Natural Vibration Characteristics Research Articles

Vibration analysis of Ti-SiC composite airfoil blade based on machine learning

In this study, machine learning (ML) methods are integrated with Rayleigh-Ritz method and first-order shear deformation theory (FSDT) to predict the vibration properties of Ti-SiC fiber-reinforced composite airfoil blade. The natural vibration characteristics of airfoil blade are largely determined by various geometric and material parameters, which leads to the high computational cost of numerical methods. Therefore, the low-cost ML models in conjunction with Ti-SiC fiber-reinforced composite material is developed to replace traditional numerical methods in order to predict the vibration characteristics of airfoil blade. Random Forest (RF), Gradient Boosting Decision Tree (GBDT) and Back Propagation (BP) neural network models are utilized to compare the predicted results with existing data. Among these models, the BP neural network demonstrates superior performance. Additionally, the SHapley Additive exPlanation (SHAP) method is utilized to elucidate BP neural network model, facilitating the prioritization of input features. This approach offers a feasible auxiliary solution for investigating the vibration characteristics of airfoil blade.

Fracture behavior analysis and fatigue assessment of the spring clip in heavy‐haul railway

AbstractThis paper proposes a novel method based on a numerical simulation approach and fatigue fracture theory to analyze the fracture behavior and assess the fatigue life of spring clips. To this end, the finite element (FE) model of the vehicle‐track‐foundation system was developed including the key parts of the type II fastening system. Meanwhile, the spring clip FE model was validated through the natural vibration characteristics. Subsequently, the numerical simulations were performed under various working conditions to obtain the fatigue characteristics of the spring clips. The fatigue crack initiation life and damage were analyzed using FE results for the spring clips with ε‐N curve and Brown‐Miller criterion. Moreover, based on the initial crack geometry of the spring clips, the maximum circumferential stress criterion with the Paris equation was employed to analyze the crack extension behavior and assess the fatigue crack extension life.

Seismic behavior of high-rise modular buildings with simplified models of inter-module connections

Inter-module connections serve as crucial components, horizontally and vertically connecting individual modules to form modular buildings. This paper presents a component-based model that divides inter-module connections into vertical and horizontal connection components, facilitating the simplification of shear and axial behaviors for input into the global numerical model. Initially, experimental studies and numerical simulations were conducted to investigate the shear and axial behavior of these connection components, following which simplified connection component models were derived. Subsequently, a component-based model of inter-module connections was established, in which the shear and axial properties of the vertical and horizontal components were represented by nonlinear connector elements. Finally, the proposed component-based model was incorporated directly into the global frame models of high-rise steel modular buildings, and the seismic behavior was evaluated. The accuracy of the proposed component-based model was investigated by comparing the natural vibration characteristics and global building responses of high-rise steel modular buildings with traditional empirical models established based on assumptions of rigid or pinned fixities. The results reveal that traditional empirical models fail to accurately represent the discontinuous properties of inter-module connections, resulting in an overestimation of structural lateral stiffness. In contrast, the component-based model accounts for the actual load-transfer mechanisms of vertical and horizontal components, providing a more accurate understanding of the natural vibration characteristics and seismic response of high-rise steel modular buildings. The proposed component-based model establishes a critical link between isolated connection behavior and structural response assessment for high-rise steel modular buildings, making it well-suited for accurately predicting global building responses.

Comparative analysis of track damping effect of structure jointly constructed by subway tunnels and high-rise buildings

The joint construction of subways and other public buildings is a relatively newer type of construction. There is little research experience in the vibration characteristics and track damping design for this type of structure. In this study, a field test was adopted to conduct site measurement analysis on the vibration response of the joint construction project consisting of a subway tunnel and a building with typical frame structures. Numerical simulation methods were also adopted to, respectively, assume the use of ordinary tracks and steel-spring floating slab tracks for the subway for the situation where the Cologne-egg high-elastic fasteners were used on the track for damping purposes. Comparisons were performed to analyze the difference in the system vibration response between three different types of track. The results showed that the high-elastic fastener track and floating slab track both have a certain degree of damping effect compared with an ordinary track. Specifically speaking, the former has a damping advantage for frequency bands below 20 Hz, while the latter has the advantage for frequency bands above 20 Hz under the impact of the structural vibration characteristics for this joint construction. For this jointly construction structure, affected by the natural vibration characteristics of the structure, the natural frequency of the floating slab track is within 4 ∼ 10 Hz, and the similar vibration reduction effect can be achieved. This indicates that the structural vibration characteristic of the jointly constructed structure is an important factor determining the appropriate natural frequency of the floating slab track.

