Mode Shapes Research Articles

A Robotic Automated Solution for Operational Modal Analysis of Bridges with High-Resolution Mode Shape Recovery

A Robotic Automated Solution for Operational Modal Analysis of Bridges with High-Resolution Mode Shape Recovery

Numerical simulation of a nebulizer with multiple orifices

A vibrating mesh nebulizer is a medical device that can break liquid medication into an aerosol of tiny droplets so that patients can inhale them to treat diseases. The volumetric flow rate of this kind of nebulizer is determined by many factors, including the orifice geometry, the vibration amplitude and the vibration mode shape. Thus, many experiments were designed to assess the effects of these different variables on flow rate and to find the optimal set of device parameters that maximizes the flow rate. However, it can be very expensive to perform such physical experimentation with physical prototypes, which needs different orifice geometries to be fabricated for different test regimes. The orifice sizes are microscopic with diameters typically between 3 µm and 5 µm, thus, they are difficult to be fabricated with the exact shape and diameter that are required. Therefore, virtual prototyping by means of numerical simulation models are required as the orifice geometries and other factors can be easily changed in the simulation models. This study aims to provide a numerical simulation model that is experimentally validated. By comparing the simulated flow rates with the experimentally obtained flow rates, and the simulated droplet diameters with the experimentally obtained droplet diameters, it was found that the errors are all less than 10 % which demonstrates this numerical simulation model is adequately validated by experiment. Thus, instead of carrying out expensive experiments, this simulation model can be used for predicting the volumetric flow rates for different prescribed orifice geometries. Furthermore, this paper also simulates the effects of viscosity and surface tension on the flow rate, where either viscosity or surface tension increases, the flow rate will decrease.

Isotopological remeshing and statistical shape analysis: Enhancing premolar tooth wear classification and simulation with machine learning

ObjectiveThe aim of this study was to evaluate the accuracy of a combined approach based on an isotopological remeshing and statistical shape analysis (SSA) to capture key anatomical features of altered and intact premolars. Additionally, the study compares the capabilities of four Machine Learning (ML) algorithms in identifying or simulating tooth alterations. Methods113 premolar surfaces from a multicenter database were analyzed. These surfaces were processed using an isotopological remeshing method, followed by a SSA. Mean Euclidean distances between the initial and remeshed STL files were calculated to assess deviation in anatomical landmark positioning. Seven anatomical features were extracted from each tooth, and their correlations with shape modes and morphological characteristics were explored. Four ML algorithms, validated through three-fold cross-validation, were assessed for their ability to classify tooth types and alterations. Additionally, twenty intact teeth were altered and then reconstructed to verify the method's accuracy. ResultsThe first five modes encapsulated 76.1% of the total shape variability, with a mean landmark positioning deviation of 10.4 µm (±6.4). Significant correlations were found between shape modes and specific morphological features. The optimal ML algorithms demonstrated high accuracy (>83%) and precision (>86%). Simulations on intact teeth showed discrepancies in anatomical features below 3%. ConclusionThe combination of an isotopological remeshing with SSA showed good reliability in capturing key anatomical features of the tooth. Clinical significanceThe encouraging performance of ML algorithms suggests a promising direction for supporting practitioners in diagnosing and planning treatments for patients with altered teeth, ultimately improving preventive care.

Analytical Framework for Tension Characterization in Submerged Anchor Cables via Nonlinear In-Plane Free Vibrations

Submerged tensioned anchor cables (STACs) are pivotal components utilized extensively for anchoring and supporting offshore floating structures. Unlike tensioned cables in air, STACs exhibit distinctive nonlinear damping characteristics. Although existing studies on the free vibration response and tension identification of STACs often employ conventional Galerkin and average methods, the effect of the quadratic damping coefficient (QDC) on the vibration frequency remains unquantified. This paper re-examines the effect of bending stiffness on the static equilibrium configuration of STACs, and establishes the in-plane transverse free motion equations considering bending stiffness, sag, and hydrodynamic force. By introducing the bending stiffness influence coefficient and the Irvine parameter, the exact analytical solutions of symmetric and antisymmetric frequencies and modal shapes of STACs are derived. An improved Galerkin method is proposed to discretize the nonlinear free motion equations ensuring the accuracy and applicability of the analytical results. Additionally, this paper presents an analytical solution for the nonlinear free vibration response of the STACs using the improved averaging method, along with improved frequency formulas and tension identification methods considering the QDC. Through a case study, it is demonstrated that the improved methods introduced in this paper offer higher accuracy and wider applicability compared to the conventional approaches. These findings provide theoretical guidance and reference for the precise dynamic analysis, monitoring, and evaluation of marine anchor cable structures.

