Natural Vibration Properties Research Articles

Reliability polynomial chaos metamodel for the dynamic behaviour of reinforced concrete bridges

The approximation of complex engineering problems and mathematical regressions serves as the authentic inspiration behind the artificial intelligence metamodeling methods. Among these methods, polynomial chaos expansion, along with artificial neural networks, has emerged at the forefront and become the most practical technique. Previous studies have highlighted their robust capabilities in solving complex problems and their wide utilization across numerous applications, particularly in structural analysis, optimization design problems, and predictive models of uncertainty outcomes. The aim of this article is to present a methodology that introduces their implementation of for structural engineering, primarily focusing on reinforced concrete bridges. The proposed approach consists of demonstrating the applicability of the polynomial chaos to evaluate the dynamic behavior of two-span reinforced concrete bridges through a predictive model of natural vibration properties for eigenvalues modal analysis. Subsequently, response spectral method is conducted according to the Moroccan guide for bridge seismic design and the prescription of the EUROCODE 8 within the context of reliability assessment using Monte Carlo simulation. The efficacy of the proposed approach is illustrated by a comparison between the predicted vibration properties and the resulting values obtained through finite element modal analysis and artificial neural networks. The polynomial chaos process is based on a collected dataset of multiple reinforced concrete bridges sourced from technical studies offices and the Regional Administration of the East, affiliated with the Moroccan Ministry of Equipment and Water. Finally, this work contributes to the field by enhancing predictive modeling and reliability evaluation for bridge engineering using artificial intelligence metamodels.

EXPERIMENTAL INVESTIGATION OF THE VIBRATION-REDUCTION CHARACTERISTICS OF THE SHAFT COATING FOR A TURBOCHARGER

A turbocharger is a system that is fitted to automotive engines to increase performance and efficiency by taking air at atmospheric pressure, compressing it to a higher pressure and passing the compressed air into the engine via the inlet valves. A turbocharger consists of a turbine and a compressor impeller interconnected with a shaft supported in most cases by journal bearings. The shaft is one of most crucial components of a turbocharger system and it operates at high speed. The shaft vibrations are an inherent phenomenon and they are travelling to the surrounding structure, effecting the stability and reliability of the turbocharger system. The selection of the appropriate shaft-material property is a critical parameter among the parameters that affect the vibration of the system. This study focuses on exploring whether it is possible to reduce the shaft vibration using different types of coating materials, including aluminum chromium nitride (AlCrN), titanium nitride (TiN) and aluminum titanium nitride (AlTiN), each having thicknesses of (2, 4, and 6) µm, for a shaft made of AISI 4140 alloy steel. The inherent natural vibration properties, such as the resonant frequencies, damping, and mode shapes of the turbocharger shaft with and without coating, were obtained by conducting an experimental modal analysis through measurements of the frequency-response function, which is about curve fitting the data using a predefined mathematical model of the turbocharger shaft. The results were validated numerically with the finite element method. From overall results, it was observed that the AlCrN, TiN, and AlTiN coating thicknesses have a small effect on the resonant frequencies, but a good damping effect. The resonant response of the turbocharger shaft at resonant frequencies was suppressed remarkably by the AlCrN and AlTiN coatings, especially those having a thickness of 6 and 4 µm.

Experimental research on vibration reduction characteristics of adhesively bonded beam structures with acoustic black hole geometry

Beam structures are widely used in industrial applications such as automobiles, aircraft, naval architecture, trains, and buildings. The vibration characteristics of beams are inherent phenomenon and directly affect usage comfort and service life, but more dangerously may damage the structure due to excessive vibrations that are transmitted through the surrounding structure of the system. Vibration reduction of beam structures is a continuous challenge for industrial applications. It is important to reduce vibrations of the beam structures for stability. In this study, experimental research on vibration reduction characteristics of adhesively bonded beam structures with Acoustic Black Hole technique is presented. The Acoustic Black Hole, which is a geometry, tapered with a power-law profile enables vibration reduction by decreasing the velocity and the wavelength of vibration. The inherent natural vibration properties called modal parameters such as the natural frequencies, damping, and mode shapes of the beam structure with and without damping layer using power-law profile having various the Acoustic Black Hole length and exponent values were investigated and evaluated with experimental modal analysis. For validation, natural frequencies are determined numerically by the finite element method, and then compared with results obtained by the experimental modal analysis. The overall results indicated that the Acoustic Black Hole has ability to significantly suppress the vibration level and showed the capability of enhancing the damping efficiency when using the damping layer attached to the Acoustic Black Hole length of the beam structure.

