Experimental Natural Frequencies Research Articles

Vibration-based damage detection of beams using Hybrid Genetic Algorithm with combined l0 and l1 regularization

Vibration-based damage detection is an effective way of identifying beam damages before they become severe and potentially catastrophic. This paper introduces a novel and robust method for detecting multiple cracks in beams using a Hybrid Genetic Algorithm (HGA). The objective function of the proposed method, based on dynamic properties, can be employed with partial modal information and is enhanced by including the initial residuals between numerical and experimental models along with combined l0 and l1 regularization. This enhancement mitigates the impact of limited modal data, experimental noise, and modeling inaccuracies. Additionally, a method of selecting an appropriate regularization parameter by analyzing residual and solution norm curves is presented. The performance of the proposed method is evaluated and verified using both numerical simulations and experimental studies on a steel cantilever beam under four damage scenarios. In the experimental study, natural frequencies and mode shapes were determined under ambient vibration conditions using Enhanced Frequency Domain Decomposition (EFDD) and the Stochastic Subspace Identification (SSI) method. Finite element models of the beam were developed in ABAQUS software for numerical analysis, and a comparative study of numerical and experimental data was conducted. The proposed approach successfully identifies, locates and quantifies single and multiple damages in the beam, demonstrating its reliability and effectiveness, particularly in scenarios with limited modal data and significant experimental noise.

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.

The Structure-Dependent Dynamic Performance of a Twin-Ball-Screw Drive Mechanism via a Receptance Coupling Approach

The drive at the center of gravity (DCG) concept-based twin-ball-screw drive mechanism (TBSDM) is vital in automated factories for its robustness and reliability. However, changes in the worktable mass or position result in changes in the center of gravity (CG), significantly affecting the system’s dynamic properties. In this regard, this paper introduces a novel analytical model using improved receptance coupling to analyze vibrations in four modes. A mathematical framework for the twin TBSDM is generated, and the effect of changing the worktable position–mass on each mode is examined. The applicability of the proposed method is verified based on dynamic experiments that were carried out on a TBSDM of a CNC grinding wheel machine tool. After thoroughly analyzing the experimental and theoretical results, it is revealed that changing the worktable position primarily influences the rotational and axial vibrations of the twin ball screw (TBS). Furthermore, changes in the worktable mass significantly affect the coupling vibration among the TBSs and rotors or bearings. Moreover, in terms of performance, the variances between the theoretical and experimental natural frequencies are consistently below 5%. Thus, the proposed method is promising for the improvement of the modeling and analysis of the TBSDM.

Vibration Performance Evaluation of Cold-Formed Steel and Plywood Composite Floors

In this study, experimental natural frequencies and mid-span deflections were used to assess the tested composite floors against vibration serviceability limit states adopted by different standards such as AS3623. It was found that existing design criteria have predicted inconsistent results. Further, the finite element (FE) model was created, updated, and validated against the experimental modal parameters. The validated numerical model examined how various design parameters, such as material properties, cross-section geometry, and achieved a degree of composite action, have influenced the vibration properties such as natural frequencies and mode shapes. It was shown that as the added mass became more dominant than the stiffness enhancement, the fundamental natural frequency of the floor system dropped. This was evident from the results of the plywood slab thickness and the added permanent load parameters. On the other hand, the fundamental natural frequency increased with thicker and deeper joist sections since they made the floor system stiffer.

A Dynamical Model for the Control of a Guyed Tensegrity Beam Under Large Displacements

Abstract Most studies regarding models of tensegrity systems miss the possibility of large static deformations or provide elaborate and lengthy solutions to determine the system dynamics. Contrarily, this work presents a straightforward methodology to find the dynamic characteristics of a guyed tensegrity beam structure, allowing the application of vibration control strategies in conditions of large deformations. The methodology is based on a low-order, adaptive, nonlinear finite element model with pre-stressed components. The method is applied to numerical and experimental models of a class 2 tensegrity structure with a high length-to-width aspect ratio. Image processing and accelerometer data are combined to extract the experimental natural frequencies of the structure, which are compared to numerical results. Prony’s method is applied to estimate damping, and a numerical control strategy is employed using the dynamical model of the structure.

