Vibration Analysis Of Structures Research Articles

Utilizing machine learning algorithm and Carrera unified formulation for vibration analysis of nanocomposite-enhanced bridge structures rested on an innovative elastic foundation: verification of the results via nondestructive testing

This paper presents an advanced vibration analysis of Al2O3 nanocomposite-reinforced concrete bridge structures resting on an innovative elastic foundation using the Carrera Unified Formulation (CUF). The primary objective is to investigate the dynamic response of these bridges under various loading conditions, accounting for the reinforcing effects of Al2O3 nanocomposites within the concrete matrix. The formulation incorporates a novel elastic foundation model designed to more accurately simulate realistic boundary conditions and soil-structure interaction. The accuracy and reliability of the CUF-based vibration analysis are further validated using nondestructive testing (NDT) techniques, which enable the detection of potential damage and anomalies in the bridge structures. Moreover, a machine learning (ML) algorithm is employed to predict the vibrational characteristics, facilitating an efficient comparison with the results obtained from CUF and NDT. The combination of theoretical modeling, experimental verification, and ML predictions highlights the robustness of the proposed method. The results demonstrate the effectiveness of using Al2O3 nanocomposites to enhance the mechanical properties of bridge structures, improving their vibrational performance, stability, and longevity. This study provides a comprehensive framework for future applications in bridge engineering, combining high-fidelity numerical methods with state-of-the-art testing and computational techniques.

Synchronous consistent integration for superconvergent isogeometric analysis of structural vibrations

A commonly used procedure to improve the frequency accuracy of isogeometric structural vibration analysis is the design of special superconvergent quadrature rules in accordance with the frequency error measure derived from the generic stencil equations. However, it is also numerically observed that such superconvergent quadrature rules may not consistently lead to the expected accuracy. The reason underlying this inconsistency is related to the failure of quadrature rules to meet the condition of variational integration consistency. Meanwhile, by means of the tensor product nature of isogeometric basis functions and quadrature rules, it is theoretically proved that in one- as well as multi-dimensional scenarios, the variational integration consistency of the isogeometric weak formulation necessitates the quadrature rules be exact through 2(p-m)th degree polynomials, where p is the complete degree of multi-dimensional basis functions or the degree of their correspondent one-dimensional basis functions, m is the order of differentiation in Galerkin weak form. A synchronous consistent superconvergent quadrature rule ensuring frequency superconvergence should simultaneously fulfill both the constraint of frequency error measure and the condition of variational integration consistency. Subsequently, the issues associated with certain quadrature rules that violate the variational integration consistency are examined for both second- and fourth-order problems, and the corresponding synchronous consistent quadrature rules are particularly elaborated.

A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

AbstractRadial basis functions (RBFs) are extensively employed in mesh‐free methods owing to their distinct properties. This study presents a novel RBF formulation based on a modified first‐kind Bessel function, introduced for the first time. The efficacy and precision of the proposed function are assessed through an examination of the free vibrations of Euler–Bernoulli beams composed of two‐directional functionally graded materials. Longitudinal and thickness property variations are modeled in polynomial and exponential forms, respectively. The performance of the novel RBF is scrutinized under various boundary conditions (clamped, simply supported, and free), and comparative analyses are conducted against similar investigations and an RBF based on the first‐kind Bessel function. Convergence analysis of the proposed modified first‐kind Bessel function‐based RBF reveals superior convergence rates compared to the first‐kind Bessel function‐based RBF. Moreover, a comparison between results obtained from modeling using the proposed RBF and exact solutions underscores the adequacy of this approach, with a maximum discrepancy of 4.933% observed under clamped‐free boundary conditions. In essence, the findings suggest that the proposed modified first‐kind Bessel function‐based RBF holds promise for analyzing the free vibrations of functionally graded Euler–Bernoulli beams. The primary aim of this research is to introduce and validate a new RBF based on a modified first‐kind Bessel function for the analysis of free vibrations in Euler–Bernoulli beams made of two‐directional functionally graded materials. The study focuses on evaluating the performance and accuracy of this novel RBF in comparison with existing RBFs and exact solutions. By addressing the limitations of conventional RBFs and proposing an innovative approach, this research aims to enhance the accuracy and efficiency of meshless methods in structural vibration analysis.

