Method For Vibration Analysis Research Articles

Physics-informed deep learning for structural vibration identification and its application on a benchmark structure

Structural vibration identification is an important task in civil engineering that is based on processing measured data from structural monitoring. However, predicting the response at unsensed locations based on limited sensor data can be challenging. Deep learning (DL) methods have shown promise in vibration data feature extraction and generation, but they struggle to capture the underlying physics laws and dynamic equations that govern vibration identification. This paper presents a novel framework called physics-informed deep learning (PIDL) that combines deep generative networks with structural dynamics knowledge to address these challenges. The PIDL framework consists of a data-driven convolutional neural network for structural excitation identification and a physics-informed variational autoencoder for explicit time-domain (ETD) vibration analysis with the generated unit impulse response (UIR) signal of the measured structure. The proposed framework is evaluated on a benchmark structure for structural health monitoring, demonstrating its effectiveness in extracting physics-related dynamics features and accurately identifying excitation signals and latent physics parameters across different damage patterns. Additionally, the incorporation of an ETD method-aided convolution function in the loss function aligns the generated UIR signals with the dynamic properties of the measured structure. Compared with conventional DL-based vibration analysis methods, the PIDL framework offers improved accuracy and reliability by integrating structural dynamics knowledge. This study contributes to the advancement of structural vibration identification and showcases the potential of the PIDL framework in civil structure monitoring applications. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 2)'.

Torsional vibration characteristics analysis and adaptive fixed‐time control of wind turbine drivetrain

AbstractThe drivetrain has an important impact on the stability and reliability of wind turbines operating in complex conditions, which belongs to the electromechanical coupling system. This work studies the two domains of research on drivetrain vibration analysis and control method in detail. The electromechanically coupled torsional vibration model is first established by considering the air gap magnetic field energy of the PMSG. Preliminary analysis in terms of Hamiltonian energy indicates that there is sufficient energy to sustain the exciting oscillation behaviors. Moreover, to reduce the vibration amplitude caused by wind speed or torsional stiffness, a novel adaptive fixed‐time control method is proposed to solve the issue of wind turbine drivetrain chaotic oscillation with uncertainties and disturbances. Furthermore, the proposed method not only can prevent the jumping and bifurcation of torsional vibration from happening, but also there are the advantages of the control scheme with high accuracy, fast convergence rate and strong robustness. For the fair comparison, three different control methods have been used to demonstrate the superiority of the control scheme by the simulation results. The research results can provide a theoretical basis for the parameter design and control of wind turbine drivetrain.

Optimized equivalent linearization for random vibration

A fundamental limitation of various Equivalent Linearization Methods (ELMs) in nonlinear random vibration analysis is that they are approximate by their nature. A quantity of interest estimated from an ELM has no guarantee to be the same as the solution of the original nonlinear system. In this study, we tackle this fundamental limitation. We sequentially address the following two questions: (i) given an equivalent linear system obtained from any ELM, how to construct an estimator such that, as the linear system simulations are guided by a limited number of nonlinear system simulations, the estimator converges on the nonlinear system solution? (ii) how to construct an optimized equivalent linear system such that the estimator approaches the nonlinear system solution as quickly as possible? The first question is theoretically straightforward since classic Monte Carlo techniques, such as the control variates and importance sampling, can improve upon the solution of any surrogate model. We adapt the well-known Monte Carlo theories into the specific context of equivalent linearization. The second question is challenging, especially when rare event probabilities are of interest. We develop specialized methods to construct and optimize linear systems. In the context of uncertainty quantification (UQ), the proposed optimized ELM can be viewed as a physical surrogate model-based UQ method. The embedded physical equations endow the surrogate model with the capability to handle high-dimensional uncertainties in stochastic dynamics analysis.

