Vibration Analysis Of Structures Research Articles

Effects of edge-crack orientation and depth on non-linear dynamics of laminated nanocomposite single-variable-edge plates

This paper presents an investigation into the free vibration and nonlinear dynamic analyses of new complex edge contour plate structures, known as single-variable-edge (SVE) plates. Cracks emerge at the center of the plate’s surface, and the effects of edge crack orientation and depth on the dynamical characteristics of the laminated nanocomposite SVE plates have been considered in this study. The functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) material was utilized for the edge-cracked plate that rests on a Winker-Pasternak elastic foundation. The Halpin-Tsai micromechanical model is used to predict the material characteristics, which are presumptively temperature-dependent. The rule of mixtures is employed to determine Poisson's ratio, density mass, and thermal expansion. The governing equations are established based on the theory of elasticity, and Von Karman-Donnell geometric nonlinearity assumption. To confirm the reliability and accuracy of this approach, the acquired findings are validated with those produced using Finite Element Analysis (FEA). Furthermore, the geometrical and material parameters, fracture properties, and environmental (temperature and elastic foundation) factors are also investigated in the study. The research findings hold significant implications for applications in aerospace and aeronautical, civil, and mechanical engineering.

Structural Trends and Vibrational Analysis of N,N,N′,N′−Tetramethylmalonamide Complexes Across the Lanthanide Series

AbstractFundamental understanding of coordination chemistry across the lanthanide series is essential for explaining chemical behavior of rare‐earth metals in complex liquid‐liquid extraction processes, which in turn affects the distribution ratios and efficacy of separations as a whole. In this work, we explore the structural trends between the lanthanides and a neutral N,N,N′,N′−tetramethylmalonamide (TMMA) ligand within four isolated families of solid‐state compounds: Ln(trans‐TMMA)2(NO3)3 Ln=La−Nd, Sm; Ln(cis‐TMMA)2(NO3)3 Ln=Eu−Tb, Er; [Ln(TMMA)3(NO3)2][Ln(TMMA)(NO3)4] Ln=Dy−Tm; Ln(Κ2‐TMMA)(iPrOH)(NO3)3 and Ln(Κ1‐TMMA)(Κ2‐TMMA)(NO3)3 Ln=Yb, Lu. Moving across the lanthanide series, we note the formation of both discrete charge‐neutral complexes, as well as charged molecular anion‐cation pairs, with variations in spatial ligand arrangement, coordination numbers, and ligand denticities. IR and Raman spectroscopy paired with DFT frequency calculations were used for an in‐depth investigation of vibrational modes unique to each structural family. The collection of isolated model compounds was also discussed in the context of liquid‐liquid separations based on reported distribution ratios from malonamide extraction.

A conical spiral piezoelectric energy harvester with parallel beams for all-directional flow energy harvesting

Piezoelectric energy harvesting technology using flow-induced vibration is a type of interference-resistant and miniaturizable power generation technology, which is promising on powering the wireless micro electromechanical system in flow filed. However, the flow direction of the natural flow field is changeable while most existing flow-induced piezoelectric energy harvesters (PEHs) are limited by their working direction. In this paper, we propose a conical spiral piezoelectric energy harvester with parallel beams (CSPEH-PB) that can collect energy under flow excitation in all directions. Based on the multi-dimensional vibration analysis of conical spiral structure, we investigate the resonance mode and effective flow velocity range of the CSPEH-PB through numerical analysis. In comparative experiments with a bimorph flat PEH, we verify the effective flow velocity range and voltage of the CSPEH-PB and polyvinylidene fluoride (PVDF) films attached. The results demonstrate that the CSPEH-PB generates an effective voltage greater than 0.53 V through the PVDF films under any direction of the water flow, and has a wider resonance bandwidth than PEH with straight beam. This study provides a practical solution for adapting PEHs to changeable flow direction.

Choosing the Best Functions for the Rayleigh-Ritz Vibration Analysis of Beams

The Rayleigh-Ritz Method is used extensively for the vibration analysis of structures. The accuracy depends on the assumed functions. In this work several different groups of functions are examined and compared for the accuracy of the resulting natural frequencies, and for the overall mode shape error norms calculated with respect to the known exact solutions. It is concluded that a set that combines low order polynomials, odd cosine and odd sine functions, or, even cosine and even sine functions, is more likely to yield the best accuracy and convergence of both frequency and mode shapes for a general beam structure.

