Additionally, closely-spaced and low-energy modes can be easily identified. The proposed method indicates the potential for automatic modal identification on field test data.

Vibration analysis of non-uniform porous beams with functionally graded porosity distribution

In this paper, the effect of different profile variations on vibrational properties of non-uniform beams made of graded porous materials is studied. Timoshenko beam theory is used to present the mathematical formulation of the problem including shear deformation, rotary inertia, non-uniformity of the cross-section, and graded porosity of the beam material. Three different variations of porosities through the thickness direction are introduced. The beam is assumed with the clamped condition at both ends. To obtain a numerical solution, finite element formulations of the governing equations are presented. The non-uniform beam is approximated by another beam consisting of n elements with piecewise constant thickness to keep the volume and hence the total mass unchanged for each element. The beam response has been calculated for the first three modes of vibration. In each case, the results for different types of thickness variation and porosity distribution are compared with those obtained for a beam with uniform thickness. The effects of non-uniformity, taper parameters, and porosity distribution on the frequencies and mode shapes are investigated. It is observed that a considerable change in frequencies and mode shapes can be achieved by selection of different thickness variation and porosity distribution.

Observed mode shape effects on the vortex-induced vibration of bending dominated flexible cylinders simply supported at both ends

The effect of varying the structural mode excitation on bending-dominated flexible cylinders undergoing vortex-induced vibrations was investigated. The response of the bending-dominated cylinders was compared with the response of a tension-dominated cylinder using multivariate analysis techniques. Experiments were conducted in a recirculating flow channel with a uniform free stream with Reynolds numbers between 650 and 5500. Three bending-dominated cylinders were tested with varying stiffness in the cross-flow and in-line directions of the cylinder in order to produce varying structural mode shapes associated with a fixed 2:1 (in-line:cross-flow) natural frequency ratio. A fourth cylinder with natural frequency characteristics determined through applied axial tension was also tested for comparison. The spanwise in-line and cross-flow responses of the flexible cylinders were measured through motion tracking with high-speed cameras. Global smooth-orthogonal decomposition was applied to the spatio-temporal response for empirical mode identification. The experimental observations show that for excitation of low mode numbers, the cylinder is unlikely to oscillate with an even mode shape in the in-line direction due to symmetric drag loading, even when the system is tuned to have an even mode at the expected frequency of vortex shedding. In addition, no mode shape changes were observed in the in-line direction unless a mode change occurs in the cross-flow direction, implying that the in-line response is a forced response dependent on the cross-flow response. The results confirm observations from previous field and laboratory experiments, while demonstrating how structural mode shape can affect vortex-induced vibrations.

Remote Distributed Vibration Sensing Through Opaque Media Using Permanent Magnets

Vibration sensing is critical for a variety of applications from structural fatigue monitoring to understanding the modes of airplane wings. In particular, remote sensing techniques are needed for measuring the vibrations of multiple points simultaneously, assessing vibrations inside opaque metal vessels, and sensing through smoke clouds and other optically challenging environments. In this paper, we propose a method which measures high-frequency displacements remotely using changes in the magnetic field generated by permanent magnets. We leverage the unique nature of vibration tracking and use a calibrated local model technique developed specifically to improve the frequency-domain estimation accuracy. The results show that two-dimensional local models surpass the dipole model in tracking high-frequency motions. A theoretical basis for understanding the effects of electronic noise and error due to correlated variables is generated in order to predict the performance of experiments prior to implementation. Simultaneous measurements of up to three independent vibrating components are shown. The relative accuracy of the magnet-based displacement tracking with respect to the video tracking ranges from 40 to 190 $\mu \text{m}$ when the maximum displacements approach ±5 mm and when sensor-to-magnet distances vary from 25 to 36 mm. Last, vibration sensing inside an opaque metal vessel and mode shape changes due to damage on an aluminum beam are also studied using the wireless permanent-magnet vibration sensing scheme.