HSDT mesh-free method for free vibration analysis of sandwich structures

The current study presents a meshless collocation method based on radial basis functions (MC-RBF) to analyze the vibrational response associated with a sandwich circular cylindrical nanopipe in a supersonic airflow and conveying fluid flow. The quasi-2D hybrid type of nonlocal strain gradient theory (QHNSGT) as a higher order shear deformation theory (HSDT) has been presented to model the size-dependent nanopipe equations extracted using the energy method for a sandwich nanopipe. The sandwich nanostructure is made of metal, ceramic, and bi-directional functionally graded (Bi-FG) material, respectively, lower, topper, and middle surfaces. By taking into account that the fluid flow is infinite, incompressible, uniform flow, Newtonian, laminar, as well as viscous, and with the help of the Navier-Stokes equation, the fluid-structure interaction is obtained. Also, the displacement fields are defined via the Quasi-2D hybrid type of high-order shear deformation theory. The governing equations are discretized via the MC-RBF method to obtain the natural frequencies. The verification section shows that the results of the current research are very near to the results of the published article in the literature. By using COMSOL multi-physics software, the results are verified, and the outputs show that the velocity of fluid flow has a significant role in the vibrational responses of the current composite structure.

A non-parametric algorithm for time-dependent modal analysis of civil structures and infrastructures

Vibration-based monitoring strategies have been demonstrated to be effective tools in providing – in nearly real-time – reliable information regarding the integrity of structures and infrastructure systems. However, commonly used methods for vibration analysis and modal identification are not able to capture the time variation of the modal properties during single acquisitions, hence they cannot perform dynamic identification in the presence of nonlinearities or non-stationary input excitations. To overcome this limitation, a novel non-parametric algorithm for automatic time-dependent modal analysis is hereby presented and discussed. This Enhanced Modal Identification for Long-term Integrity Assessment (EMILIA) algorithm can compute time-dependent estimations of the natural frequencies and mode shapes that can be critical to the early identification of hidden damage. The dynamic characterization of a beam-like structure in sound and damaged conditions is carried out for numerical validation purposes, allowing to evaluate the reliability of the proposed method over different scenarios and comparing its efficiency against traditional algorithms. Finally, further tests are conducted to analyse the sensitivity of the EMILIA algorithm to its main parameters and components.

A general simplified method for static and free vibration analysis of coupled shear walls of a bay

In recent years, coupled shear walls have been used more often because they provide a significant percentage of the total stiffness of a tall building total horizontal bracing system. This article presents an analytical procedure for the static and dynamic analysis of coupled shear walls of a bay using a continuous model type – CTB of three fields. The coupled shear wall is modeled as a continuous structure consisting of the parallel coupling of a Timoshenko extensible beam and a shear beam. Using a variational approach, the equilibrium equations, constitutive laws, and boundary conditions are derived by applying Hamilton’s principle to the relevant Lagrangian function. Closed-form solutions are provided for the static deflection of the coupled shear wall under general profile lateral loads and the periods of vibration of the coupled shear wall under vertical loads uniformly distributed along its height. A validation of the static analysis was carried out, and to find the range of validity of the continuous model and proposed solution methods, a parametric analysis was carried out. The results are encouraging and show that the proposed analytical solutions have excellent correspondence with respect to the finite element method; they are accurate, reliable and involve low computational cost at a preliminary stage, and can be used as a verification method at the final stage of structural analysis and design.

Vibration Analysis and Suppression Methods of the Wing of an Underwater Glider

Vibration analysis and suppression methods are widely studied in mechanical systems. In this study, rubber damping materials were employed to enhance the vibration suppression performance of the wing of an underwater glider. A finite element model was established to analyze the vibration characteristics of the wing. The excitation characteristics of the actuator were determined by experimental methods. The wet mode shapes and corresponding frequencies of the wing of the underwater glider were investigated. The vibration suppression performance of rubber damping materials with different thickness and hardness was discussed. The optimal parameters of the rubber pads on various positions were provided to minimize the excitations from the actuator. This paper provides valuable insights for developing vibration suppression techniques for the wings of an underwater glider.