Optimization of Pyroshock Test Conditions for Aerospace Components to Enhance Repeatability by Genetic Algorithms

Electronic components assembled in satellites should be able to withstand the vibration, noise, and impact loads generated by space vehicles during launch. To simulate the impact loading in a laboratory environment, a pyroshock test simulates an impact load resulting from explosions during the stage and pairing separation of launch vehicles, which imposes significant stress on the components, potentially leading to failures and damage. To ensure component reliability before the flight model (FM) stage, where components are mounted on the actual launch vehicle and sent into orbit, a pyroshock test is conducted during the qualification model (QM) stage using identical parts and specifications. This process involves measurements of the acceleration induced by pyroshock to calculate the shock response spectrum (SRS) and evaluate the components’ reliability against the required SRS to confirm their ability to endure the shock and operate normally in post-tests. The aerospace developer determines the SRS requirements based on the space launch vehicle and the installation location of the electronic components. Configuring a suitable pyroshock test to meet these requirements typically involves extensive trial and error. This study aims to minimize such trial and error by examination of SRS changes through a numerical approach by table structural vibration analysis. The structure is subjected to in-plane impacts using a steel ball via a pendulum method. Various SRS profiles are calculated by test factors such as the weight of the steel ball, the pendulum angle, and the installation position of the test specimen. Furthermore, a genetic algorithm is utilized to derive the optimal test conditions that satisfy the required SRS. An automated pyroshock test system is developed to enhance repeatability and reduce human errors.

An Alternative Series Solution for Free Vibration Analysis of Asymmetric L-Shaped Membranes

This study revisits the freely vibrating problem of asymmetric L-shaped membranes using a three-segmented domain decomposition (3-SDD) strategy. Motivated by the need for more accurate and flexible methods, the 3-SDD strategy is compared with the previously proposed two-segmented domain decomposition (2-SDD) strategy. The region-matching technique is used to derive an alternative series solution, and the eigenvalues obtained are compared with those in existing research. The convergence behavior and sensitivity analyses reveal that the 3-SDD strategy offers improved accuracy and stability, particularly for higher truncation terms. Detailed comparisons of the first four eigenvalue squares show strong agreement between the 3-SDD and 2-SDD strategies, confirming the reliability of both methods. This research establishes a foundation for the vibration analysis of complex membrane structures, emphasizing the benefits of the 3-SDD approach for upcoming engineering applications and showcasing its potential for broader applicability in practical scenarios. The findings underscore the importance of utilizing multi-segmented decomposition strategies to enhance the accuracy and flexibility of free vibration analysis.

Experimental study of a viscous damped portal frame

The prototype analysed is based on the structure of a gantry made to scale for didactic purposes, relating its dimensions to large structures used in buildings. The present work contributes substantially in the vibrational analysis of structures, simulating in a practical way the behaviour of the portal against the action of external loads. Additionally, the contribution provided by the incorporation of a viscous damper in the structure is observed. The structure includes a mechanism that generates dynamic loads inducing horizontal movement in the system exactly as it happens during a telluric movement. The graphs that characterize the movement of the system are obtained, showing the notable reduction of the acceleration when including a viscous shock absorber. The behavior of a building that incorporates a viscous dampening system in its gantry presents ideal characteristics during a seismic movement reducing the damage generated to the structure during the event.

An inspection of the metal-foam beam considering torsional dynamic responses

Metal foam is a multifunctional material with a lower specific weight, high stiffness and compressive strength, and high energy absorption. These remarkable properties make metal foams a promising candidate for conventional materials in different industrial fields. Despite numerous researches on mechanical behavior either static or dynamic of structures made of metal foams, torsional vibration analysis of metal foam structures is still uninvestigated. In this investigation, the influence of various imperfection distribution patterns on the torsional dynamic response of metal foam beams is examined within the framework of Timoshenko-Gere's theory. Two common materials i.e. SUS304 and Aluminum foams are considered the constructive materials of structure. Moreover, three imperfection distribution patterns are taken into account. The virtual work's principle has been employed to derive the torsional governing equation of metal foam beams. Then, the derived governing equation has been solved via an analytical method. The accuracy of the employed methodology has been compared with the findings of former research in the literature. Finally, the influences of different notable parameters on the variation of natural torsional frequency have been examined and demonstrated in a group of tables and diagrams.

