Vibration Analysis Of Structures Research Articles

Review of Vibration-Based Structural Health Monitoring Using Deep Learning

With the rapid progress in the deep learning technology, it is being used for vibration-based structural health monitoring. When the vibration is used for extracting features for system diagnosis, it is important to correlate the measured signal to the current status of the structure. The measured vibration responses show large deviation in spectral and transient characteristics for systems to be monitored. Consequently, the diagnosis using vibration requires complete understanding of the extracted features to discard the influence of surrounding environments or unnecessary variations. The deep-learning-based algorithms are expected to find increasing application in these complex problems due to their flexibility and robustness. This review provides a summary of studies applying machine learning algorithms for fault monitoring. The vibration factors were used to categorize the studies. A brief interpretation of deep neural networks is provided to guide further applications in the structural vibration analysis.

Vibration Analysis of Chenderoh Dam Physical Model Spillway Structure due to the Effect of Water Spilling: Numerical and Experimental Validation

Dam can be defined as a barrier built across the river to restrain and control the flow of water. However, the safety of the dam structure can be threatened by the uncertainties vibration induced from internal and external sources. Thus, in this paper, the vibration analysis in terms of Experimental Modal Analysis (EMA) and Operational Deflection Shapes (ODS) are carried out to determine the reliability of the dam structure. This study only focused on the spillway structure of the Chenderoh Dam that located in Perak, Malaysia. For the simulation, a 3D physical model with 1:20 scale is developed using SolidWorks software and simulated using ANSYS software. Whilst, for validation of the simulation results, EMA and ODS experiment are performed on the physical model of the Chenderoh Dam. The validation will be in terms of mode shape, ODS, natural and operating frequencies. From the results, the first natural frequency of the spillway occurred at 220.87 Hz with the maximum deflection of 1.6 mm and the ODS deformation happened at operating frequency of 45 Hz with the amplitude value of 0.003 m. The operating frequency value is far from the natural frequency of 220.87 Hz; thus, the transient vibration only induces a minimal effect on the spillway structure and the spillway is considered safe for the operation.

Free Vibration Analysis of Nonlinear Circular Plates Resting on Winkler and Pasternak Foundations

Dynamic behaviour of nonlinear free vibration of circular plate resting on two-parameters foundation is studied. The governing ordinary differential equation is solved analytically using hybrid Laplace Adomian decomposition method. The analytical solutions obtained are verified with existing results in literature. The analytical solutions are used to determine the influence of elastic foundation, radial and circumferential stress on natural frequency of the plate. Also, the radial and circumferential stress determined. From the results, it is observed that, increase in elastic foundation parameter increases the natural frequency of the plate. It is recorded that the modal radial and circumferential stress affect the extrema mode of the plate. It is hoped that the present study will contribute to the existing knowledge in the field of vibration analysis of engineering structures.

The Effect of Soil Type on Seismic Response of Tall Telecommunication Towers with Random Vibration Analysis

Random vibration analysis of tall structures faces multiple problems due to the large number of elements and high degrees of freedom; that is why this type of analysis is mostly used in simple structures and low degrees of freedom. In the past two decades, changes have been occurred in this type of analysis to be used in complex structures and the large number of elements. Pseudo-Excitation Method (PEM) presents a simple formulation for reducing the volume of operations. In this paper, a tall telecommunication tower is fully modeled as an example of such towers; it is analyzed by random vibration analysis with the help of the above method. Different conditions of the soil under the tower and different damping are used in modeling and analysis. The results show that structure response is strongly influenced by the soil conditions. In addition, higher modes have significant effects on the telecommunication tower response

Free and steady forced vibration characteristics of elastic metamaterial beam

The propagation of elastic waves in infinite elastic metamaterials (EMs) is studied by using the effective medium theory (EMT). However, when EMs are applied in engineering practice, finite EM structures should obviously be the most cases, in which the propagation of elastic waves corresponds to the problem of vibration. Therefore, it is necessary to establish a reasonable vibration analysis method for typical EM waveguides and investigate their unique modal characteristics and related vibration characteristics. At present, the relevant exploration is relatively limited, especially analytical analysis. As one typical EM finite structure, an EM beam was chosen to be investigated in this study. Based on the EMT, the Euler beam theory is extended to the analysis of EM finite beams, and the analysis process of free and steady forced vibration is established, the particular characteristics are revealed, including the gathering of natural frequencies in the vicinity of band edges, the absence of natural frequencies within bandgap (BG), and the particular modal correspondence before and after BG. Then, the formation mechanisms of the characteristics are explained from the perspective of standing waves. The obtained results may give insights into the vibration analysis of other finite EM structures, such as EM rods, shafts, plates, and shells.