Free Vibration Analysis of Elastically Restrained Tapered Beams with Concentrated Mass and Axial Force

This study proposes a new numerical method for the free vibration analysis of elastically restrained tapered Rayleigh beams with concentrated mass and axial force. The beam model had elastic support, concentrated mass at both ends, and axial force at the right end. The elastic supports were modeled as translational and rotational springs. The shear force and bending moment were determined under the assumption that the sum of the forces at arbitrary positions and the joint between the beam and elastic supports always becomes zero. Therefore, a frequency determinant is established considering the free-free end condition at both ends, but various boundary conditions were constructed by adjusting the values of the elastic springs in the frequency equation. This assumption simplified the deduction procedure, and the method’s efficiency was demonstrated through various comparisons. In particular, the value of compressive loading at which the first natural frequency vanished was investigated by considering the taper ratio based on the relationship between the elastic support and compressive loading. The analyzed results can be adopted as benchmark solutions for other approaches. The frequency determinant employs the transfer matrix method; however, numerical methods can easily be utilized in other approaches.

Human-Induced Vibration Serviceability: From Dynamic Load Measurement towards the Performance-Based Structural Design

Since the well-known Millennium bridge accident happened at the beginning of this century, both researchers and engineers realized that the human-induced vibration may lead to unaffordable consequences. Although such vibrations hardly threaten the safety of the structure, the large vibration may affect the functionalities of the structure, causing the serviceability problem. The first study on the human-induced vibration serviceability problem started from the measurement of human-induced load, with many mathematical models proposed. The strong randomness of the measured data led to the investigation on the randomness feature of the load. With the research going deeper, the phenomenon of human–structure interaction was found, which attracted the researchers to study the randomness of the human body dynamic properties that may affect the structural response. Once the interaction mechanism and the system parameters became available, random vibration analysis methods could be proposed to calculate human-induced random vibration, providing the foundation of the reliability analysis from the perspective of vibration serviceability. Such reliability is highly related to subjective feelings of the human body, which has also been deeply studied in the literature. Furthermore, the purpose of studying the dynamic reliability is to conduct the reliability-based structural design. This paper provides a review of the research on human-induced vibration serviceability following the above logic, from the first attempt on load measurement towards the modern techniques for performance-based vibration serviceability design.

Differential transformation method for free vibration analysis of an axially loaded overhung rotor

The aim of this work is to analyze the dynamic behavior of axially loaded Timoshenko flexible shafts with cantilevered overhung disk based on the differential transformation analysis. The equations of motion are derived using Hamilton’s principle. The set of the latter consists of four coupled partial differential equations, which can be reduced to a set of two coupled equations by using a complex transformation to further improve the computational effort. An efficient mathematical recursive technique called the differential transformation method (DTM) is then used to solve the differential equations of motion. The natural frequencies of the shaft are obtained, the influence of intrinsic and extrinsic parameters on the natural frequencies is investigated, and the results are compared to those found in the literature. The results reflect the high accuracy and precision of the DTM. The novelty of the work is the application of the DTM to determine the frequency characteristics and the stability of an axially loaded overhung rotor’s free vibration analysis. These results show that the current analysis is accurate and offers an effective approach that is relatively simple and more direct regarding previous modal analyses.

A Nonlinear Free Vibration Analysis of Functionally Graded Beams Using a Mixed Finite Element Method and a Comparative Artificial Neural Network

Based on the Hamilton principle combined with the Timoshenko beam theory, the authors developed a mixed finite element (FE) method for the nonlinear free vibration analysis of functionally graded (FG) beams under combinations of simply supported, free, and clamped edge conditions. The material properties of the FG beam gradually and smoothly varied through the thickness direction according to the power-law distributions of the volume fractions in the constituents, and the effective material properties of the FG beam were estimated using the rule of mixtures. The von Kármán geometrical nonlinearity was considered. The FE solutions of the amplitude-frequency relations of the FG beam were obtained using an iterative process. Implementing the mixed FE method showed that its solutions converged rapidly and that the convergent solutions closely agreed with the accurate solutions reported in the literature. A multilayer perceptron (MP) back propagation neural network (BPNN) was also developed to predict the nonlinear free vibration behavior of the FG beam. After appropriate training, the prediction of the MP BPNN’s amplitude-frequency relations was entirely accurate compared to those obtained using the mixed FE method, and its central processing unit time was less time-consuming than that of the mixed FE method.