Transfer Matrix Method for the Analysis of Multiple Natural Frequencies

Multiple natural frequencies may be encountered when analyzing the essential natural vibration of a symmetric mechanical system or sub-structure system or a system with special parameters. The transfer matrix method (TMM) is a useful tool for analyzing the natural vibration characteristics of mechanical or structural systems. It derives a nonlinear eigen-problem (NEP) in general, even a transcendental eigen-problem. This investigation addresses the NEP in TMM and proposes a novel method, called the determinant-differentiation-based method, for calculating multiple natural frequencies and determining their multiplicities. Firstly, the characteristic determinant is differentiated with respect to frequency, transforming the even multiple natural frequencies into the odd multiple zeros of the differentiation of the characteristic determinant. The odd multiple zeros of the first derivative of the characteristic determinant and the odd multiple natural frequencies can be obtained using the bisection method. Among the odd multiple zeros, the even multiple natural frequencies are picked out by the proposed judgment criteria. Then, the natural frequency multiplicities are determined by the higher-order derivatives of the characteristic determinant. Finally, several numerical simulations including the multiple natural frequencies show that the proposed method can effectively calculate the multiple natural frequencies and determine their multiplicities.

Vibration transmission model of buildings based on virtual spring model and energy functional variation principle

In recent years, the “metro depot + over-track buildings” development model has witnessed rapid growth in China, driven by its advantages of high land utilization and investment return rate. However, the issue of vibration and noise caused by trains entering and exiting the depot has become a major impediment to its sustainable development. To predict the vibration of over-track buildings induced by trains, this paper presented a vibration transmission model of buildings based on the virtual spring model and the energy functional variation principle. The model was then applied to an actual engineering project at a metro depot in Guangzhou, China, and its accuracy was validated by comparing the results with finite element analysis and field measurements. Additionally, the vibration transmission characteristics of the over-track building were studied. The results indicated that the vibration transmission model of buildings presented in this paper aligns well with the results obtained through finite element analysis and field measurements. This approach eliminates the need to disassemble structural members, and the introduced virtual spring model effectively simulates non-ideal connections and boundary conditions. Consequently, it offers convenient structural connection and boundary condition settings, as well as high computational efficiency. Due to the edge effects on the top floor of the buildings, vibration waves in the higher floors experience a combination of reflected and incident waves, resulting in slow attenuation and, in some cases, amplification of vibrations as they propagate from the middle floors to the top floor. The vibration of the over-track building is closely related to the natural vibration characteristics of the floor and the frequency spectrum characteristics of the vibration source. When the natural frequency of a building's floor aligns with the main frequency of the vibration source, significant vibration amplification occurs due to local resonance.

Nonlinear resonant responses and chaotic dynamics of three-dimensional braided composite cylindrical shell

The advanced three-dimensional braided composite structure has excellent integrity, which can effectively avoid the problems of interlayer stress jump and interface debonding that may occur in traditional composite laminated structures. However, most of the existing references on the three-dimensional braided composite structure are fragmented, and there is little research on their vibrations. Taking the cylindrical shell of a rocket as the object and considering the complex flight environment, a general framework for the vibration problems of the three-dimensional braided composite shell is proposed for the first time. The equivalent mechanical parameters of the three-dimensional braided composite material are calculated based on the volume averaging method. Then, the nonlinear dynamic model of the three-dimensional braided composite cylindrical shell is established, and the natural vibration characteristics are analyzed. Under the case of 1:1 internal resonance, the pseudo-arc length continuation method is used to solve the nonlinear resonant responses of this nonlinear system. Finally, we apply the fourth-order Runge-Kutta algorithm to study the chaotic dynamics of the three-dimensional braided composite cylindrical shell model. This framework presented in this paper can be extended to the study of nonlinear vibrations and chaotic dynamics of other three-dimensional braided composite structures.

Seismic Response Analysis of Continuous Beam Bridges with Engineered Cementitious Composite (ECC) in Plastic Hinge Region

This study investigates the seismic performance of potential plastic hinge regions in small and medium-sized bridges using Engineered Cementitious Composite (ECC) concrete. A 4×40m continuous beam bridge is used as an example, with time-history analysis conducted using the OpenSees finite element software, and the type of concrete material in the cross-section of the bridge pier’s plastic hinge region is varied to analyze the structural natural vibration characteristics and seismic responses of the bridge structure under earthquake action. The time-history analysis of seismic motion shows that after replacing the bridge pier’s plastic hinge region with ECC, the stiffness of the bridge pier significantly decreases, and the natural vibration period of the bridge increases. Under the action of longitudinal earthquakes, the energy dissipation capacity and seismic performance of the bridge pier increase with the increase in ECC content in the plastic hinge region at the bottom of the bridge pier. Furthermore, under earthquake action, the concrete at the edge of the cross-section using ordinary concrete throughout cracks under tension, while the tensile stress in the cross-sections using different proportions of ECC concrete remains the same and does not crack under tension, remaining elastic under compression, which also reflects the good seismic performance of ECC concrete.