Innovative multi-setup modal analysis using random decrement technique: a novel approach for enhanced structural characterization

PurposeThis paper introduces a novel multi-setup merging method and assesses its performance using simulated response data from a Finite Element (FE) model of a five-storey frame and experimental data from a cantilever beam tested in a laboratory setting.Design/methodology/approachIn the research conducted at the Central Building Research Institute (CBRI) in Roorkee, India, a cantilever beam was examined in a laboratory setting. The study successfully extracted the modal properties of the multi-storey building using the merging technique. Identified frequencies and mode shapes provide valuable insights into the building's dynamic behavior, which is essential for structural analysis and assessment. The sensor layout and data merging approach allowed for the capture of relevant vibration modes despite the limited number of sensors, demonstrating the effectiveness of the methodology.FindingsThe results show that reducing the number of sensors can impact the accuracy of the mode shapes. It is recommended to use a minimum of 8 sensor locations (every two floors) for the building under study to obtain reliable benchmark results for further evaluation, periodic monitoring, and damage identification.Originality/valueThe results demonstrate that the developed algorithm can improve the system identification process and streamline data handling. Furthermore, the proposed method is successfully applied to analyze the modal properties of a multi-storey building.

Dynamic Effect of Ply Angle and Fiber Orientation on Composite Plates

Composite materials have revolutionized industries such as aerospace and automotive with their impressive strength-to-weight ratios and customizable properties. Ply angle and fiber orientation are critical factors that significantly impact the dynamic behavior of composite structures, influencing stiffness, strength, and vibrational characteristics. This research delves into the dynamic characteristics of composite plates, explicitly examining how ply angle and fiber orientation affect vibrational behavior. Through finite element analysis (FEA), composite plates with varying ply angles and fiber orientations were modeled to understand their influence on natural frequencies, mode shapes, and dynamic responses under various loading conditions. The study reveals that cross-ply [0/0/0/0] exhibits the highest stiffness and superior stress handling, while the cross-ply balanced laminate [90/0/0/90] demonstrates better vibrational characteristics. The findings highlight the intricate relationships between design parameters and structural vibrational behavior, offering opportunities for optimizing composite structures. Additionally, harmonic analysis showed that a cut-out increases the natural frequency. The results underscore the importance of optimizing composite plate configurations to enhance vibrational characteristics and align natural frequencies with operational requirements, thereby mitigating resonance-related issues.

A Method to Obtain Frequency Response Functions of Operating Mechanical Systems Based on Experimental Modal Analysis and Operational Modal Analysis

The characteristics of a mechanical structure under operating conditions may differ from those in a static state. It is often more desirable to obtain the frequency response function (FRF) of the operating structure in engineering applications. While operational modal analysis (OMA) can estimate modal parameters during operation, it fails to provide mass-normalized mode shapes for FRF synthesis. This paper presents a new method using experimental modal analysis (EMA) to compensate for the absent information in OMA. It categorizes operational mode shapes into changed ones and those that remain the same compared to the static state, applying different scaling techniques accordingly. This method adapts to changes in dynamic characteristics without altering the operating conditions. Stability is emphasized throughout the process. Two examples are provided to verify the method, considering noise and incompleteness in measurement, and disturbances in dynamic properties. The proposed method is proven to be feasible and reliable to capture the changes in operational FRFs.