Natural vibration of elastic metamaterial beam under arbitrary elastic boundary conditions

Elastic metamaterial (EM) is a kind of new composite material/structure that provides a new feasible way of vibration control in many scenarios. Although some analytical means for solving the vibration behavior of EM components with simple shapes and classic boundary conditions (BCs) have been presented, the analyses of those with complex shapes or BCs that are common in reality remain to be studied further. In this paper, the natural vibration problem of a typical EM beam under arbitrary elastic boundary conditions (EBC) is investigated by using the effective medium theory (EMT) and the Rayleigh-Ritz method. The inherent correlations between the EM beam and corresponding modified matrix beam together with the modified static equivalent beam are disclosed for their modal behaviors. The extraordinary natural vibration properties of the EM beam under arbitrary EBC are revealed and some common features are concluded. This work may provide a useful reference for further investigations of many other similar EM structures.

Natural vibration analysis of an embedded elastic metamaterial beam based on effective medium theory and Rayleigh–Ritz method

Elastic metamaterial (EM) beam is a kind of special composite structure with peculiar dynamic properties that are beneficial for relevant vibration isolating applications. The vibration properties and proper analysis methods of these special structures are the main concerns in practical designs and analyses. Existing analytic methods can only be applied to a few cases with simple geometric shapes and boundary conditions, hence more general analysis means are needed to be developed. In this paper, a general analysis method is proposed by combining the effective medium theory (EMT) and Rayleigh–Ritz method. Based on the method, the natural vibration properties of a typical EM beam are revealed clearly and correctly, such as absence of natural frequencies within bandgap, gathering of natural frequencies in the vicinity of band edges and particular modal correspondence before and behind bandgap. The effectiveness of the proposed method is validated by the analysis results, thus providing a feasible way for analyzing many complex cases where EM beams are included.

Thermal Aeroelastic Characteristics of Inflatable Reentry Vehicle Experiment (IRVE) in Hypersonic Flow

The inflatable reentry vehicle provides a new technical way in aerospace entry, descent, and landing. The structural failure of inflatable reentry vehicle experiment caused by thermal aeroelastic effect is serious, which needs to be further studied. A traditional numerical method about flexible vehicles separates the aeroheating and aeroelastic problems, resulting in poor matching with the actual test. In this paper, a thermal-fluid-solid coupling model considering inflation gas effect was established, which associates the aeroheating and aeroelastic modules and adopts the LES to improve the depicting ability of hypersonic flow. The model was used to solve the thermal aeroelastic characteristics under extreme aeroheating load. From aeroheating results, the large-scale vortex on windward generated by the interaction of the shock layer and boundary layer has great influence on aeroheating due to the heat dissipation, and the skin deformation also increases the surface friction and local heating near depressions. From aeroelastic analysis, the flexible structure performs violent forced vibration induced by the unsteady large-scale vortex on windward, and the aeroheating effect will significantly increase the thermal stress and natural vibration properties. The thermal-fluid-solid coupling method for the flexible structure proposed in this paper provides a reasonable reference for engineering.

Parametric CAD Modelling of Aircraft Wings for FEA Vibration Analysis

Excessive vibration of aircraft wings during flight is harmful and may cause propagation of existing cracks in the material, leading to catastrophic failures as a result of material fatigue. This study investigates the variations of modal characteristics of aircraft wings with respect to changes in the structural configurations. We develop parametric Computer-Aided Design (CAD) models to capture new design intend on the aircraft wing architectures. Subsequent Finite Element Analysis (FEA) based vibration analysis is performed to study the effects of architecture changes on the wing’s natural frequencies and mode shapes. It is concluded that the spar placement and the number of ribs have significant influence on the wing’s natural vibration properties. Integrating CAD modelling and FEA vibration analysis enables designers to develop alternative wing architectures to implement design requirements in the preliminary design stage.