Local Instability and Deformation Control of Steel Roof of Factory Building in a Smart City

Abstract The traditional control methods of instability and deformation of steel structure neglect the analysis of its natural vibration characteristics, which lead to the poor effect of hysteretic vibration of steel structure nodes, and the stability optimization of steel structure is not ideal. Therefore, a new method to control the local instability and deformation of the steel roof is proposed. According to the steel structure composition of the upper door rigid frame and the connection mode of the frame beam and column, the roof steel structure characteristics of the workshop are analyzed. Multi-order natural frequency method is used to obtain the cumulative modal mass contribution rate of steel structure and analyze the natural vibration characteristics of steel structure. Based on the characteristics of natural vibration and element transfer matrix, the local instability control method of roof steel structure is designed. Simulation of strong vibration, using space analysis of tall-building with wall-elements (SATWE) software analysis of strong vibration under elastic load state, to obtain the external deformation of steel structure, under simulation of vibration deformation control model. Taking a chemical plant as an example, a finite element model was established to simulate the vibration wave, and the numerical simulation results of plastic deformation resistance of steel structure were analyzed. The experimental results show that the proposed method can effectively enhance the stability of steel structure and reduce its deformation degree.

Analysis of Natural Vibration Characteristics of Modified Timoshenko Cracked Beam

This study utilizes the transfer matrix method to analyze the modified Timoshenko beam with and without cracks. The massless torsional spring is assumed to represent the section where the crack is located. The matrix equation is simplified using boundary conditions and solved using MATLAB. Additionally, the influence of different crack depths and positions on the first three natural frequencies is compared to finite element analysis using three common types of beams as examples. The results indicate that increasing the crack depth leads to a decrease in the natural frequency of the beam. However, the impact on certain specific positions is insignificant, with a maximum error between the two methods not exceeding 2.73%. Furthermore, the study investigates the influence of crack depth on natural frequency under different span-to-height ratios. The findings reveal that increasing the span-to-height ratio reduces the influence of crack depth on natural frequency, thereby validating the proposed method and its applicability in modified Timoshenko cracked beams.

Simulation analysis and collaborative optimization of key components of the precision detection platform for high precision encoder

To realize the error detection of the high-precision photoelectric encoder, the optical small-angle precision measurement principle of the photoelectric autocollimator and single-sided mirror, and the 360° full circle measurement principle of angle inversion of the compound biaxis turntable are used to establish the precision detection platform of the encoder. The error model of the biaxial structure in the photoelectric coding error detection platform is established by introducing the error sources of the biaxial structure, such as the coaxiality error, angular position error, and installation error. At the same time, the biaxis structure and error models are used to optimize the compound biaxis structure system. By analyzing the natural frequency and vibration characteristics of the structure, the rationality and reliability of the compound biaxis system of the high-precision encoder precision detection platform are verified.

Numerical assessments of observed seismic performances of Lexington Dam during the 1989 Loma Prieta earthquake

Seismic performances of Lexington Dam during the 1989 Loma Prieta earthquake are assessed. Linear and nonlinear analyses are used to identify locations of tension zones where cracks are likely to occur. Numerical analyses are for longitudinal and transverse sections of the dam. Assessments of natural vibration characteristics of the dam are based on numerical simulation of geophysical and forced vibration testing procedures. Nonlinear analyses are based on equivalent linear and elastoplastic solution procedures. The acronyms of computer programs used are SHAKE, SHAKEM and FLAC. Analyses procedures and computer programs used are commonly used in dam engineering practice. Relative movements of observers representing onsite accelerometers are included. The information presented is expected to be of interest to engineers and seismologists in dam engineering practice.

