Vibration Analysis Of Structures Research Articles

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.

Design optimization of irregularity RC structure based on ANN-PSO

Seismic design principles advocate for simple and regular structures to minimize earthquake damage. However, this frequently does not lead to unique and aesthetically pleasing designs, leading some engineers to select irregular structures despite the potential risks. The primary aim of this investigation is to achieve the optimal design of torsional irregularity coefficients for planar irregular reinforced concrete (RC) frames under static and dynamic loads, utilizing a 3D 6-layer model. Structural ground vibration analysis was conducted using the ETABS software. By imposing limits on the torsional irregularity coefficients for each layer of the frame layout, we subsequently applied the combination of artificial neural networks (ANN) with the particle swarm optimization (PSO) algorithm, namely ANN-PSO, to address the size distribution issue across the structure. The design variables included the dimensions of the columns located in each layer of the layout. The results demonstrate that the ANN-PSO algorithm optimizes the cross-sectional area of columns with significant variations. The coefficients of the torsion inequality rule in the optimized solution closely approach the minimum values. The dimensions and orientations of the optimized columns slightly differ from the pre-optimized scheme. In the optimized scheme, the coefficients of the torsional irregularity in the Y-direction meet the requirements, preventing any torsional irregularities from occurring. The research presented an effective method, including an innovative combination of ANN-PSO and the finite element method (FEM), for designing RC structures. The findings of the research provided a practical solution to fulfill torsional regularity criteria, indicating the proposed approach is an effective method for the economical and safe design of RC structures in earthquake-prone areas. The outcomes of the present study highlighted the innovative framework to achieve optimal and safe designs for irregular RC structures while minimizing torsional damage during earthquakes.

Analytical exploration of generic undamped mass–spring chains: A comprehensive study

Analysis of structural vibrations presents challenges due to the coupling between different degrees of freedom, often preventing the derivation of analytical expressions for quantities such as poles, vibration amplitude, etc. While numerical methods are commonly employed to tackle such challenges, their purely numerical nature prevents achieving a comprehensive understanding of the system behaviour. This paper builds on a novel recursive transfer function formulation recently proposed by the authors to analytically characterise the dynamics of generic undamped mass-chain systems. This approach provides fundamental properties and analytical insights that cannot be obtained through current numerical approaches, representing a significant breakthrough in the understanding of vibrations and offering valuable insights for analysing complex vibrating systems. These results presented in this paper allow for a rapid assessment of the minimum phase nature of the vibration system through straightforward stability assessment, and present analytical expressions for sums and multiplications of natural frequencies squared by induction and Vieta’s formulas. Furthermore, it derives conditions for existence of repeated roots using direct analytical derivation of the characteristics equations, including purely imaginary roots and repeated roots at the origin, showing that repeated roots can only occur when some forms of spatial symmetries exist, and confirms bounds for the arithmetic mean of natural frequencies by using inequalities between geometric, arithmetic and quadratic means. Additionally, analytical conditions are established for systems with different degrees of freedom to share the same roots, providing a theoretical foundation for eigenvalue assignment in the time domain or pole placement in the frequency domain. This foundation enables the determination of desired natural frequencies from scratch using transparent analytical conditions, without relying on complex algorithms typically required by current inverse methodologies involving passive structural modifications or active controllers. Moreover, this paper also explores the relationship between independent and coupled vibrations, providing insights for comparing natural frequencies. Overall, this paper contributes to a deeper understanding of structural vibrations through analytical exploration and offers practical guidance for eigenvalue assignment and natural frequency analysis.

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.