Dynamic characteristic study of composite box beam with corrugated webs considering interface slip and shear deformation

In order to study the effect of interface slip and shear deformation on the natural vibration of composite box girders with corrugated webs (CBBCW), based on the Hamilton principle, the effects of the slip, shear deformation and moment of inertia of CBBCW have been investigated. Further, the flexural vibration differential equations and natural boundary conditions of the CBBCW have been deduced. The formula for the flexural natural vibration frequency of CBBCW has been developed. The influencing rule of the interface slip stiffness and web shear deformation on the flexural natural vibration frequency of the CBBCW has been analyzed. The results of this study show that the analytical results are in good agreement with the results of the ANSYS finite element calculation, and some significant conclusions can be applied to the engineering design. The interface slip stiffness has some effect on the flexural natural vibration frequency of the CBBCW, and the maximum interface slip effect is up to 13.7%. The shear deformation has a significant effect on the natural vibration properties of the CBBCW, and the shear deformation effect increases significantly with the increase of the order of flexural natural vibration frequency. The formula has been developed further as compared with the earlier developed calculation theory for the flexural natural vibration of CBBCW. It can also provide a reference for future study of dynamic characteristics of CBBCW.

Vibration of thin cylindrical shells on an elastic foundation coupled with multiple discrete stiffnesses

Vibration properties of thin cylindrical shells on an elastic foundation coupled with multiple discrete stiffnesses were investigated. The discrete stiffnesses were modelled as external forces. Hamilton’s principle was applied to deduce the governing equations. To study the natural vibration properties, the wave-like solutions were applied. Then the governing equations were discretized in matrix form to obtain the eigenvalues. The properties of natural frequencies and vibration modes of thin cylindrical shells were studied. The results illustrate that each natural frequency of cylindrical shells is mainly dominated by one vibration mode, that is, flexural, longitudinal and shear modes. The natural frequency will get closer with the increase of circumferential wave numbers. The influences of several parameters to vibration properties of cylindrical shells were also investigated.

Simulation of vibration harvesting mechanism for sea buckthorn

Sea buckthorn (SBT) is an ideal plant for ecological management and thus planted widely in western China. Its fruit is of high nutritional and medicinal values. However, its economic value is far from development because of high cost for harvesting SBT fruits. Mechanical vibration is one of feasible way to make fruit separation. To design proper vibratory harvesters for tree crops, the vibration harvesting mechanism of SBT was simulated and analyzed by the finite element method. First, a three-dimensional solid model of SBT tree was built by Pro/E and imported into ANSYS. Next, modal analysis was performed to determine the natural vibration properties of SBT tree such as the natural frequency and vibration mode. Finally, harmonic response analysis was applied to determine the steady-state response when a sine load was added to the SBT tree. The modal analysis results indicated that the first twenty order natural frequencies of SBT tree varied from 6.6 Hz (the first order frequency) to 31.8 Hz (the twentieth order frequency). Results of harmonic response analysis showed that the application of vibration force to the side branches is effective than to the trunk, with a slight damage to the tree. Moreover, the vibration force applied to the side branches was 58–78 N with a frequencies range of from 20 to 30 Hz, which ensured that the majority of SBT fruits were harvested from the tree. The simulation analysis results obtained in this study could provide a basis for the design and development of SBT vibration harvesters.

Sensitivity Metrics for Maximum Likelihood System Identification

AbstractThis paper introduces a set of sensitivity metrics to be used along likelihood-based modal identification methods. In maximum likelihood (ML) estimation theory, the precision of ML point estimates can be measured by the curvature of the likelihood function. This paper presents closed-form partial derivatives, observed information, and variance expressions for discrete-time stochastic state-space model parameters as well as state matrix features that influence modal estimates. The results are derived for the observation matrix and the state matrix as well as eigenvalues and eigenvectors of the state matrix; these model entities correspond to natural vibration properties of a structural system. Confidence intervals are constructed for natural frequencies, damping ratios, and mode shapes using the derived asymptotic covariance matrices and the asymptotic normality property of ML estimators. The results are a supplement to the ML-based structural identification using expectation maximization (STRIDE) ...