On the Similarity Relationship between the Structural-Steel Prototype and the 304-Stainless-Steel Dynamic Scale Model

Due to the size limitations of shaking tables, dynamic scale models of large-span space structures for engineering have small cross-sections and thin wall thicknesses. It is difficult to use the structural steels commonly used in prototypes to make dynamic scale models. In this paper, 304 stainless steel is proposed for making the scale model, and the similarity relationship between the structural-steel prototype and the 304-stainless-steel dynamic scale model was studied. Firstly, a uniaxial test was conducted to study the elastic modulus similarity and the yielding stress similarity. The test results demonstrated that the elastic modulus similarity ratio was 1:1, and the stress similarity ratios of the 304 stainless steel and the three typical structural steels were 1:1 (Q235 steel), 1:1.5 (Q355 steel) and 1:1.8 (Q420 steel). Then, the similarities of other variables were derived using the dimensional analysis method. In the end, a numerical analysis was conducted to verify the similarity relationship between the structural-steel prototype and the 304-stainless-steel dynamic scale model. In the numerical analysis, a single-layer spherical reticulated shell structure and a dynamic scale model with a length similarity ratio of 1:20 were established by using the ABAQUS 2021 software, and the node displacement, the element internal force and natural vibration characteristics were analyzed. The results show that standard deviations of the displacements, the internal forces and the natural vibration frequencies between the prototype and the scale model were within 5%. It turns out that the proposed similarity between the structural-steel prototype and the 304-stainless-steel dynamic scale model was applicable in the elastic stage. The findings provide a reference for designing a dynamic scale model of large-span space structures for engineering by using 304 stainless steel.

Research on the mechanism of rail corrugation of steel spring floating slab track on metro

Steel spring floating slab track (SSFST) is an effective vibration and noise reduction measure, which is gradually used in urban rail transit in recent years. In order to better solve the problems of vibration noise and abnormal rail corrugation on metro lines, the dynamic model of vehicle-track system including metro vehicle and track structure is established by using the simulation software. The relationship between the passing frequency of vehicle and the vibration frequency of track structure, as well as the resonance characteristics of the elastic track structure are analyzed so as to obtain cause of rail corrugation on SSFST. The results show the following: (1) It is a more obvious resonance phenomenon between the inner rail and the floating slab at the vibration frequency of 116 and 161 Hz (R300 m), 262 Hz (R1000 m) and 320-387 Hz (R1500 m), and the simulation of rail corrugation wavelength is closer to field measured data. (2) Comparing the vibration frequency distribution of ordinary track and SSFST under the same curve radius, the rail corrugation is related to the natural vibration characteristics of track structure. (3) The vibration characteristics of the track structure and the periodic wear characteristics of the rail are the key factors for the formation of rail corrugation.

Analysis of Natural Vibration Characteristics of Metal Roof Panel of Large-Span Standing-Seam Metal Roof System

Metal roof systems are widely used in various landmark buildings. Understanding the natural vibration characteristics and primary influence of the roof system is useful for improving the roof system’s service life and maintaining the project’s safety. In addition, it is helpful to analyze the vibration force of the structure under earthquake and wind load. In this paper, the experimental investigation of the natural vibration characteristics (NVC) of two commonly used structural forms of standing-seam metal roof systems is carried out, and the influence of different boundary conditions, specimen width, panel width, and other parameters on the NVC are considered. The influence of different factors on the NVC of the roof system is analyzed in detail, and the main influencing factors and secondary influencing factors are studied. The research results show apparent differences in the NVC of the side and middle span of the roof panel under different parameters. The structural form has the most significant influence on the NVC of the roof panel, and the maximum influence on the peak acceleration (PA) and the fundamental frequency (FF) of the roof panel are 83.7% and 60%, respectively. The width of the specimen has a minor influence on the FF of the roof panel, and the minimum influence range is 6.9%. The influence of structural form, constraint form, specimen width, and panel width on the PA of the roof panel is far more significant than it is on the FF, with the difference between the two reaching 44.2%.

Effective-mode superposition response spectrum method for three dimensional seismic response analysis of underground structures

Response spectrum method (RSM) has been applied in seismic analysis of underground structures. However, the RSM is computationally low efficient for processing large soil domains. In this paper, the dynamic characteristics of underground structures are first investigated through three rectangular subway station structures. The results show that only a small number of effective frequencies and modes of soil-structure interaction (SSI) system significantly affect the seismic response of underground structure. These effective frequencies and modes are related to the natural vibration characteristics of site. An effective method is then developed to obtain the effective natural frequencies and modes of the SSI system. Subsequently, the effective modal superposition response spectrum method (ERSM) for seismic analysis of underground structure is developed by only combining the effective natural frequencies and modes of the SSI system to improve efficiency. Finally, the accuracy of ERSM is investigated through seismic response analysis of subway station structures. Numerical examples show that the ERSM can be used for seismic analysis of underground structures considering 3D SSI.