Numerical Simulation of the Response of an Unreinforced Brick-Masonry Cross Vault Subjected to Seismic Loading

ABSTRACTThis paper presents the numerical evaluation of the seismic response of a masonry cross vault using the Discrete Macro-Element Method (DMEM). The case study corresponded to a full-scale unstrengthened cross vault that was experimentally investigated within the scope of the SERA Project — Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations. The cross vault was subjected to repeated shaking table and dynamic identification tests until reaching significant damage. The numerical simulations involved the calibration of the Young’s modulus of the masonry material aiming at reproducing the cross vault’s experimental natural frequencies and mode shapes. The comparison of frequencies was carried out by estimating the difference between experimental and numerical results, whereas the correspondence between mode shapes was studied using the Modal Assurance Criterion. Subsequently, a sensitivity analysis was performed to identify the influence of nonlinear properties on the seismic response of the cross vault (displacement and acceleration time histories and failure mechanism). The accuracy of the numerical time histories was evaluated by estimating magnitude and phase discrepancies. The results aimed at demonstrating the applicability of the DMEM for assessing the seismic response of masonry cross vaults with an acceptable degree of accuracy and low computational cost.

Dynamic Response of a Polyvinylidene Fluoride (PVDF) Sensor Embedded in a Metal Structure Using Ultrasonic Additive Manufacturing

This study aims to examine the dynamic response of a polyvinylidene fluoride (PVDF) piezoelectric sensor which is embedded into an aluminum coupon using ultrasonic additive manufacturing (UAM). Traditional manufacturing techniques used to attach smart materials to metals on the surface have drawbacks, including the potential of exposing the sensor to adverse environments or physical degradation during manufacture. UAM can avoid these issues by integrating solid-state metal joining with subtractive processes to enable the fabrication of smart structures. A commercial PVDF sensor is embedded in aluminum with a compression technique to provide frictional coupling between the sensor and the metallic matrix. The PVDF sensor’s frequency bandwidth and impact detection performance are evaluated by conducting cantilever and axial impact tests, as well as harmonic excitation tests with an electrodynamic shaker. Under axial loading, the embedded sensor displays high linearity with a sensitivity of 43.7 mV/N, whereas impact tests in the cantilever configuration exhibit a steady decay rate of 0.13%. Finally, bending tests show good agreement between theoretical and experimental natural frequencies with percentage errors under 6% in two different clamping positions, and correspond to the maximum voltage output obtained from the embedded PVDF sensor at resonance.

Vibrational behavior of a 3D printed biomimetic dual‐core composite sandwich beam: An experimental and numerical study

AbstractComposite sandwich structures have been used in various applications like aerospace, automotive, and maritime sectors. The process of identifying the core design and the selection of a prominent core is crucially important in sandwich structures. In this study, biomimetic core development and vibration responses of composite sandwich beams with a dual biomimetic honeycomb core are investigated. The composite face layers are fabricated by the hand lay‐up method, and the fused deposition modeling is used to 3D print the PLA honeycomb cores. Based on ASTM‐E1876 and the alternative dynamic approach, the face layer elastic properties and rigidity modulus of the cores are evaluated, respectively. The numerical simulation is used to predict the sandwich panels' natural frequencies and mode shapes and verified with experimental results. There was an excellent agreement between the calculated and experimental natural frequencies. Due to the presence of the core and enhanced rigidity modulus, the dual lamellar honeycomb core sandwich beam produces the highest natural frequencies among all‐composite sandwich beams, followed by the dual regular honeycomb, single lamellar honeycomb, and single regular honeycomb cores. The geometric parametric studies, including core thickness, length‐to‐breadth ratio, lamination schemes, support conditions, and transverse vibration responses were also analyzed for different sandwich patterns. As a result of this work, thick composite sandwich panels in aeronautical and marine structures can be replaced with dual biomimetic core structures. The study highlights the fact that the dual‐core sandwich beam provided greater modal frequency than the single‐core beam with the same weight proportions.Highlights Pistachio nut shell‐based biomimetic honeycomb core has been developed. Alternative dynamic approach is used to find sandwich‐core shear properties. Lamellar‐infused biomimetic model yields higher shear modulus and stiffness. Dual‐core beam having high flexural stiffness enhances the natural frequency. Various parametric studies were analyzed for different sandwich patterns.