Enhanced Sensitivity for Structural Damage Detection Using Incomplete Modal Data

The necessity of detecting structural damages in an early stage has led to the development of various procedures for structural model updating. In this regard, sensitivity-based model updating methods utilizing mode shape data are known as effective tools. For this purpose, accurate estimation of the mode shape changes is desired to achieve successful model updating. In this paper, Wang’s method is improved by including measured natural frequencies of the damaged structure in derivation of the sensitivity equation. The sensitivity equation is then solved using an incomplete subset of mode shape data in evaluation of the changes of the structural parameters. A comparative study of the results obtained by the proposed method with those by the modal method for a truss and a frame model indicated that the former is significantly more effective for damage detection than the latter. Furthermore, the capability of the proposed method for model updating in the presence of measurement and mass modeling errors is investigated.

Vibration of carbon nanotubes with defects: order reduction methods.

Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone-Wales defects, though the methods described can be extended to other defects.

Structural Damage Detection with Different Objective Functions in Noisy Conditions Using an Evolutionary Algorithm

Dynamic properties such as natural frequencies and mode shapes are directly affected by damage in structures. In this paper, changes in natural frequencies and mode shapes were used as the input to various objective functions for damage detection. Objective functions related to natural frequencies, mode shapes, modal flexibility and modal strain energy have been used, and their performances have been analyzed in varying noise conditions. Three beams were analyzed: two of which were simulated beams with single and multiple damage scenarios and one was an experimental beam. In order to do this, SAP 2000 (v14, Computers and Structures Inc., Berkeley, CA, United States, 2009) is linked with MATLAB (r2015, The MathWorks, Inc., Natick, MA, United States, 2015). The genetic algorithm (GA), an evolutionary algorithm (EA), was used to update the damaged structure for damage detection. Due to the degradation of the performance of objective functions in varying noisy conditions, a modified objective function based on the concept of regularization has been proposed, which can be effectively used in combination with EA. All three beams were used to validate the proposed procedure. It has been found that the modified objective function gives better results even in noisy and actual experimental conditions.

Neutron scattering studies on the magnetic interaction in iron-based superconductor BaFe<sub>2</sub><sub>−</sub><sub><italic>x</italic></sub>Ni<sub><italic>x</italic></sub>As<sub>2</sub>

Iron-based superconductivity emerges from the suppression of the long-ranged antiferromagnetic order in the parent compounds. To solve the microscopic mechanism of the superconductivity, the key issue is fully understanding about the evolution of magnetic interaction and its relationship between superconductivity. Here, we take the electron-doped iron-based superconductor BaFe2- x Ni x As2 as atypical example, and summarize the neutron scattering results on the electronic phase diagram, magnetic ordered state, low-energy spin excitations and high-energy spin fluctuations, particularly for their systematic evolution versus electron dopings and the recent progress on the spin nematicity. Firstly, we will introduce about the crystal structure and magnetic structure, detailed procedure of the single crystal growth is also presented. By focusing on the structural transition temperature ( T s) and magnetic transition temperature ( T N) near the optimal doping level, we have found both T s and T N vanish above the superconducting transition temperature ( T c) as a first order manner, due to the lattice distortion and magnetically ordered moment decrease beyond the lower limit of the instrument resolution, giving an avoid quantum critical point at the optimal doping. In addition, the magnetic order becomes incommensurate and short-ranged magnetic cluster and competes with superconducting order, suggesting strong interplay between magnetism and superconductivity. Secondly, we will discuss about the itinerant magnetism and spin resonance mode at low energy for spin dynamics. The spin resonance mode in iron pnictides is explained as the collective quasiparticle excitations from the Fermi surface nesting between the hole pocket at the Γ point and electron pocket at the M point. This requires itinerant magnetism from the electrons near Fermi surfaces, which is further confirmed by neutron scattering by discovering the longitudinal mode and line shape change of low-energy spin excitations upon doping. Thirdly, we will present the doping evolution of spin fluctuations throughout the whole phase diagram. Although the spin waves in the parent compound can be described by an effective Heisenberg mode with anisotropic exchange coupling in FeAs plane, the damping features and unexpected low total fluctuation moments reveal both local moments and itinerant electrons contribute to the magnetism. Upon Ni doping, the high energy spin fluctuations is very robust, but the low energy spin excitations are suppressed quickly to zero when cross the boundary of the overdoped superconducting regime. The analysis on the change of the magnetic coupling energy associated with the superconducting transition gives evidence that the magnetic fluctuations are strong enough to drive the condensation of the Cooper pairs. Fourthly, we will further introduce the recent progress on the spin anisotropy by polarized neutron scattering experiments, and spin nematicity measured on detwinned samples. Anisotropic spin excitations at low energy are discovered by polarized neutron scattering, which is caused by the in-plane orbital ordering and persists away up to the tetragonal paramagnetic state. Further experiments on the detwinned sample under uniaxial pressure give direct evidence of the spin nematicity shown as breaking C4 rotation symmetry spin excitations in the tetragonal phase, similar to the anisotropic resistivity and electronic nematic phase discovered in other probes. Such novel electron state in these materials suggests the iron pnictides are unconventional. Finally, we summarize the results about the magnetic phase transition and spin dynamics and discuss its physical origin. Then a possible picture about the spin driven unconventional superconductivity in these materials is proposed. Further perspectives on the research of magnetism in iron-based superconductivity are also given.

Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

Damage methodology approach on a composite panel based on a combination of Fringe Projection and 2D Digital Image Correlation

Abstract The recent improvement in accessibility to high speed digital cameras has enabled three dimensional (3D) vibration measurements employing full-field optical techniques. Moreover, there is a need to develop a cost-effective and non-destructive testing method to quantify the severity of damages arising from impacts and thus, enhance the service life. This effect is more interesting in composite structures since possible internal damage has low external manifestation. Those possible damages have been previously studied experimentally by using vibration testing. Namely, those analyses were focused on variations in the modal frequencies or, more recently, mode shapes variations employing punctual accelerometers or vibrometers. In this paper it is presented an alternative method to investigate the severity of damage on a composite structure and how the damage affects to its integrity through the analysis of the full field modal behaviour. In this case, instead of punctual measurements, displacement maps are analysed by employing a combination of FP + 2D-DIC during vibration experiments in an industrial component. In addition, to analyse possible mode shape changes, differences between damaged and undamaged specimens are studied by employing a recent methodology based on Adaptive Image Decomposition (AGMD) procedure. It will be demonstrated that AGMD Image decomposition procedure, which decompose the displacement field into shape descriptors, is capable to detect and quantify the differences between mode shapes. As an application example, the proposed approach has been evaluated on two large industrial components (car bonnets) made of short-fibre reinforced composite. Specifically, the evolution of normalized AGMD shape descriptors has been evaluated for three different components with different damage levels. Results demonstrate the potential of the presented approach making it possible to measure the severity of a structural damage by evaluating the mode shape based in the analysis of its shape descriptors.

A symmetry measure for damage detection with mode shapes

This paper introduces a feature for detecting damage or changes in structures, the continuous symmetry measure, which can quantify the amount of a particular rotational, mirror, or translational symmetry in a mode shape of a structure. Many structures in the built environment have geometries that are either symmetric or almost symmetric, however damage typically occurs in a local manner causing asymmetric changes in the structure's geometry or material properties, and alters its mode shapes. The continuous symmetry measure can quantify these changes in symmetry as a novel indicator of damage for data-based structural health monitoring approaches. This paper describes the concept as a basis for detecting changes in mode shapes and detecting structural damage. Application of the method is demonstrated in various structures with different symmetrical properties: a pipe cross-section with a finite element model and experimental study, the NASA 8-bay truss model, and the simulated IASC-ASCE structural health monitoring benchmark structure. The applicability and limitations of the feature in applying it to structures of varying geometries is discussed.