A novel isogeometric scaled boundary finite element method for bending and free vibration analyses of laminated plates with rectilinear and curvilinear fibers constrained or free from elastic foundations

In this paper, a novel numerical approach based on isogeometric analysis and the scaled boundary finite element method is performed, focusing on improving the computing performance (such as accuracy, efficiency and flexibility) of bending and free vibration analyses for laminated composite plates with rectilinear and curvilinear fibers constrained or free from elastic foundations. The non-uniform rational B-splines are used as shape functions for both the construction of exact geometry and the approximation of field variables. The governing formulations are derived from the 3D theory of elasticity, while only discretization for the 2D in-plane dimension is required, with the displacement and stress fields expressed analytically along the thickness direction. Compared to traditional methods, the proposed method possesses the following major advantages: a) The powerful calculation accuracy and less computation consumption due to the higher-order continuity of non-uniform rational B-splines and the intrinsic semi-analytical property from the scaled boundary finite element method; b) The geometric exact description encapsulated in the non-uniform rational B-splines basis ensures the excellent adaptability of the present approach to arbitrary free-form geometries; c) Interaction between laminated plates and elastic foundations can be easily constructed by using the proposed formulations due to discretizations are restricted only to the 2D in-plane; d) Outstanding capability of the presented formulation for the mechanical analysis of variable stiffness laminated composite plates with curvilinear fibers; e) The robust flexibility of the non-uniform rational B-splines in handling curved boundaries makes a strong adaptability of the present method to irregular meshes. Numerical examples on both static and free vibration analyses demonstrate the excellent performance of the present approach.

Stochastic collocation method for thermal buckling and vibration analysis of functionally graded sandwich microplates

Thermal buckling and vibration behaviors of functionally graded (FG) sandwich microplates are investigated by using a unified higher-order shear deformation theory and stochastic collocation (SC) method. Uniform and linear distributions are considered for thermal effect and lognormal distributions are used to characterize the variability of the materials properties. The governing equations are derived by using Hamilton’s principle and solved by Ritz’s approach. To demonstrate the effectiveness and accuracy of the current model, the results from SC are compared with those from Monte Carlo Simulation. The effects of boundary conditions, temperature distribution, thickness-to-length ratio, material scale characteristics and power-law index on the fundamental frequencies and critical buckling temperature of the FG sandwich microplates are investigated. The FG sandwich microplates’ stochastic analysis provides some new findings that may be utilized as references in the future.

Numerical analysis method of ship-ice collision-induced vibration of the polar transport vessel based on the full coupling of ship-ice-water-air

As the Arctic Channel continues to be developed, collisions between polar navigation vessels and sea ice are inevitable, which will directly affect structural safety and vibration comfort. However, the numerical analysis method of ship–ice collision-induced vibration is not perfect, and the effect of fluid coupling is not typically considered. In this paper, a simplified numerical analysis method for ship–ice collision-induced vibration is proposed, in which a reliable ice load is obtained by first performing ship–ice–water–air coupled collision calculations, followed by ship–ice–water coupled vibration calculations to obtain the vibration response of the structure. In addition, this paper investigates the full coupling method and the modeling ranges and meshing sizes involved in the analysis ship–ice collision-induced vibration, and the computational efficiencies of the traditional ALE algorithm and S-ALE algorithm are compared. The results indicate that the simplified simulation analysis method and gradient meshing model improve the calculation accuracy and efficiency in ship-ice collision and vibration response analysis. Moreover, the modeling range of the water and air models cannot be less than 6 times the ship width, 2 times the ship length, and 1 times the ship depth, and the S-ALE algorithm saves 47.86% time compared to the ALE algorithm. The research results in this paper can provide a reference for the numerical simulation of ship–ice collision-induced vibration.

A Transformer Condition Identification Model under Crossing Measuring Points Sampling

Due to the difference in sampling data distribution among different measuring points, the common transformer condition identification method of vibration analysis combined with machine learning has decreased accuracy. This work proposes a non-deep transformer condition identification model based on domain adaptation to solve it. Firstly, multi-scale feature extraction of vibration data is fulfilled by variational mode decomposition and time-frequency analysis. Then, manifold embedding method is employed to adapt source and target domains, which are sampled from different measuring points of transformer. The experimental results manifest that the presented approach could improve the accuracy of the transformer condition identification to a certain extent.