Digital twin framework using agent-based metaheuristic optimization

Despite advances in instrumentation and measurement techniques, it is still necessary to update numerical models to simulate or predict some structural responses, for example. Thus, this work proposes a metaheuristic framework based on hybrid agents, an approach within the Artificial Intelligence (AI) topics for updating Finite Element (FE) numerical models. This framework aims to provide flexible non-deterministic strategies to guide the updating process, ranging from simple local search procedures to complex learning processes. Two case studies are presented: (i) a free–free aluminium beam tested under laboratory conditions and; (ii) a catamaran tested during a sea trial under real operating conditions. The updating process aimed to optimize the stiffness matrix while maintaining the mass matrix unchanged. The objective function seeks to minimize the differences between numerical and experimental modal parameters, namely, natural frequencies and vibration modes. Results from the digital twin framework showed that the difference in natural frequencies significantly decreased, for example, 9% to 1% for the free–free aluminium beam and 15% to 4% for the catamaran’s main deck, when comparing the experimental with the updated FE model. As for the updated FE vibration modes, the Modal Assurance Criteria (MAC) values decreased slightly in both cases but within the acceptable MAC values (above 0.9), thus showing good consistency with the experimental vibration modes. In the end, the proposed framework was able to update the FE model directly using its respective reduced model, circumventing the”black box” of commercial packages.

Free Vibration of Rectangular Composite Cantilever Plate and Its Application in Material Degradation Assessment

Many composite cantilever plate-like structures have found engineering applications in different industries. For attaining a meaningful assessment of the plate vibration characteristics, it is important to have efficient and effective methods for determining the natural frequencies/mode shapes of composite cantilever plates. In this paper, a method formulated on the basis of the Ritz method and a simple first-order shear deformation theory (SFSDT) is presented to analyze the free vibration of thin as well as thick rectangular composite cantilever plates for determining their natural frequencies. In the SFSDT, the total deflection is the sum of two deflection components, namely, bending and through-thickness shear-deformation-induced deflections. The successful application of the Ritz method together with the SFSDT for the free vibration analysis of thick composite plates relies on the selection of two independent sets of characteristic functions for the bending and through-thickness shear-deformation-induced deflections, respectively, to satisfy the requirements for the displacement and force conditions at the fixed edge of the plate. The novelty of the proposed method is that two independent sets of characteristic functions, namely, polynomials and trigonometric functions, which satisfy the displacement and force conditions at the fixed edge have been identified and used in the variational method to construct the eigenvalue problem for extracting the modal characteristics (natural frequencies and mode shapes) of the plate. It has been shown that the uses of the selected characteristic functions can produce excellent natural frequencies for both thin and thick composite cantilever plates. Some existing theoretical and experimental natural frequencies of thin as well as thick composite plates have been used to demonstrate the accuracy of the proposed method in predicting natural frequencies. The significant effects of through-thickness shear deformation on the natural frequencies of composite cantilever plates are studied to show the merit of the present method. Finally, for illustrating the application of the proposed method in free vibration analysis, a novel procedure established on the basis of the sensitivity analysis of natural frequencies is presented to assess the material degradation of composite cantilever plates. The numerical examples have shown that fewer than 10 iterations are required in the identification process to produce a good estimation of the current value for each material constant.