Research on vibration response distorted similitude of cylindrical shells under modal distribution disorder

Similitude theory enables local-scale models to reflect the dynamic characteristics of full-scale models and is widely employed in engineering experimentation. However, shell structures, constrained by wall thickness, cannot undergo experiments through proportional downsizing. Existing similitude studies with retained wall thickness exhibit only minimal distortion, and accurate prediction of vibration responses is hindered by modal distribution disorder. To address these challenges, a method based on modified frequency response functions of natural frequencies and mode shapes is proposed. Scaling laws for natural frequencies and mode shapes of cylindrical shells with retained wall thickness are established. This method yields a maximum prediction error of 4.29 % for prototype natural frequencies, compared to 50.57 % for existing methods. Predicted prototype vibration acceleration responses correspond well with theoretical calculations in both frequency and amplitude, while existing methods fail entirely. The phenomenon of modal distribution disorder and the effectiveness of the proposed method in mitigating it are verified by modal experiments and response tests. Research reveals that the sensitivity of different modal frequencies to the wall thickness scaling factor varies, serving as the cause of modal distribution disorder. The modal distribution with the same circumferential wave number is unaffected by wall thickness. Modes above the bending frequency, with axial half-wavelength consistent with bending modes, are prone to disorder due to wall thickness distortion. During wall thickness distortion, a mode originally with the lowest frequency is surpassed towards lower frequency by the mode with larger circumferential wave number and the same axial half-wave number, leading to disorder. The proposed method addresses the challenge of minimal distortion in structural vibration response and poor performance, advancing the development of distorted similitude.

Effect of clamshell powder on the mechanical and damping properties of epoxy-bamboo composites

Compared to single natural fibre composites, hybridising natural fibres with filler particles presents a promising avenue for enhancing composites physical, mechanical, and damping properties. This study delves into incorporating clamshell powder, a filler derived from clams’ hard protective outer shells, into polymer composites. The focus is on investigating the potential of clamshell powder as a filler material to augment the mechanical and damping properties of epoxy-bamboo mat composites. The weight ratio of clamshell fillers varied from 0% to 9%, and the compression moulding method was used to fabricate the composites. As per ASTM standards, mechanical properties were evaluated by conducting tensile and flexural tests. Free vibration tests by impact hammer technique were employed to evaluate the natural frequency, damping ratio, and mode shapes of developed composites to measure damping properties. Results revealed that adding clamshell filler significantly improved composites tensile strength, flexural strength, and damping properties. The addition of clamshell elevated the tensile strength by 18.5%, and flexural strength by 24.2% for composite with 6 wt% filler, which can be attributed to the efficiency of load transfer and the interfacial bonding between fillers and epoxy matrix. SEM analysis supported the experimental results obtained. The highest damping value is received for 9 wt% filler, showing 30% enhancement compared to composites without clamshell filler. Modal analyses using ANSYS software further validated the positive impact of clamshell filler. This study underscores the potential of clamshell filler in enhancing the mechanical and damping properties of epoxy-bamboo composites, broadening their applicability in various fields.

Exploring the thermomechanical and dynamical mode switch transition of a reversible solid oxide cell

Reversible solid oxide cells (r-SOCs) are regarded as a solution form of clean energy generation towards a green hydrogen energy transition. However, during transportation, installation, and operation, they are required to withstand dynamic conditions as they face thermal, mechanical, and vibrational effects. Assessing the interplay of the thermomechanical and dynamical impacts on r-SOC materials during the mode-switch from electrolysis to fuel cell operation is the subject of this current comprehensive study. Advanced FEM-based homogenisation techniques have been harnessed in predicting and evaluating the detailed transients during static and dynamic loading. The intricate 3D thermal profiles throughout the transient reversible dual-modus operation from a typical r-SOC study have been derived using advanced image processing. Orthotropic material properties were incorporated into a unified macroscopic scale model by deriving the complex 3D microstructure geometry characteristics of the cell materials and component layers. The comprehensive thermomechanical and pre-stressed modal analysis results showed that the static and dynamic forces in fuel cell mode are more pronounced, whereas, in electrolysis operation, the dynamical behaviour highly depends on geometrical and operating conditions. Smaller component size shows higher natural frequencies and more intense vibration, leading to higher deformation attributed to complex mode shapes and reduced flexural rigidity. These insights are essential for optimizing r-SOC design parameters, enhancing their dynamic and structural reliability throughout their dual-mode operation lifespan.