Analysis of Dynamic Characteristics of Attached High Rise Risers

The exhaust chimney of third-generation nuclear power units is a typical attached high-rise riser structure. In this paper, the simplified mechanical model and dynamic model of China’s third-generation nuclear power Hualong-1 VNA system, including multiple nonlinear factors, are established for the first time. The DTM (differential transformation method) was first applied to solve the natural vibration characteristics of a multi-point constrained variable cross-section riser structure, and the effects of variable cross-section, variable mass, variable axial force, and different elastic constraint parameters on the natural vibration characteristics of the system were studied. The dynamic behavior of the VNA system under the combined action of internal flow velocity, vortex excitation, and foundation excitation was studied. The results show that the outer diameter function of the VNA system pipeline should be designed as a quadratic function or a near quadratic multi-segment constant value function. The “limiting” effect of constraining large stiffness can force low-order vibration modes with high constraint stiffness to jump to high-order vibration modes with low constraint stiffness. The elastic constraint arrangement scheme with near center symmetry can make the system vibration mode present a half stable and half-curved form. A new optimization design scheme has been proposed regarding the layout and stiffness parameters of the VNA system guide bracket. This can enable the VNA system pipeline to avoid severe oscillations near the response extreme values caused by multiple frequency excitations of seismic loads under design and accident conditions and ensure the service life of the equipment.

An improved equivalent beam model of large periodic beam-like space truss structures

Space truss structures are essential components for space-based remote sensing loads with high spatial and temporal resolutions. To achieve high-precision vibration control, an accurate and efficient dynamics model is essential. In addition to the current equivalent beam model (EBM) based on the classical continuum theory, an improved equivalent beam model (IEBM) is proposed that considers the impact of the distinction between trusses and beams on torsional and shear deformations, as well as the impact of shear deformation on flexural rigidity. According to the displacement expressions of spatial beams, torsional, shear, and bending correction coefficients are introduced to derive expressions of strain energy and kinetic energy. The energy equivalence principle is then utilized to calculate the elasticity and inertia matrices, and dynamics equations are established using the finite element method. Subsequently, an IEBM is constructed by employing the particle swarm optimization approach to determine the correction coefficients with the truss natural frequency as the optimization target. The natural vibration characteristics of the structure are estimated for various material properties. Compared with the full-scale finite element model, the EBM reaches a maximum error of 80% for a low modulus of elasticity, while the maximum error of the IEBM is less than 2% for any given parameters, indicating its superior accuracy to the EBM.

Influence of pier-water interaction on natural vibration characteristics of bridge with complex piers in water

In order to clarify the influence of water on the natural vibration of bridge with complex piers, based on a continuous beam with 4-column pier, the numerical analysis model is established. Single column circular pier is taken to discuss the range of waters. Then the influences of water on the natural vibration are analyzed. The research shows that waters reduce the natural frequency. When waters area width is less than 10 m, the natural frequency of the pier decreases. And the first-order longitudinal bending frequency is reduced by 3.36%. When waters area width is more than 10 m, the vibration frequencies tend to be stable gradually. Therefore, the waters 10 m can be regarded as an infinite boundary. The natural frequencies of single column pier and 4-column pier decrease with the increase of water depth. When the water depth is less than 10 m, the changes of natural frequency of the first four orders of single column pier are relatively small, and the changes of 5–10 order natural frequency are large. The maximum effect of the first ten orders is 14.84%. The natural vibration frequency of the bridge decreases gradually with the increase of water depth. The maximum effect of the first five orders is 3.33%.

Structural performance of long-span truss structures in ultrahigh voltage substations under multi-hazard action of earthquake and icing

The transmission line is a vulnerable lifeline system when subjected to extreme loads, such as earthquakes and heavy ice loads. This study numerically investigates the structural performance of ultrahigh voltage long-span truss structures (LSTSs) under the multi-hazard action of earthquake and icing to mitigate disaster losses. A typical LSTS-3-tower-3-line system was selected as an analytical model. Its finite element model was established using a simplified spring model to simulate an ice-covered transmission conductor; it was excited by seven multi-component far-field ground motions. The natural vibration characteristics, structural responses, earthquake failure modes, and bearing capacities of LSTS affected by icing were comprehensively analyzed. The results showed that the seismic response of LSTS decreased, and its total response (induced by the tension of the conductor, ice load, and earthquake) increased with an increase in ice thickness. In addition, icing severely reduced the bearing capacity of LSTS with average reductions of 11.7% and 39.1% when the ice thicknesses were 15 and 50 mm, respectively. Moreover, the influence mechanism of icing on LSTS seismic responses and the failure mechanism of LSTS under the multi-hazard action of earthquake and icing were revealed. Specifically, the failure modes of LSTS, namely flexural (mode 1), mixed (mode 2), and shear failures (mode 3), were determined by the ice condition. Finally, prediction models for the structural responses and bearing capacity of LSTS were developed to facilitate the design of electrical equipment and LSTS and improve design efficiency.