Structural and Random Vibration Analysis of LEDs Conductive Polymer Interconnections

Many devices consist of electronic parts and can be operated in a certain vibration environment for some instant without undergoing failure. Interconnection or joint plays a very important role in electronic devices to connect various electrical and mechanical parts altogether. The main objective of this study is to investigate the effect of interconnection performance under vibration loading in terms of natural frequency, mode shapes and transfer function. Four different models of LEDs are built for pull strength and vibration tests. The structural analysis of these models are carried out by using universal testing machine. The dynamic responses of four build matrices under certain random frequency are observed by random vibration analysis. In structural analysis, the samples are subjected to vertical displacement loading while in random vibration analysis, the models run in a frequency range of 3 Hz to 500 Hz. It is observed that the structure of the adhesive joints affect the strength of interconnection between circuit pad and LED joints. Furthermore, FEA analysis is also carried out to determine the stresses at solder joint under vibration condition. The models are excited from natural frequency and good comparison of the experimental results and FEA analysis are observed.

Efficient global sensitivity analysis of structural vibration for a nuclear reactor system subject to nonstationary loading

The structures associated with the nuclear steam supply system (NSSS) of a pressurized water reactor (PWR) include significant epistemic and aleatory uncertainties in the physical parameters, while also being subject to various non-stationary stochastic loading conditions over the life of a nuclear power plant. To understand the influence of these uncertainties on nuclear reactor systems, sensitivity analysis must be performed. This work evaluates computational design of experiment strategies, which execute a nuclear reactor equipment system finite element model to train and verify Gaussian Process (GP) surrogate models. The surrogate models are then used to perform both global and local sensitivity analyses. The significance of the sensitivity analysis for efficient modeling and simulation of nuclear reactor stochastic dynamics is discussed.

Fundamental natural frequencies investigation for a typical 5-MW wind turbine blade

Continuous structures such as beams, rods and plates can be modelled by discrete mass and stiffness parameters and analysed as multi-degree-of-freedom systems. The analysis of structural vibration is necessary to obtain the natural frequencies of a structure and the response to the external excitation. In this way, it can be determined whether a particular structure will fulfil its intended function and, in addition, the results of the dynamic loadings acting on a structure can be predicted. The lack of a sober analytical research about the vibrational behaviour of the 5-MW wind turbine blade pushed us to investigate about this crucial issue, however, most of the discreet researches are concerned with the aerodynamic effects rather than structural analysis. In this article, Rayleigh–Ritz method was implemented for a typical 5-MW wind turbine blade. MATLAB codes were developed and natural frequencies were obtained for both flapwise and edgewise vibrational behaviour. A good agreement was observed between the analytical results and the manufacturer results.

Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method

This study conducts the first-known free vibration analysis of functionally graded carbon nanotubes-reinforced (FG-CNTRC) shell structures using the meshfree radial point interpolation method (RPIM). The modified first-order shear deformation theory (modified FSDT) is implemented to get the realistic effect of the transverse shear deformation with its parabolic distribution. Numerical examples are carried out to examine the convergence and accuracy of the element-free RPIM method in its application to the free vibration FG-CNTRC analysis of shell structures. Results obtained using the proposed meshfree method, demonstrate that the improved FSDT is very successful compared to closed-form solutions and finite element results using different shell theories.

Application of asymptotic expansion homogenization in vibration analysis of masonry structures using finite elements

The asymptotic expansion homogenization (AEH) method, which is a rigorous mathematical homogenization theory, is applied here to the modeling of the mechanical behavior of masonry structures for practical dynamic analysis applications. A homogenization process reduces the modeling complexity associated with a detailed component representation of masonry structures and permits the use of a continuous macro-scale model. The method is validated and demonstrated through several applications to masonry structures with the aid of the commercial finite element software ABAQUS in conjunction with a simple self-made program to automate the procedure. The obtained equivalent elastic coefficients for the continuous macro-scale model are used to evaluate the performance of AEH method in determining natural frequencies and modal shapes of various masonry panels and structures. Comparison of results between analyses based on the AEH model and the discrete element model demonstrates the high potential of the AEH model in the seismic analysis of masonry structures.

Numerical simulation of vibration damping by granular materials

The present paper proposes a novel simulation method combining the finite-difference time-domain (FDTD) method and the discrete-element method (DEM) in order to investigate the damping effect of bending vibration of a plate caused by granular materials. The DEM is used to obtain the motion of the granular material, whereas the FDTD is used for vibration analysis of the plate-like structure. Firstly, the numerical scheme of each method and the coupling scheme of these methods are described in detail. Then, the validity of the proposed method was confirmed by comparing the calculation and measurement results. Finally, based on the numerical and measurement results, we confirmed that the damping of the plate caused by additionally arranged granular materials varies greatly depending on the excitation force acting on the plate.

Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

A semi-analytical mesh-free method for 3D free vibration analysis of bi-directional FGP circular structures subjected to temperature variation

In this present paper, a semi-analytical mesh-free method is employed for the three-dimensional free vibration analysis of a bi-directional functionally graded piezoelectric circular structure. The dependent variables have been expanded by Fourier series with respect to the circumferential direction and have been discretized through radial and axial directions based on the mesh-free shape function. The current approach has a distinct advantage. The nonlinear Green-Lagrange strain is employed as the relationship between strain and displacement fields to observe thermal impacts in stiffness matrices. Nevertheless, high order terms have been neglected at the final steps of equations driving. The material properties are assumed to vary continuously in both radial and axial directions simultaneously in accordance with a power law distribution. The convergence and validation studies are conducted by comparing our proposed solution with available published results to investigate the accuracy and efficiency of our approach. After the validation study, a parametric study is undertaken to investigate the temperature effects, different types of polarization, mechanical and electric boundary conditions and geometry parameters of structures on the natural frequencies of functionally graded piezoelectric circular structures.

A laser triangulation sensor for vibrational structural analysis and diagnostics

The industrial progress has reached a level in which it is necessary to understand the behavior of mechanical components and to monitor their conditions without disassembling them. Nowadays, a suitable methodology is based on vibrational analysis usually performed through acceleration signals measured directly on the system to be tested. However, in the last years, the industrial scenario has deeply changed due to the need for time reduction, in particular, for the control operations at the end of the productive line. The genuine methods based on acceleration measurements, for example, through piezoelectric accelerometers, came into conflict with the industrial need as the sensors used for the quality control have to be easily and fastly mounted and unmounted. A valid alternative is represented by the exploitation of laser triangulation sensors that are able to measure the dynamic displacement in a contactless way, strongly reducing the (un)mounting time. The target of this paper is to highlight pros and cons of the contactless displacement analysis through laser triangulation sensors with respect to the contact one through genuine accelerometers by means of a comparison between the results obtained both for experimental modal analysis and vibrational diagnostics of rotating machines.

An approximate method for one-dimensional structures with strong nonlinear and nonhomogenous boundary conditions

There is a lack of analytic methods for vibration analysis of structures with strong nonlinear and non-homogenous boundary conditions. This paper proposes such a method. A distinct feature of the method is to introduce the generalized coordinates for nonlinear and nonhomogeneous boundary conditions. The total solution of the structure consists of a sum of a spatial particular solution for the boundary conditions and a field solution satisfying linear and homogeneous boundary conditions. The field solution can be obtained in terms of the modal expansion. The modal coefficients together with the generalized coordinates for the boundary conditions satisfy a set of nonlinear ordinary differential equations, which are solved with the harmonic balance method. Two examples are presented to study the convergence and accuracy of the solution. The first example is the longitudinal vibration of a bar subject to a base excitation on the left and restrained by a damper on the right. The wave method and the differential quadrature method (DQM) are compared with the proposed method, and are found in good agreement. The second example is a beam with nonlinear torsional boundary absorbers. The method shows a good accuracy to deal with the complex boundary conditions as compared with the differential quadrature element method (DQEM). The proposed method is also compared with the multi-scale method (MSM) and shows an advantage to deal with strong nonlinearities. The proposed method is highly promising for vibration analysis of complex structures with nonlinear and nonhomogeneous boundary conditions.

Quantum chemical calculation based investigation of synergistic chelating between multiple hydroxyamide ligands and La3+ ion

In this paper, Density Functional Method at B3LYP/SDD level has been implemented in order to study enhanced interaction with lanthanum ion (La3+) in presence of multiple molecules of chelating ligand hydroxyamide (HA) for efficient extraction of lanthanides. Geometrical analysis of optimized structure, thermochemical analysis, potential energy surface study, electron density profile determination and localized orbital locator analysis, molecular orbital analysis, density of states analysis and vibrational spectral (IR spectra) analysis of the complex consisting of one, two, three, and four hydroxyamide ligands with lanthanum have been performed. Calculated geometrical parameters, interaction energies, change in Gibb’s free energy, change in enthalpy, change in entropy, and HOMO-LUMO study indicate the formation feasibility, as well as stability of the complexes, is enhanced while a higher number of hydroxyamide ligand interact with La(III). Structural analysis and vibrational analysis exhibit the formation of hydrogen bond-like non-bonded interaction between hydroxyamide and lanthanum. The orbital analysis provides the underlying reason for the bond formation between lanthanum and doubly bonded oxygen atom with carbon in the hydroxyamide ligand. The above study helps to analyse the interaction of lanthanum with hydroxyamide in order to design chelating extractant for efficient extraction of this rare earth element.