Bridge damage identification based on synchronous statistical moment theory of vehicle–bridge interaction

AbstractConsidering the weak noise resistance and low identification efficiency of traditional bridge damage identification methods, a data‐driven approach based on synchronous statistical moment theory and vehicle–bridge interaction vibration theory is proposed. This method involves two main steps. First, a two‐axle test vehicle is used to collect acceleration response signals synchronously from adjacent designated measurement points while stationary. This operation is repeated to calculate the second‐order statistical moment curvature (SOSMC) difference of entire bridge points corresponding signals in different states. By comparing with the reference value, the preliminary damage location of the bridge can be obtained. Second, the first‐order modal shape curve is constructed using the second‐order statistical moment (SOSM). The refined identification of bridge damage is then based on an improved direct stiffness back calculation of the bridge's stiffness. This article proposes the synchronization theory for the first time and combines it with the statistical moment clustering method, forming an innovative approach to obtaining structural vibration modes. The effectiveness of this method has been well validated through numerical simulations with different parameters and on‐site bridge tests. The research results indicate that SOSMC indicators have better noise resistance and higher recognition efficiency in identifying damage locations, compared to modal curvature and flexibility curvature indicators. Additionally, compared to transfer rate and random subspace methods, the SOSM method results in smaller error and higher identification efficiency.

Modal coupling characteristics of primary hunting in metro vehicles: Carbody suspension modes and hunting modes

Due to coupling with carbody suspension modes in railway vehicles, primary hunting can lead to significant low frequency swaying of the carbody, severely deteriorating ride quality. In order to address this issue, this paper conducts a detailed investigation into the coupling effect between suspension modes and hunting modes of metro vehicles. Initially, a simplified lateral dynamics model is established, and a continuous modal tracking method is adopted for track suspension modes and hunting modes. The results indicate that when the modal frequency of one hunting mode approaches that of corresponding suspension mode, the damping ratio of the two modes exhibits abnormal variation, and the modal frequency curve veers or is slightly disturbed. In exploring the coupling characteristics of hunting modes and suspension modes, revealing the variation trends and similarity of modal shapes, polar diagrams of modal shapes are presented, and the correlation distance is calculated. Equivalent conicity exerts a substantial influence on the effect of modal coupling, influencing minimum damping ratio and modal shape similarity within the modal coupling zone. To ensure sufficient stability margin for metro vehicles, it is necessary to avoid excessively low equivalent conicity. Finally, the phenomenon of vibration response deterioration within the modal coupling zone is confirmed through both a simplified model and a full DOF model.

Finite element modeling and modal testing of a wind turbine lattice tower component with interference pin connections

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.

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

A Novel Image-Based Long-Range Continuously Scanning Laser Doppler Vibrometer for Operational Modal Analysis of a Rotating Structure

ABSTRACT A novel image-based long-range tracking continuously scanning laser Doppler vibrometer (CSLDV) is developed to measure vibration of a rotating structure with a complex background. The image-based long-range tracking CSLDV can track and scan the rotating structure by processing its images captured by a camera in the image-based long-range tracking CSLDV. A novel image-processing method with a background averaging technique is developed to extract the rotating structure from the background in captured images and determine its location. A one-dimensional scan scheme is used to scan along a straight line along the rotating structure. An improved demodulation method is used to process measurements of the image-based long-range tracking CSLDV to estimate modal parameters of the rotating structure, including damped natural frequencies and undamped mode shapes. Experiments of tracking and scanning a rotating blade are conducted to validate vibration measurement of a rotating blade using the image-based long-range tracking CSLDV. Measured responses of the rotating blade are processed to estimate its speeds and modal parameters. The first three damped natural frequencies of out-of-plane vibration of the rotating blade and the first three undamped mode shapes of the rotating blade along its middle line are successfully estimated and compared with results from the finite element model of the corresponding stationary blade.