Automatic modal identification of bridges based on free vibration response and variational mode decomposition technique

Free vibration tests are often performed for the dynamic characterization of structural systems and components. In the field of road bridges monitoring, such tests require minimal equipment (i.e., a sparse network of few sensors, even a single one) in order to gather – quickly and at low cost – some essential information about the dynamic behavior of the structure. The experimental free-vibration response is thus processed for estimating structural modal features which, in turn, can be useful to corroborate or update available numerical models as well as to evaluate current bridge conditions. Within this framework, an efficient computational strategy is here developed for the modal identification of bridges based on their free vibration response. The procedure combines the variational mode decomposition technique with the area ratio-based damping identification method, which ensures enhanced robustness to noise-related effects in field-test signals. A novel procedure is implemented to make the whole identification process fully automatic, in such a way that it does not depend on specific structural features (e.g., to identify even closely-spaced modes) or subjective user’s settings. After a preliminary validation with a synthetic multi-modal signal, the proposed procedure is applied to two real case-studies. The first case-study deals with the identification of natural frequencies, modal damping ratios and mode shapes of prestressed concrete girder bridge decks. Particularly, experimental natural frequencies and mode shapes are compared with numerical predictions obtained from a finite element model of the bridge. The dynamic characterization of the cables of a cable-stayed bridge is considered in the second case-study. Herein, experimental natural frequencies of all the stay-cables are initially analyzed for estimating their stress levels, which have been critically analyzed to detect the existence of relaxation losses. Moreover, modal damping ratios of all the stay-cables are identified and compared to estimates obtained by alternative ambient-vibration-based techniques.

Dynamic Characterisation of a Heritage Structure with Limited Accessibility Using Ambient Vibrations

Historic Cairo has been a UNESCO World Heritage Site since 1979. It has more than 600 historic structures, which require extensive studies to sustain their cultural, religious, and economic values. The main aim of this paper is to undertake dynamic investigation tests for the dome of Fatima Khatun, a historic mausoleum in Historic Cairo dating back to the 13th century and consisting of mainly bricks and stones. The challenge was that the structure was difficult to access, and only a small portion of the top was accessible for the attachment of accelerometers. Current dynamic identification procedures typically adopt methods in which the sensors are arranged at optimal locations and permit direct assessment of the natural frequencies, mode shapes, and damping ratios of a structure. Approaches that allow for the evaluation of dynamic response for structures with limited accessibility are lacking. To this end, in addition to in situ dynamic investigation tests, a numerical model was created based on available architectural, structural, and material documentation to obtain detailed insight into the dominant modes of vibration. The free vibration analysis of the numerical model identified the dynamic properties of the structure using reasonable assumptions on boundary conditions. System identification, which was carried out using in situ dynamic investigation tests and input from modelling, captured three experimental natural frequencies of the structure with their mode shapes and damping ratios. The approach proposed in this study informs and directs structural restoration for the mausoleum and can be used for other heritage structures located in congested historic sites.

Boundary element model for the analysis of the dynamic response of the Soria arch dam and experimental validation from ambient vibration tests

This paper presents a 3D boundary element time–harmonic model for the analysis of the dynamic behavior, under low-level vibrations, of the Soria arch dam (Gran Canaria, Spain). The model takes into account dynamic Soil–Structure Interaction (DSSI), Fluid–Structure Interaction (FSI) and the actual geometry of dam wall and reservoir. The rock and the dam wall are considered as viscoelastic regions, and the water in the reservoir is modeled as an inviscid fluid. The influence of DSSI, FSI, height of the water in the reservoir, accuracy of the geometric modeling of the canyon, and type of transmitting boundary conditions at the truncated end of the reservoir, are evaluated. DSSI and FSI have a significant influence on the dynamic response of the dam, and the accurate representation of the geometry of the canyon is relevant for the correct estimation of the modal shapes. Ambient vibrations tests were also performed, from which the first and third modes could be clearly identified. The comparison between the experimental and numerical natural frequencies and mode shapes suggests that the proposed complete numerical model is able to capture the dynamic response and can be used for the structural health monitoring of the wall of this dam.