Numerical Analysis of Structural Vibrations in Masts—A Practical Study Applied to a 28-Meter Tugboat

This article investigates the vibration analysis of the mast on the bridge top of a 28 m tugboat, in the quasi-static regime. The study aims to determine the natural frequencies using an equivalent dynamic model of the mast and considers the accelerations of different degrees of freedom of the vessel. Practical design and reinforcement strategies for the local bridge top structure are proposed, utilizing numerical and analytical tools. The investigation explores various alternatives to optimize the structural arrangement. By analyzing the modal behavior, insights are provided for efficient design and reinforcement. The results contribute to understanding the mast’s vibration characteristics, offering guidance for similar structures. This study employs numerical and analytical methods, enhancing the optimization of the mast’s behavior. It determines natural frequencies, proposes practical design strategies, and explores alternatives for structural optimization. The findings provide insights for shipbuilding and mast design applications in other vessels and industries such as radar mast, compass deck, and guyed mast.

Finite element numerical analysis of structural vibration of a certain pump station

Abstract In the process of pump station operation, the vibration of factory structure caused by hydraulic or mechanical factors will seriously threaten the ordinary operation of pump station; reduce the efficiency of units; shorten the service lifespan of equipment, and even lead to failure of units. In this paper, ANSYS software and modal analysis method are applied to simulate the vibration effect on pump station under natural vibration, unit vibration excitation and hydraulic excitation. The intrinsic vibration features of pump station structure under diverse boundary conditions, different working conditions and distinct external excitation sources are studied. According to the results of modal and harmonic response analysis, it can be concluded that: 1. A cross relationship has been found existing between pump station structure and unit excitation of speed frequency. 2. In addition to the upper part of the pump station fragile structure, the vibration of the pier is more noteworthy. 3. The vibration amplitude of the whole pump station along vertical direction is larger than that in other directions while the deformation following the unit axis and flow direction presents a strong tendency. 4. In general, the influence of hydraulic load on the structural force of pump station is relatively small.

Semi-analytical modeling and vibration analysis of bolted frame structure under non-uniform pretension

Most of the frame structures in mechanical equipment are connected by bolts, and the non-uniform pretension among the bolts will have an obvious impact on the vibration characteristic parameters of the frame structure. In this paper, semi-analytical modeling and vibration analysis of a frame structure considering non-uniform pretension of bolts are carried out based on the Timoshenko beam theory and Rayleigh-Ritz method. Specifically, a method is proposed to decompose the frame structure into several substructures and model them respectively, and further the coupling springs are applied among the substructures. Through the vibration test of a beam lap structure with a bolted joint, the analytical expressions between bolt pretension and bolted joint stiffness and damping parameters are obtained. Moreover, the method of simulating the non-uniform pretension among each bolted joint is proposed. Considering the external factors such as reinforcing rib structures and flexible rod exciter, and a complete semi-analytical dynamic model of the bolted frame structure introducing the non-uniform pretension is further established. A case study is carried out on a frame structure that contains four connecting bolts with non-uniform pretension. The natural characteristics of the frame structure are solved by using the developed modeling method, and the rationality of the analysis results is verified by experiments. Based on this, the increasing trends of the resonant frequencies and the resonant response of the frame structure under different pretension conditions are analyzed from two aspects of experiment and simulation.

Coupled 3D-flexibility theory and wave propagation approach for vibration analysis of the sandwich structures: introducing deep neural networks to predict vibration problem

Coupled 3D-flexibility theory and wave propagation approach for vibration analysis of the sandwich structures: introducing deep neural networks to predict vibration problem

Vibration analysis of active composite structures embedded with long and short shape memory alloy (SMA) fibers

The shape memory effect (SME) is a source of internal compressive stresses that modify the vibration behavior of shape memory alloy (SMA) embedded composite structures. Generally, long fibers are used due to their suitability for activating SMA using resistive heating. Longer SMA fibers embedded in composite structures have their limitations in design and manufacturing. Minimal research work has been done on tuning the vibration behavior of composite structures embedded with short SMA fibers. In this research paper, an analytical model for evaluating the natural frequencies of an SMA embedded composite beam has been proposed. Effects of various design parameters for long (continuous) and short (discontinuous) SMA fibers embedded in composites have been investigated. It was observed that short SMA fibers with a higher aspect ratio can tune their frequencies similarly to long SMA fiber composites and are more effective in thicker beams. Matrix material with negative coefficient thermal expansion is more suitable for embedding SMA for modifying natural frequency in active mode.