On the complex mode shapes and natural frequencies of clamped-clamped fluid-conveying pipe

In the present study, the closed-form expression for complex mode shapes of a fluid-conveying pipe using Timoshenko beam theory is developed for the first time. By applying the method of separation of variables, the complex mode shapes and eigenvalues are obtained. To the best knowledge of the authors, there is no study carried out on the complex eigenvalue problem for vibration analysis of the Timoshenko fluid-conveying pipes. Given this oversight, in this study the effects of fluid velocity on the imaginary and real parts of the mode shapes and natural frequencies of a clamped-clamped fluid-conveying pipe are investigated. The results show that for very low fluid velocities, the first and the second mode shapes are similar to that of an equivalent beam. For high fluid velocities, the first mode shape experiences some deviation so that it looks like the second mode shape of a pipe having very low fluid velocity. The results show that fluid flow in the pipeline effectively reduces its bending moment as well as the energy of vibration. In addition, the nodal points corresponding to the second mode are replaced with quasi-node points.

Crack detection and localization in composite plates by intersection of first three normalized mode shape curves from experimental modal analysis

Crack detection and localization in composite plates by intersection of first three normalized mode shape curves from experimental modal analysis

Modeling the dynamic interaction between machine tools and their foundations

The performance of a machine tool is directly influenced by the characteristics of the floor, subsoil, and their interaction with the installed machine. Installing a machine tool in its operational environment poses a distinct challenge that bridges mechanical and civil engineering disciplines. This interdisciplinary issue is often overlooked within the individual separate disciplines. However, effectively addressing this challenge requires a comprehensive understanding of mechanical and civil engineering principles. To address this problem, the present study proposes a method for improved modeling of the dynamic properties of the machine tool by considering the foundation and the subsoil on which it is installed. The method is based on finite element modeling. Linear models of the system components and the connections between them were used. These, supplemented with damping expressed by complex stiffness, made it possible to determine the natural frequencies, mode shapes, and frequency response functions (based on which the transmissibilities were obtained). Based on the experimentally verified models of vertical and horizontal lathes, the sensitivity analysis aimed at estimating the impact of changes in system parameters on vibration transmissibility for a floor-type and a block-type foundation was conducted. Thus, it was possible to identify those machine tool-support-foundation-subsoil system parameters that had the most significant impacts on the vibration's transmissibility. After analyzing the cases discussed, it became evident that the transmissibility of vibrations is primarily influenced by two key factors. First and foremost, the properties of the structural loop of the machine tool played a significant role. Additionally, the characteristics of the subsoil on which the foundation was situated emerged as a crucial determinant in the observed vibration transmissibility.

Detection of Total Hip Replacement Loosening Based on Structure-Borne Sound: Influence of the Position of the Sensor on the Hip Stem.

Accurate detection of implant loosening is crucial for early intervention in total hip replacements, but current imaging methods lack sensitivity and specificity. Vibration methods, already successful in dentistry, represent a promising approach. In order to detect loosening of the total hip replacement, excitation and measurement should be performed intracorporeally to minimize the influence of soft tissue on damping of the signals. However, only implants with a single sensor intracorporeally integrated into the implant for detecting vibrations have been presented in the literature. Considering different mode shapes, the sensor's position on the implant is assumed to influence the signals. In the work at hand, the influence of the position of the sensor on the recording of the vibrations on the implant was investigated. For this purpose, a simplified test setup was created with a titanium rod implanted in a cylinder of artificial cancellous bone. Mechanical stimulation via an exciter attached to the rod was recorded by three accelerometers at varying positions along the titanium rod. Three states of peri-implant loosening within the bone stock were simulated by extracting the bone material around the titanium rod, and different markers were analyzed to distinguish between these states of loosening. In addition, a modal analysis was performed using the finite element method to analyze the mode shapes. Distinct differences in the signals recorded by the acceleration sensors within defects highlight the influence of sensor position on mode detection and natural frequencies. Thus, using multiple sensors could be advantageous in accurately detecting all modes and determining the implant loosening state more precisely.

Quantifying stress distribution in ultra-large graphene drums through mode shape imaging

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here, we introduce a methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a manufacturing process to create ultra-large graphene drums with diameters of up to 1000 μm. We solve the inverse problem of a Föppl–von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced methodology allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.