In-plane free vibration analysis of multi-folded beam structures

Folded beam structures have been widely used in mechanical engineering, aerospace engineering, and other fields due to their flexibility and extensibility in applications. Although the components of a folded beam are simple beam structures, building an accurate dynamic model is complex due to its multi-degree-of-freedom, multi-mode, and close-mode features. This study presents a novel method to analyze in-plane free vibration of a multi-folded beam structure with arbitrary numbers of beam segments with different beam lengths and folding angles. The governing equations of the system can be easily obtained based on the beam theory and the work-energy principle. However, the key issue is how to solve the eigenvalue problem of a multi degree of freedom system defined by a 6 n × 6 n matrix. As the coefficient solution vector of the modal function is unknown, solving equations defined by high-order determinants involving variables has considerable complexity. In this work, the intricate matrix is initially turned into a single matrix of block Hessenberg form using numerous "6 × 6" block square matrices. Furthermore, by combining the characteristics of the block Hessenberg matrix with the approach to solve block determinants, a considerable reduction in the determinant's size can be attained, diminishing it from a dimension of 6 n × 6 n to 6 × 6. This procedure markedly simplifies the computational intricacies involved in the analysis. Finally, four kinds of multi-folded beams, namely L-shaped beams, Z-shaped beams, C-shaped beams, and four-segment folded beams with arbitrary lengths, folding angles, and numbers of beam segments are considered and studied, and the mode shapes and the influence of geometric parameters on the first three natural frequencies are discussed in detail. The results are also verified by the finite element method (FEM), and good agreement is found between the two methods. The results show that the proposed method can offer a unified framework for the in-plane vibration analysis of multi-folded beam structures.

Vibration analysis of metallic structure of an innovative dam gate

An analysis of the vibrations that may occur at the gate of a dam is proposed. Thus, the determination of an optimal constructive solution is sought from the point of view of vibration behavior. The dam gate is part of a constructive solution of an oscillating center pivot dam, which closes the gates if the downstream water level rises above a certain limit. This constructive solution is new. The gates are controlled by the water level. Such a system is easy to implement practically and the construction and maintenance costs are lower than in the case of classic dams. The problem that arises is that of the behavior of such a structure to vibrations. The eigenvalues of the gate structure are determined for a constructive solution proposed by the designers and the behavior of the forced vibrations that can stress the gate is studied. The analysis is performed for the case where the dam gates are closed. The work continues previous research on the structure's resistance to static loads and justifies the use of this solution in design. The method used to carry out the study is the finite element method. The advantages of the studied structure consist of lower costs for the proposed relatively simple constructive solution.

In-plane and out-of-plane vibration analysis of laminated composite frames with warping effects

This paper addresses the free vibration analysis of a general planar frame structure, consisting of an assembly of laminated composite beam members. A mathematical model is established for the beams by introducing a novel displacement field, which encompasses the influence of shear deformation, rotary inertia, material coupling, warping phenomenon, as well as in-plane and out-of-plane deformations. By incorporating these various factors, a comprehensive representation of the beam's behavior is achieved. The continuity equations for displacements and rotations of two adjacent members are formulated to derive the equations for the entire frame structure. The assembled equations are solved using the Finite Element Method (FEM). The numerical results obtained are compared with existing results in the literature and new results from 3D models in ANSYS. The present results for torsional modes are closer to the ANSYS results than the results of previous studies. An extensive analysis is performed to investigate the impact of various parameters, including stacking sequence, frame angle, relative frame length, and anisotropy ratios on the system response.