Utilizing data-driven algorithms for blind modal parameter identification of structures from output-only video measurements

In structural dynamics and vibration analysis, modal identification plays a pivotal role in understanding and characterizing the dynamic behavior of complex systems. Traditional modal analysis techniques heavily rely on accurate sensor placement and knowledge of the excitation forces, which may not always be feasible or practical in real-world scenarios. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using computer vision techniques have gained much importance. But these methods need to know ahead of time where the structure's natural frequency ranges are, and they use steerable pyramids, which are complicated multi-scale image decomposition filters. To address these issues, a blind modal identification technique is suggested to extract the modal parameters (modal frequency and mode shapes) from the recorded structural vibration video signal. The proposed algorithm for unsupervised machine learning is the Non-Negative Matrix Factorization (NNMF) method, which is combined with the Generalized Complexity Pursuit (GCP) method for blind source separation. The NNMF algorithm is directly applied to the raw pixel-time series made from the video data to get the temporal components, which are then separated using GCP to find the individual modal frequencies and mode shapes. The above algorithm is first validated on a numerical model and then implemented on laboratory scale models (cantilever, single-degree, and multi-degree frame models). Finally, the proposed methodology is implemented on real-world recorded structural vibration videos to determine its noise sensitivity, such as the Tacoma Narrows bridge and the London Millennium footbridge. The modal parameters extracted are compared with those from the available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural vibration monitoring by identifying and reproducing complex vibration modes.

Vibration analysis of cylindrical shell discontinuously coupled with annular plate with arbitrary boundary conditions

Discontinuously coupled cylindrical shell-plates or plate-like structures are common components of underwater vehicles, and their vibration characteristics change significantly due to modal coupling. The vibration of discontinuously coupled annular plate-cylindrical shell structures is analyzed based on the wave propagation method(WPM) and virtual spring(VS). Taking uniform annular plates and cylindrical shells as spectral elements, the displacement solutions are described by the trigonometric function and Bessel function respectively, and the vibration responses of the annular plate-cylindrical shell with arbitrary boundaries are obtained. Based on VS and weighted least square norm least square method(WLSNLSM), the discontinuous coupling between the annular plate and cylindrical shell is described as the non-uniform distribution of stiffness of virtual spring by continuity condition, and the dynamic stiffness matrices of continuously and discontinuously coupled structure can be obtained simultaneously. The reason for vibration characteristic change under discontinuous coupling is explained from the perspective of modal superposition. Finally, a finite element model is established to verify the accuracy of the proposed method. The influence of general discontinuous coupling on the dynamic behavior of shell structure is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous coupling.

Acoustic vibration analysis of high-temperature thin-walled structures

Advanced aerospace structures are subjected to extremely harsh working environment, including of mechanical, acoustic, thermal, and aerodynamic loads. These combined loads can make the structures exhibit complex response, which has already attracted increasing concern in the design of advanced aerospace structures. To tackle the problem, a finite element model (FEM) by discretizing the theoretical differential equation is established to calculate the dynamic response of thin-walled structures under combined thermal and acoustic loads. The numerical analysis indicates that three types of nonlinear responses of the thin plate under combined thermal-acoustic loads are obtained, and the mechanism of snap-through is revealed through two ways: thermal buckling analysis and thermal modal analysis. which can be used to explain the nonlinear response characteristics.

Theoretical modeling and vibration analysis of composite laminated wing-box structures of hydrogen-electric aircraft under hygrothermal environment

For the sake of achieving the goal of ultra-low or even zero carbon emissions during flight, hydrogen-electric aircraft has been receiving increasing emphasis. Nevertheless, the hydrogen-electric aircraft owns an all-composite fuselage configuration and is subjected hygrothermal environment, which have a significant effect on the aircraft dynamics, especially for wing structure. In this study, an improved orthogonal polynomial solution based on the Rayleigh-Ritz method is developed for the dynamic analysis of composite laminated wing-box structures (CLWBSs) of hydrogen-electric aircraft with humid and hot environment and elastic boundary. In this solution approach, the potential energy, kinetic energy, elastic potential energy and hygrothermal potential energy of CLWBSs are derived from the framework of Kirchhoff thin plate hypothesis. A set of artificial springs is imported to the free edges of CLWBSs to simulate the elastic boundary and connection between two plates. The convergence, accuracy and computational efficiency of the proposed formulation are validated by experiment and finite element analysis. The effect of the coupling parameters and the elastic boundaries due to flexible composite fuselage in hygrothermal environment created by the hydrogen fuel cells are systematically investigated which have been confirmed by theoretical research, finite element analysis and experiment. The related findings indicate that the present approach provided an effective formulation for the vibration analysis and optimization of flexible composite wing-box structures. It can be applied in the field of aerospace and navigation industry at the same time.