A beam formulation with 3D capabilities for the free vibration analysis of thin-walled metallic and composite structures

Abstract The present article proposes an advanced Ritz formulation with 3D capabilities for the analysis of thin-walled metallic and composite beam structures. Various set of admissible functions such as: Legendre, Chebyshev and algebraic polynomials, as well as hybrid functions are employed. The investigation is carried out by using the method of power series expansion of displacement components based on 2D-Taylor polynomials. The governing equations (GEs) are derived in their weak form via Hamilton's Principle and are solved by using the Ritz method. Convergence and stability of both cross-section and admissible functions have been thoroughly analysed. The high level of accuracy of the proposed formulation has been comprehensively examined in three selected case studies: (i) slender beams with arbitrary boundary conditions, and both solid and thin-walled cross-sections; (ii) a fully-clamped three-layer non-homogenous circular cylindrical shell; (iii) a fully-clamped functionally graded material (FGM) box resting on two-parameter elastic foundation.

A Review on the Discrete Singular Convolution Algorithm and Its Applications in Structural Mechanics and Engineering

The discrete singular convolution (DSC) algorithm is a relatively new numerical method. It has not only the advantage of high accuracy of global methods but also the advantage of the flexibility of local methods, and thus has been projected by its proponents as one of the potential alternative approaches to the conventional finite element method, especially for solving problems of structures in high frequency vibrations. Although the progression on the DSC algorithm and its applications is clear from past researches, but this has been scattered over lots of published articles. This paper presents a comprehensive review on the DSC algorithm and the application of the DSC for solutions of a variety of problems in structural mechanics and engineering, which should be of general interest to the computational community. The DSC algorithm is introduced first in a concise and clear manner to help the beginners and engineers who are going to use the DSC algorithm for structural analysis. Emphasis of the review is placed on the DSC analysis of bending, buckling, free vibration and dynamic analysis of structural elements and structures, although the DSC algorithm with a proper singular kernel can solve a wide range of science and engineering problems.

Fast computation for vibration study of partially submerged structures using low resolution hydrodynamic model

A fast computation scheme is presented for simulating fluid–structure interaction of partially submerged structures. Fluid added mass is simulated using the boundary element method, which only requires a mesh at the fluid–structure interface while satisfying the far field boundary conditions in a semi-infinite domain. The boundary element solver is coupled to a finite element solver for structural vibration analysis. To speed up the boundary element simulation, a low resolution and geometrically simplified surface mesh was used. A projection scheme is introduced to map fluid elements to structural elements, allowing proper transfer of displacement and fluid loading between the two solvers. A series of low-resolution meshes for a realistic container ship model were used to study the efficiency of the proposed scheme, comparing the errors incurred in calculating the wet natural frequencies against the speed-up in computation. With a 20 times decrease in the number of boundary elements, the relative error in wet natural frequency calculation was found to be less than 10%, while computation speed-up was found to be almost 500 folds.

Vibration analysis of complex fractional viscoelastic beam structures by the wave method

The vibration analysis of fractional viscoelastic beam structures with complex shapes and boundaries is a difficult task. In this paper, the wave method is applied to analyse the dynamic characteristics and steady-state response of fractional viscoelastic beam structures, and the effects of fractional order on wave propagation, transmission and reflection are discussed. Based on the fractional constitutive equation for viscoelastic materials, a fractional partial differential equation for a uniform viscoelastic beam is established. In the vibration analysis process, the beam is discretized according to the discontinuous feature positions, and then the vibration amplitude of the beam is obtained by a matrix calculation of the wave propagation, transmission and reflection associated with the beam. To verify the effectiveness of this method in studying fractional-order structures, a fractional-order viscoelastic beam is used as an example, and the results obtained by this method are compared with those obtained by the modal superposition method. In addition, the natural frequencies, mode shapes, frequency response function and amplitude response of viscoelastic beams with uniform symmetrical supports and beams with support positions that are optimized by a particle swarm optimization(PSO) are obtained with different fractional constitutive models. Moreover, the relationship between the dynamic characteristics and fractional order is also analysed. Actually, the model of viscoelastic material is changed under external excitation, which can be described by the variation of fractional order. The results show that this method has high accuracy in calculating the vibration properties of fractional viscoelastic beam structures.