Mid-frequency vibration analysis of built-up structures using WFE-SEA method

The idea of classifying built-up structures into hybrid deterministic-statistical subsystems is formed as a framework to deal with the dynamical response in the mid-frequency region. This paper explores the potential combination of the wavelet finite element method and SEA, resulting in the hybrid WFE-SEA method, to achieve a solution with reduced computational burdens and increased accuracy. The development of the hybrid WFE-SEA method commences with the formulation of a 3-D B-spline wavelet theory, utilizing the semi-orthogonality of B-spline wavelet. A multi-resolution analysis of this theory facilitates the creation of a 3-D B-spline wavelet on an interval element model, incorporating nodes distributed on both the surface and inside of the hexahedron. Subsequently, the 3-D B-spline wavelet on an interval element is integrated with SEA theory, producing in a hybrid WFE-SEA framework suitable for examining dynamic problems of built-up structures. The energy-balance equation is derived by coupling the 3-D B-spline wavelet theory with diffuse field reciprocity relation to estimate the mid-frequency dynamic response. Furthermore, the validity of the proposed approach is rigorously assessed by comparing it against detailed mid-frequency analyses, including the hybrid FE-SEA method and the hybrid ES-FE-SEA method. The conclusion highlights the substantial agreement of the present hybrid method with other approaches, achieved at a small cost in terms of degrees of freedom.

Vibration Analysis of Internally Perforated Annular Plate with Discontinuous Boundary Conditions

Because of the introduction of modal coupling, discontinuous boundaries have a significant impact on the vibration characteristics of annular plates. Based on the spectral element method (SEM) and parametric equivalent method (PEM), the vibration calculation and analysis of internally perforated annular plate with discontinuous boundary are explained. Firstly, a uniform annular plate is regarded as a spectral element, and the vibration response of an annular plate with general elastic boundaries is obtained based on the motion equation of the annular plate and the virtual spring method (VSM). The displacement solution is described by the Bessel function, and a fitting method of discontinuous spring stiffness coefficient based on the weighted least square norm least square method is proposed. Based on the force equilibrium condition, the vibration response of an annular plate with a discontinuous boundary is derived, and the reasons for the change of vibration characteristics with a discontinuous boundary are explained from modal superposition. The dynamic stiffness matrix method is used to establish the vibration equation of an annular plate with a discontinuous boundary, and the influence of internal openings on the vibration characteristics of an annular plate is effectively calculated by the parametric equivalent method. Finally, a finite element simulation model is established to test the accuracy and stability of the proposed method. The influence of general discontinuous boundary conditions on structural dynamic behavior is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous boundary conditions.

Free vibration analysis of sandwich structure via point interpolation meshfree method based on polynomial basic function

The stability of circular and annular sector plate structures under aerodynamic pressure in supersonic conditions is crucial for aircraft components. Conventional uniform materials lead to heavy structures, which are undesirable for aircraft. This study explores the use of functionally graded materials to enhance flutter stability. It employs a refined logarithmic shear deformation theory to describe plate displacement, classical elasticity theory for constitutive equations, and Hamilton’s principle for equations of motion. Two methods, finite element, and Meshfree radial point interpolation, are used to solve these equations and verify the results. Parameter studies are conducted to assess the effects of grading index, Biot’s coefficient, span angle, and geometrical aspect ratio, revealing unexpected adverse effects of grading material on stability.

AT-PINN: Advanced time-marching physics-informed neural network for structural vibration analysis

Solving partial differential equations through deep learning has recently received wide attention, with physics-informed neural networks (PINNs) being successfully used and showing great potential. This study focuses on the development of an efficient PINN approach for structural vibration analysis in “long-duration” simulation that is still a technical but unresolved issue of PINN. The accuracies of the standard PINN (STD-PINN) and conventional time-marching PINN (CT-PINN) methods in solving vibration equations, especially free-vibration equations, are shown to decrease to varying degrees with the simulation time. To resolve this problem, an advanced time-marching PINN (AT-PINN) approach is proposed. This method is used to solve structural vibration problems over successive time segments by adopting four key techniques: normalization of the spatiotemporal domain in each time segment, a reactivating optimization algorithm, transfer learning and the sine activation function. To illustrate the advantages of the AT-PINN approach, numerical simulations for the forced and free vibration analysis of strings, beams and plates are performed. In addition, the vibration analysis of plates under multi-physics loads is also studied. The results show that the AT-PINN approach can provide accurate solutions with lower computational cost even in long-duration simulation. The techniques adopted are verified to effectively avoid the offset of the spatiotemporal domain, reduce the accumulative error and enhance the training efficiency. The present one overcomes the drawback of the existing PINN methods and is expected to become an effective method for solving time-dependent partial differential equations in long-duration simulation.