Vibration testing and performance evaluation of Hagia Sophia bell tower after recent restoration

Historical structures are very valuable in terms of culture and history because they are the legacy of the past and the trust of the future. These structures require structural investigation and assessment to survive their life. By developing technology, the continuous and/or partial monitoring of these structures has become widespread in many parts of world for last decades. This study presents the structural dynamic parameter identification and the seismic performance evaluation of Hagia Sophia Bell Tower. This historical tower was built by using masonry cut stones in 1204 in Trabzon, Türkiye. Many restorations were made on the bell tower in different times in the past and the last one was executed in 2020. After this restoration, ambient vibration tests were performed on the tower by using developed measurement systems. The dynamic characteristics were attained by analyzing the collected data and were compared the results of previous studies to determine the effects of the last restoration. Also, an initial finite element model was generated by using solid elements in ANSYS Workbench software and the model was calibrated according to the experimental natural frequencies attained from the last restoration. The structural performance was evaluated by performing seismic analyses according to the current Türkiye Building Earthquake Code by considering the local site effects and seismicity. These analyses were performed on the weak direction of the tower in the initial and calibrated finite element models. The maximum top displacement, drift ratios, principal stress values and their distributions were determined and the seismic vulnerability was evaluated by considering these values.

Finite element model updating of microwave welded lap joint with direct updating algorithm

Microwave joining is a non-conventional joining method that can be used to join bulk metals. Different types of joints such as butt-joint, lap joint, etc can be successfully joined with this novel green technique of joining. In this paper, a domestic microwave oven having a power output of 700W, frequency of 2.45 GHz, and capacity of 25L is used to weld the SS202-SS202 and SS304-SS304 bulk metals. To characterize the lap joints Vicker’s hardness test and SEM of the welded specimens are carried out. The experimental modal analysis is used to measure the experimental eigenvalues and eigenvectors of the welded lap joints. The finite element method has been used to develop the simulated finite element model of the microwave welded joints. The developed finite element model may be very beneficial to predict the dynamic characteristics of the welded structures. However, the finite element method is a numerical tool that gives approximate results. The finite element modeling of the structures depends upon various uncertain factors such as structural material properties, dimensions, boundary conditions, etc Due to these uncertainties in the simulated finite element model, there is always an error between the simulated and experimental observations. In this paper, a lap joint of bulk metals is fabricated by using microwave hybrid heating and a finite element model updating technique such as a direct updating algorithm is proposed to update its simulated finite element model. The objective is to update the simulated mass and the stiffness matrices of the microwave welded lap joint. The experimental modal analysis is used to measure the natural frequencies of the lap joint specimen experimentally. It is observed that the direct updating algorithm can successfully update the simulated finite element model of the welded joints and reduces the error between the simulated and experimental natural frequencies. It is found that the maximum error between the predicted and measured natural frequencies reduces to 0.56% by using the proposed algorithm for welded joints.

Dynamic parameters identification of rolling joints based on the digital twin dynamic model of an assembled ball screw feed system

Currently, due to the rare consideration on the coupling of the various rolling joints and their directional dynamic parameters, and the constraints of the traditional modeling methods, the dynamic modeling precision of the ball screw feed system and the dynamic parameters identification accuracy of the rolling joints are difficult to be further improved. In this paper, a novel method to identify the dynamic parameters of rolling joints based on the digital twin dynamic model of the assembled ball screw feed system is proposed. Firstly, synchronizing information of the physical entity, the geometric model is constructed. Then the finite element analysis (FEA) model is constructed which can simultaneously consider multiple rolling joints and their dynamic parameters at multiple directions. Based on the FEA modal data, the deep neural network (DNN) model is constructed to reflect the mapping between the dynamic parameters and the natural frequencies. Thus, the digital twin dynamic model can be established by fusion of these sub-models. Combining the digital twin-driven and experimental natural frequencies, the optimization model is built, and the dynamic parameters can be identified by particle swarm optimization (PSO) algorithm. Finally, the relative error of dynamic parameters identification is less than 3%, which indicates that the proposed method is feasible, effective, and has greater accuracy.