Design of a mechanical automatic transmission system for automobiles based on torsional vibration damping

Abstract In order to reduce the vibration damage of the engine and improve the automatic transmission adjustment performance of the automobile, an automatic transmission system based on torsional damping is constructed in this paper to optimize the hardware function of the shift speed. The torsional damper is used as the core control element to reciprocate the automotive mechanical automatic transmission system, and the calculation method of torsional vibration analysis of the crankshaft shaft system is used to determine the indexes of rotational inertia, stiffness, and damping parameters of torsional vibration. The damping coefficient values are set near the equilibrium point, and the loss factor of the automatic transmission system is signal processed to obtain the best damping effect. Using the intrinsic frequency as the central processing unit of the automatic transmission system, the differential equation is used to calculate the excitation torque vector of each cylinder of the engine, and the characteristic module of the automatic transmission system is developed. The tests showed that the cylinder burst pressure of the automatic transmission system with the torsional damper reached a maximum of 67.9 pressure at 4800 amp. The crankshaft front-end torsional angle of the 4th-order main harmonic excitation reached a maximum of 0.57 degrees, which exceeded the engineering allowance of 0.2 degrees and reduced the automatic shift shock by about 28.36%. It indicates that the torsional damper can improve the control performance of the automatic transmission system, which is conducive to enhancing the stability and self-adaptive capability of the transmission adjustment.

A vibration analysis and control method of a heavy buoyancy regulator in an underwater vehicle

Vibration analysis and control are the main issues of heavy buoyancy regulators, which can improve the runtime performance and reduce the power loss. It is an effective approach to add rubber-based isolators to control the vibrations of the heavy buoyancy regulator. However, the vibration reduction effect of the rubber-based isolators is closely related to their structures and material performance. In this study, according to the geometrics of the connecting components, the structures of the rubber-based isolators are designed by using the vibration theory. The rubber-based isolators with different structures and hardness are considered in the finite element models, whose results are used to achieve the optimal design cases. The vibration isolation transmissibility and static deformation ratio of the rubber-based isolator are discussed. The frequency–displacement characteristics of the heavy buoyancy regulator are also analyzed. The results show that the two presented rubber-based isolators can be used to control the vibrations of the heavy buoyancy regulator. It seems that the presented method can be used for the vibration analysis and control of the heavy buoyancy regulators in underwater vehicles.

An analytical method for nonlinear vibration analysis of submerged tensioned anchors

An analytical method for nonlinear vibration analysis of submerged tensioned anchors

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.

Free vibration analysis of functionally graded composite rectangular plates reinforced with graphene nanoplatelets (GPLs) using full layerwise finite element method

The current investigation is the first endeavor to apply the full layerwise finite element method (FEM) in free vibration analysis of functionally graded (FG) composite plates reinforced with graphene nanoplatelets (GPLs). Unlike the equivalent single-layer (ESL) theories, the layerwise FEM focuses on all three-dimensional (3D) effects. Therefore, it can compute interlaminar stresses and other local effects with the same accuracy as 3D FEM, requiring a lower computational cost. The GPLs weight fraction is presumed invariable in each layer but varies through the plate thickness in a layerwise model. The modified Halpin-Tsai model is employed to acquire the effective Young’s modulus. The rule of mixtures is applied to specify the effective Poisson’s ratio and mass density. First, the current method is validated by comparing the numerical results with those stated in the available works. Next, a thorough numerical study is performed to examine how various factors involving the pattern of distribution, weight fraction, geometry, and size of GPLs, together with the thickness-to-span ratio and boundary conditions of the plate, affect its free vibration behaviors. Numerical results demonstrate that employing a small percentage of GPL as reinforcement considerably grows the natural frequencies of the pure epoxy. Also, distributing more square-shaped GPLs, involving a smaller amount of graphene layers, and vicinity to the upper and lower surfaces make it the most efficient method to enhance the free vibration behaviors of the plate.