Improved modal analyses using the novel quadrilateral overlapping elements

In this work, the novel quadrilateral overlapping element incorporated with the harmonic trigonometric functions is presented to reduce the efforts in mesh division for modal analysis. The new partition of unity functions in the overlapping element are cubic polynomials. Therefore, low-order polynomials can be utilized to augment local approximation space without the linear dependence problem. Moreover, the original polynomial approximation spaces are further enriched by the harmonic trigonometric functions without introducing additional rank deficiencies in the system matrices. Thus, the presented enriched overlapping finite element method (EOFEM) provides very precise eigenfrequencies and eigenmodes by using a very coarse mesh. However, the shape functions in the presented EOFEM do not possess the Kronecker delta function property. Hence, a conforming method that modifies the shape functions rather than the variational principle is proposed to impose the essential boundary conditions. Several numerical examples in two dimensions are then investigated to elaborate on the performance of the presented EOFEM in modal analyses. Besides, a block-diagonal lumped mass matrix is presented and further extended to the structure vibration analysis by incorporating the explicit time integration method. It is proven that the enriched overlapping element is computationally more efficient than the quadratic finite element and the original overlapping element.

Complex modal analysis of structural vibration and acoustic radiation of plates

Inhomogeneous damping distribution leads to the occurrence of complex modes of structures. Complex modes' vibration and acoustic radiation characteristics are different from real modes. This paper studies the complex modal characteristics of inhomogeneously damped plates for forced vibration. We used the state space method to obtain the complex eigenvalues and eigenvectors of the vibration system and calculated the relationship between modal coordinates and frequency under unit force. The results show that the absolute values of the modal coordinates of two conjugate complex eigenvectors are different, and the structure's vibration is dominated by the eigenvectors corresponding to eigenvalues with positive imaginary parts near natural frequencies. When investigating the structural sound radiation in the vibration mode space, each mode's acoustic radiation is not independent but coupled with each other. The influence of the coupling between complex modes on the calculation results of the acoustic radiation power of the plate is studied in this paper. The results show that the coupling effect between modes cannot be ignored when calculating the acoustic radiation power based on complex modes. Finally, the error of calculating acoustic power using the decoupling approximation instead of the complex mode method is analyzed.

An efficient hybrid collocation scheme for vibro-acoustic analysis of the underwater functionally graded structures in the shallow ocean

In this paper, a novel hybrid collocation scheme based on the generalized finite difference method (GFDM) and the Burton–Miller singular boundary method (BMSBM) is developed to study the vibration and acoustic radiation characteristics of an underwater functionally graded (FG) structure immersed in the shallow ocean. By utilizing the individual strengths of both methods, the GFDM is adopted for the vibration analysis of the FG structures, while the BMSBM is applied for the acoustic wave radiation analysis. Numerical examples verify the accuracy and efficiency of the proposed hybrid collocation scheme for the natural frequency and acoustic radiation behavior of the underwater structures consisting of the functionally graded materials (FGMs). The influences of the material parameters, structural geometries and shallow ocean environment on the natural frequencies of the structural vibration and the underwater acoustic wave radiation field are investigated in detail. Numerical study shows that the variation trend of the natural frequencies of the structural vibration is consistent with that of the resonance peak frequencies of the underwater acoustic radiation field. The present results may provide valuable references for the design and application of underwater marine structures consisting of the FGMs.

A Seven-Parameter Spectral/hp Finite Element Model for the Linear Vibration Analysis of Functionally Graded Shells with Nonuniform Thickness

This contribution presents a finite element shell model capable of performing linear vibration analyses of shell-type structures made of functionally graded material (FGM). The model is based on the seven-parameter spectral/hp finite element formulation, which allows the analysis ofFG shells of either uniform or nonuniform thickness. Equations of motion are derived using the Hamilton’s principle and the material properties of the constituents are considered to follow a power-law volume distribution through the thickness direction. The verification of the present model is carried out by comparing with numerical results available in the literature, and with numerical simulations performed in a commercial software. To demonstrate the capabilities of the present formulation, the free vibration response of different shell structures, with nonuniform thickness, to the variation of the geometrical parameters (e.g., radius-to-thickness ratio) and the mechanical properties is reported.

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.