Coupled Vibration Analysis of a Beam-Arch Composite Continuous Rigid Structure with Parallel Traffic Flow

To investigate the structural dynamic characteristics of a beam-arch composite continuous rigid structure bridge under the action of parallel moving loads on a multi-lane highway, a joint simulation analysis program based on Easy Language and ANSYS was developed. This study was conducted using a six-span beam-arch composite continuous rigid structure bridge located in Shaanxi Province as the reference project. The research focused on the most adverse dynamic coupled responses of the main beam midspan, arch crown, and suspension rods caused by double-axle cars, double-axle trucks, and three-axle trucks on a single-direction three-lane road surface.

A Nonlinear Beam Finite Element with Bending–Torsion Coupling Formulation for Dynamic Analysis with Geometric Nonlinearities

Vibration analysis of wing-box structures is a crucial aspect of the aeronautic design to avoid aeroelastic effects during normal flight operations. The deformation of a wing structure can induce nonlinear couplings, causing a different dynamic behavior from the linear counterpart, and nonlinear effects should be considered for more realistic simulations. Moreover, composite materials and aeroelastic tailoring require new simulation tools to include bending–torsion coupling effects. In this research, a beam finite element with bending–torsion coupling formulation is used to investigate the effects of the deflection of beam structures with different aspect ratios. The nonlinear effects are included in the finite element formulation. The geometrical effect is considered, applying a deformation dependent transformation matrix. Stiffness effects are introduced in the stiffness matrix with Hamilton’s Principle and a perturbation approach. The results obtained with the beam finite element model are compared with numerical and experimental evidence.

Free vibration of cracked FGM Mindlin plate in fluid

The free vibration of cracked functionally graded material (FGM) plate in fluid is investigated in this paper. The material components are supposed following the power law and formulated by the Voigt model. The Mindlin plate theory (MPT) including the shear deformation effect is established and the physical neutral plane is adopted to simplify the derivation due to the in-plane displacements of this plane assumed as zero. A massless linear rotational spring model (LRSM) is established to simulate the through-width surface crack. The hydrodynamic pressure at the fluid-plate interface is derived by the potential flow theory, and is regarded as the added mass of cracked FGM plate during the analyses of fluid-plate coupled vibration. The derivation and discretization of vibrational equations for cracked FGM plates in fluid are respectively achieved though the Hamilton’s principle and differential quadrature (DQ) method. The frequencies and mode shapes are iteratively calculated with these values of the vacuum case. The influences of immersed depth, fluid density, gradient index, crack depth, crack location, length-to-width ratio, length-to-thickness ratio, and boundaries on vibration characteristics are conducted in the section of numerical results. The present vibration analyses of cracked structures can be applicable to avoid structural resonance and failure.

Coupled Vibration Analysis of Multi-Span Continuous Cable Structure Considering Frictional Slip

As important load-bearing structures, suspension cables have been widely used in suspension bridges, engineering ropeways, cable suspension systems and other special equipment. Their dynamic problems have always been a research hotspot. Especially for complex cable systems such as engineering ropeways and cable lifting equipment, there will be moving loads acting on multi-span continuous friction-slip cable structures, resulting in nonlinear coupled vibration. Therefore, few scholars have studied how to calculate the nonlinear coupling vibration effect between such moving loads and multi-span continuous cables considering friction slip. Therefore, this paper proposes the use of the combination of the direct stiffness method and the Newmark-β integration method to solve the nonlinear system of equations of motion, which can be derived from the coupled vibration response between the moving load and the main cable. The corresponding calculation program is prepared. Combined with the dynamic load test and simulation results of engineering cases, the correctness and reasonableness of the coupled vibration equations and the program can be verified through comparative analysis. The results show that the calculation results of the self-programmed program are in good agreement with the dynamic load test results, in which the maximum error of the vertical displacement in the span is −4.40% and 0.86%, and the error of the static calculation reaches −13.90%. The impact effect is more obvious when hoisting the weight out of the pulling cable, in which the impact coefficient of the main cable can be up to 2.0. The impact coefficient of the deviation of the cable tower is 4.0. During the traveling process of the moving load, the vertical downward deflection of the main cable at the action point is the largest, and the upward deflection is in the region of 0.2~0.8L from the action point.