Hydraulic calculation and dynamic analysis of columnar reversing gate

According to the hydraulic calculation principles of the orifice outflow, the discharge capacity of the columnar reversing gate under the partial opening condition was calculated and checked. Using ANSYS, a large finite element analysis software, the discharge process was simulated. The distribution rule of the velocities in the gate chamber and downstream channel was obtained. An FEM model of the columnar reversing gate was built, and the natural vibration properties of the gate were analyzed. Based on the Westergaard added mass method, the added mass caused by the fluid-structure coupling motion was taken into account, and the effects of the coupling interaction were discussed. The results show that the size of the small gates meets the demand for discharge capacity, the current in the gate chamber is quite turbulent, the trunnion and arms are obviously impacted by flow, and the effects of water on vibration characteristics are remarkable. The study provides a reference for the design and calculation of gates of the same type.

Effect of 3D isotropic resolutions of sequenced images on natural vibration properties of trabecular bone

The voxel based finite element (FE) method used to obtain primary data for non-invasive imaging techniques has emerged as a major focus of interest in several disciplines such as medicine, mechanics and material engineering for solving micro and nano-scale problems. Owing to the fact that, voxel based FE models are directly affected by parameters of imaging techniques such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), the consequences of these effects on the natural vibration analysis of structures having complex geometry in micro scale, are investigated in this study. In this context, voxel based FE models are obtained using Micro-CT imaging data that has three different resolutions of vertebral trabecular bone tissue. Furthermore, resolutions of image data sets are artificially increased and equalized for evaluating voxel based FE models that are free from FE size effects. Natural vibration characteristics of voxel based FE models are investigated not only numerically but also including associated mode shapes. Unpredictable vibrational behavior for various voxel sizes, is, thus, revealed. Element size effects of voxel based FE models are considerably different from the effects on structural components with regular prismatic shapes. Obtained results show that, investigated parameters have a crucial influence on the natural vibration behavior of trabecular bone tissue which is selected as an example of complex geometries. Modal behaviors that are effective in micro local regions, but less in the whole body, where there are possibilities for working with approximate geometry without considering the micro structure have been observed. Moreover, the results are new from a theoretical point of view, and they also represent the importance of quality in imaging data, which, in practical applications must be taken into consideration.

Coupled Vibration Analysis of Vehicle-Bridge System Based on Multi-Boby Dynamics

For establishing the refined numerical simulation model for coupled vibration between vehicle and bridge, the refined three-dimensional vehicle model is setup by multi-body system dynamics method, and finite element method of dynamic model is adopted to model the bridge. Taking Yujiang River Bridge on Nanning-Guangzhou railway line in China as study background, the refined numerical simulation model of whole vehicle and whole bridge system for coupled vibration analysis is set up. The dynamic analysis model of the cable-stayed bridge is established by finite element method, and the natural vibration properties of the bridge are analyzed. The German ICE Electric Multiple Unit (EMU) train refined three-dimensional space vehicle model is set up by multi-system dynamics software SIMPACK, and the multiple non-linear properties are considered. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and finite element method when the ICE EMU train passes the long span cable-stayed bridge at different speeds. In order to test if the bridge has the sufficient lateral or vertical rigidity and the operation stability is fine. The calculation results show: The operation safety can be guaranteed, and comfort index is “excellent”. The bridge has sufficient rigidity, and vibration is in good condition.

Elastic Seismic Response of Steel-Concrete Composite Frames with Partial Interaction

The finite element formulations of steel-concrete composite (SCC) beams considering interlayer slip with end shear restraint is established. Elastic seismic response of SCC frame structures under different shear connection stiffness and slip boundary conditions are examined. The influences of the shear connection stiffness and the slip boundary condition on elastic seismic response are analyzed. With the shear connection stiffness increasing, the free vibration frequencies increase and the seismic responses decrease. The natural vibration properties of SCC frame structures and seismic responses are also significantly affected by the slip boundary condition, and it should be properly imposed on all composite beams in seismic response analysis.