Experimental and numerical modal analysis of a reduced scale Kaplan turbine model

This paper presents an experimental modal test of a Kaplan turbine model and provides the corresponding analysis of the results. The modal test of the rotor including the runner, the shaft and the generator was performed using, as exciters, an impact hammer and a shaker and, as sensors, several accelerometers. Additionally, numerical models of the rotor with the runner surrounded by air (dry condition) or submerged in water (wet condition) were also built. By comparing the numerical and experimental results, the main modes of vibration of a runner blade in dry conditions and of the rotor shaft both in dry and wet conditions have been identified and discussed. The most significant deviations between experimental and numerical natural frequencies were found around 10% for the rotor shaft and around 6% for the runner blade. Moreover, it was observed that the fourth mode of vibration presents the highest added mass effect with a Frequency Reduction Ratio of about 6.7% and the second mode of vibration shows the lowest damping ratios in both dry and wet conditions with values of about 1.5 and 2.1%, respectively.

Operational modal analysis of a catamaran using a limited set of accelerometers

ABSTRACT Experimental modal analysis tests were performed during the catamaran’s normal operation and using only 06 accelerometers on the main deck. This work focuses on estimating and comparing modal parameters using experimental (time and frequency domain techniques) and numerical analyses. Ten (10) experimental natural frequencies and (incomplete) mode shapes were estimated, in the range of 4–50 Hz, using Balance Realisation, Frequency-Spatial Domain Decomposition and Enhanced Frequency Domain Decomposition techniques. As only 06 accelerometers had been used for modal testing, a finite element (FE) model was used to augment the spatial resolution of the experimental mode shapes. Experimental and numerical natural frequencies showed good correlation with only the 3rd bending mode shape exhibiting 13.5% deviation. It was concluded that the experimental techniques can: (i) identify natural frequencies in the presence of harmonic components and, (ii) estimate mode shapes using a limited set of accelerometers, aided by a FE model.

Диссипативные свойства трехслойных композитных структур. 2. Метод решения

Object and purpose of research. This paper discusses a three-layered plate made up by two rigid anisotropic layers and soft isotropic medium layer of viscoelastic polymer. Each of the two rigid layers is an anisotropic structure formed by a finite number of arbitrarily oriented orthotropic viscoelastic composite layers. The purpose of this work is to develop a numerical solution method for decaying vibration equations of three-layered unsupported rectangular plates. Materials and methods. The system of algebraic equations is constructed as per Ritz method using Legendre polyno-mials as coordinate functions. The first step is to find real solutions. To find complex natural frequencies of the system, their initial values are taken as real natural frequencies thus found, with subsequent calculation of complex frequencies as per the method of third-order iterations. Main results. This paper discusses the results of convergence analysis for a numerical solution of differential motion equations with respect to an unsupported rectangular three-layered plate with transversally isotropic rigid layers. The material for these rigid lay-ers is unidirectional carbon-reinforced plastic (CRP) with elastic dissipation properties, within the investigated range of frequencies and temperatures, independent on its vibration frequency. For the soft isotropic medium layer of viscoelastic polymer, temperature-frequency curve governing the real part of complex elasticity modulus and mechanical loss coefficient is taken into account. Validation of the mathematical model and the numerical solution method, the comparison of calculated and experimental natural frequencies and mechanical loss coefficients for the two variants of three-layered unsupported plate has demonstrated their good correlation. Conclusion. This paper suggests and validates the numerical solution method for decaying vibration equations of three-layered unsupported rectangular plate made up by two rigid monoclinic layers and soft isotropic medium layer of viscoelastic polymer.

Identification of Material Constants of Single-Layer CFRP Thin Plate Using Vibration Analysis with General Purpose FEM Code and Differential Evolution Method

This study discusses identification of material constants of Single-Layer CFRP thin plate using vibration analysis with general purpose FEM code and differential evolution method. This identification method is a method to select material parameters to match the vibration characteristics of the experiment and the vibration characteristics of the analysis. In the method, a general-purpose FEM code calculates vibration modes and natural frequencies of thin CFRP plate using material parameters which are selected by differential evolution method (DE). To reduce number of generations, ILSDE (DE based on Improved Learning Strategy) is used instead of DE. The number of generations is lowest when the number of random select individual is three. Comparison of the reference data and the two FEM models show no significant difference in the identification results. The results show that the identification method has sufficient capability to reproduce well the experimental natural frequencies.