Development of a new CVAP structural analysis methodology of APR1400 reactor internals using scaled model tests

The U.S. Nuclear Regulatory Commission (NRC) Regulatory Guide (RG) 1.20 provides guidance on the comprehensive vibration assessment program (CVAP) to be performed on reactor internals during pre-operational and startup tests. The purpose of the program is to identify loads that could cause vibration in the reactor internals and to ensure that these vibrations do not affect their structural integrity. The structural vibrational analysis program involves creating finite element analysis models of the reactor internals and calculating their structural responses when subjected to vibration loads. The appropriateness of the structural analysis methodology must be demonstrated through benchmarks or any other reasonable means. Although existing structural analysis methodologies have been proven to be appropriate and are widely used, this paper presents the development of an improved new structural analysis methodology for APR1400 reactor internals using scaled model tests.

Bending and free vibration analyses of CNTRC shell structures considering agglomeration effects with through-the-thickness stretch

The present work investigates an enhanced finite element model and numerical analysis to illustrate the agglomeration effect of Carbon Nanotubes (CNTs) on static and free vibration responses of reinforced composite plate and cylindrical panel shell. The developed model is based on the kinematics of the improved first-order-shear deformation theory (FSDT), assuming a parabolic variation of the transverse shear strains and fulfilling the zero circumstance of the transverse shear stresses at the extreme structure’ surfaces omitting the use of shear correction factors. The material properties of the nanocomposite are determined using a developed micromechanical model based on the Mori–Tanaka approach. The developed finite element formulation is based on three-dimensional constitutive equations without reduction involving the addition of one parameter of thickness change combined with the Enhanced Assumed Strain (EAS) method. Four enhancement models are established and discussed. In a first attempt, the improvement of the third bending strain using one or four parameters are presented. In a second attempt, the membrane strain is enhanced with four parameters. Due to lack of investigations on structural behavior of composite structures reinforced with agglomerated CNTs, new static and free vibration results for shell structures with three level of CNT agglomeration are examined. Parametric studies are here in developed to present the influences of the characteristic parameters on the structural behavior of the CNTRC shell in a new graphic way; such as the volume fraction and agglomeration of nanofibers, geometrical parameters, and boundary conditions. Based on numerical results, it is found that the agglomeration and distributions of the reinforcing fibers are really crucial and play a significant role on the static and vibrational performances of the structure.

Template mass and stiffness for vibration analysis and damage detection of plane structures

This paper investigates he vibration properties of template plane elements in both themes of optimum mass matrix formulation and damage identification. To find the optimum mass matrices for the elements, the classical and unconventional mass formulations for the plane problems are explored. The optimum mass is obtained by the template approach, along with an optimization procedure, based on the perturbation theory and sensitivity analysis. The efficiencies of the proposed optimum mass are investigated through numerical examples for some plane structures. Those pairs of the optimum mass and stiffness, which yield more accurate results in the vibration analysis, are utilized for damage identification. A novel damage localization index based on the in-plane transverse vibrations is proposed and applied successfully in a new two-stage damage identification procedure for planar structures. By using Test Analysis-Model correlation (TAM) and the element damage equations; authors' algorithm overcomes the challenges of limitations in measuring all the degrees of freedoms. Furthermore, the proposed algorithm has the potential to diagnose the false alarms and prevents the ill-condition problem in damage identification. The abilities of the suggested method are demonstrated through 11 different damage scenarios and the presence of noise.

Similar Model for Accurate Structural Vibration Analysis of Elevated Track-Box Girder Coupling System

Model similarity experiment is an effective method to predict the vibration response of track-box girder structure under complex working conditions. In this paper, the coupling similarity relationship between the layers of the multilayer structure is deduced theoretically. In addition, according to the elasticity similarity law and the π theorem, a track-box girder coupling vibration model with a 10:1 geometric similarity ratio was designed. The influence of parameters on the system similarity was further discussed, including the density and elastic modulus of track plate, the stiffness of fastener and CA mortar layer. Finally, a scale track-box girder model was built. Based on the modal test and finite element method, the model design and the similarity relation between prototype and model were verified. The results show that the scale model can be employed to forecast vibrations for an elevated track bridge, and the vibration level under different working conditions can be inverted from the model test results in model design. When the geometry size of a certain structural layer in the direction of load is much larger than that of the other structural layers, the similarity relation derived from the material properties of the structural layer is approximately equal to the similarity of the system between the prototype and the scale model.