Effect of Slice Step Size on Prediction of Natural Vibration Properties of Bone Tissue

Several vibration analysis procedures are used for determination of the level of bone loss, status of implant stability, modal damping factor and numerous other properties of tissues. The detection methods of bone properties are to compare the results of theoretical work with practical results. So, there are many options for processing of image data and establishing the finite element (FE) model that differentiation of calculated outputs is inevitable. Uncertainty of outputs can lead to mistakes while mechanical parameters or behaviors of tissue are determined. In this study, the effect of Micro-CT scanning intensity in connection with the reconstruction process on properties of the modal behavior of bone tissue were investigated. Results have shown that examined parameters have important effects on numerical values of the natural frequencies and modal behaviors. Furthermore, it has been revealed that numerical values and mode shapes must be considered together for properly understanding the natural vibration analysis of bone tissue.

The Practical-Analytical Solutions of the Wind Turbine Tower System’s Natural Vibration Properties

Wind turbine tower structure system’s natural vibration properties have important effects on the system of wind power tower wind vibration and seismic response, especially the low order modes often plays a control function. How to calculate tower system vibration characteristics correctly and effectively in the design phase has important practical value. In this paper, some practical analytic solutions formulas were deduced on considering the simplified model using Rayleigh quotient method. Moreover, the results of a tower frequency and mode which were calculated by these formulas were compared with the continuous distribution parameters system’ theoretical solution and FEM method’s solutions. Analysis show that: these natural vibration properties practical analytic solutions formulas of a wind turbine tower about simplified model are useful and precision in a tower design, especially suitable for cone cube tower.

Dynamic Analysis of Steel-Concrete Composite Frames with Partial Interaction

The finite element formulations of steel-concrete composite (SCC) beams considering interlayer slip with end shear restraint were established. Free vibrations of SCC beams and frame structures under different slip boundary conditions were examined. The influences of the shear connection stiffness and the slip boundary condition on dynamic characteristics were analyzed. It is shown that the low order 8-DOF element may exhibit slip locking phenomenon in free vibration analysis for very stiff connection. The free vibration frequencies of composite beams and frame structures increase with the shear connection stiffness increasing. Besides, it is found that the natural vibration properties of SCC frame structures are significantly affected by the slip boundary condition, and it should be suitably imposed on all composite beams in dynamic analysis.

Experimental Study of the Influence of Beam-Reduction and Rib-Addition Strengthening Method on Bridge Natural Vibration Properties

In order to study the influence of beam-reduction and rib-addition strengthening method on the natural vibration properties of hollow slab bridges, based on bridge natural vibration frequency and the vibration mode in the first three orders as main comparison parameters, according to the comparison between the theoretical values as well as experimental values of the natural vibration properties before and after strengthening, the practical effect of this strengthening method is studied. The test data show that the beam-reduction and rib-addition strengthening method results in an obvious enhancement of the natural vibration frequency of simply supported hollow slab bridges, which proves that the strengthening method has remarkable improvement effect on the rigidity of bridges. It can be seen from the comparison of the changes of the vibration mode in the first three orders before and after strengthening that the transverse connection of bridge is strengthened and the integrity is prominently enhanced after strengthening. The study result is that the beam-reduction and rib-addition strengthening method can greatly enhance the structural behavior of hollow slab bridges.

Effect of micro-ct slice intensity on natural vibration behavior of cancellous bone models based on reverse engineering techniques

Identification of natural vibration properties of bone structure in macro and micro levels is important because of increasingly vibration inclusion of current methods in recognition and treatment of bone diseases. In this scope, results which are obtained from non-destructive reverse engineering approaches are crucial especially in living tissue studies. The results may differ from each other because of the multi-staged methods and differences in constituted models due to the redundancy of options.In this paper, effect of differences due to the slice intensity on natural vibration analysis results by using constant resolution Micro-Computational tomography (Micro-CT) data of L3 vertebrae in voxel based finite element models are investigated. In addition to this investigation, another approach which is different from classic approach where non-cubic voxel based finite elements can be generated and only about the effect of slice thickness and cubic voxels is improved. The results obtained from the study show that solutions of proposed model are more conservative than the results of voxel based finite element (V-FEM) and these results are purified from the effects of element aspect ratio