Low-order Natural Frequency Research Articles

A new concept reduced scale aeroelastic model of the four-cable suspension bridge with truss girder and its validation

The accuracy of the aeroelastic model or truss girders has consistently been a decisive factor influencing the results of full-bridge aeroelastic wind tunnel tests. A novel design approach, termed the Multi-Spine Frame System, is introduced for the reduced-scale model of the stiffening girder. This system incorporates multiple spines, thinner beams and columns to minimize aerodynamic interference while accurately simulating overall stiffness, mass, and constraints. The design procedure is formulated as an optimization problem with the objective of optimizing the low-order natural frequencies (lateral bending, vertical bending, and torsion) of the aeroelastic model. Pattern search method and penalty functions are employed to identify a locally optimal solution that satisfies engineering applications for this optimization problem. This design method is applied to an actual project involving a four-cable suspension bridge with a truss girder, and the test results demonstrate the accuracy of this approach in simulating the dynamic characteristics of the aeroelastic model. Corresponding wind tunnel tests on flutter instability, as well as numerical multi-modal flutter analysis, are conducted to analyze the critical flutter speed, vibration shapes, and frequencies of this bridge. Furthermore, the impact of deviation in structural mode shapes and natural frequencies on flutter instability is investigated using ten design schemes achieved by altering boundary conditions, mass distributions, and stiffness distributions, were examined. Significant differences in critical flutter speed (up to 9%) are observed due to deviations in mode shapes, emphasizing the necessity of considering modal frequencies and other modal information, such as mode shapes, in aeroelastic model design. This approach contributes to the advancement of aeroelastic model design for bridges with truss girders by introducing an effective system and an optimization method, providing a basis for future studies on wind instability and structural dynamics and also underscores the importance of accurate mode shape representation in flutter analysis.

Modal Frequency Shifts Measured on Xinjiang Bridge Excited by Traveling Vehicles

To excite sufficient vibrations of bridges for more effective modal experiments to take place, traveling vehicles were utilized in many bridge field inspection campaigns in history. However, the dynamics of a bridge subjected to the traveling vehicles are of changed resonant properties compared with those of the same structure with the ambient excitation in nature. Therefore, the field modal experiments employing vehicle excitations might unfavorably lead to shifted measurement results of low-order natural frequencies for long-span bridges of large mass. Using Xinjiang Bridge (a single-tower pre-stressed concrete cable-stayed bridge with spans [Formula: see text]) as the engineering background, this paper validates this technical notion based on reliable physical experiments and numerical simulations and seeks a practical approach to deal with the issue. It is found that the maximum deviation between the low-order modal frequencies measured on Xinjiang Bridge for the vehicle excitation case and those measured for the ambient excitation case (the accurate values) reaches 0.65[Formula: see text]Hz, and the deviation between the lower limit of the usual vehicle excitation’s energy band and the modal frequency measured (factor 1) and the traveling vehicles’ speed (factor 2) are the two key factors influencing the modal frequency shifts. An empirical model to compensate for modal frequencies’ deviations is formulated considering the two key factors accordingly, which is of high-practical significance in future applications of the modal experiments using vehicle excitations to other long-span bridges.

Analysis and optimization of the dynamic response characteristics of aircraft cargo rack

In order to effectively achieve the optimization design of the aircraft cargo rack, based on finite element modal simulation, the structure was redesigned and analyzed using two schemes of surrogate model size optimization and topology optimization, ensuring the strength requirements while improving the natural frequency and reducing the weight. According to the modal shape of vibration, additional bridge structures were added at the weak points to improve the dynamic stiffness of the structure. According to the optimization design requirements, the response surface function was constructed, and the particle swarm optimization algorithm was applied in the size optimization and surrogate model solution. A multi-objective optimization model was established for flexibility and low-order natural frequencies, and topology optimization was carried out in HyperWorks. The structural dynamic modification of the topology optimization model was performed using the modal strain energy analysis method. The research results show that both optimization methods can achieve good lightweight design. The static performance of the optimized structure is stable, and the overall modal frequency is improved.

Multi-objective Topology Optimization Design for a Certain Launcher Bracket

To achieve weight reduction and enhance the firing accuracy of a specific type of launch device, the bracket was selected as the optimization subject for multi-objective topology optimization. Single-objective optimization often overlooks other influencing factors. To address the limitations of single-objective optimization, this study adopts the variable density method from the SIMP approach and proposes a multi-objective topology optimization based on compromise programming. This study, through multi-objective topology optimization of the bracket, obtained an optimized topology structure that maximizes static stiffness and the dynamic low-order natural frequencies of the launch device bracket at launch angles of 0°, 53°, and 85°, with an azimuth angle of 0°. Finally, the obtained topology structure was validated using finite element software. The design method presented in this paper not only enhanced the stiffness of the bracket structure for such launch devices and increased the first two natural frequencies of the bracket but also achieved weight reduction. The optimization design process also provides a reference for other mechanical structures.

Dynamic Response Study of Overhead Contact System Portal Structure Based on Vehicle–Track–Bridge Coupled Vibration

In light of the rapid development of electrified railways, the safety and stability of train operations, as well as the catenary’s interaction with current quality, have garnered widespread attention. Electrified train operation with additional track irregularities serves as a principal excitation source within the vehicle–bridge–catenary system, significantly influencing the vibration characteristics of the system. Addressing the aforementioned issues, we first established the vehicle–track dynamics model and the bridge–catenary finite element model based on the principles of coupled dynamics of the vehicle–track system. These models are interconnected using dynamic forces between the wheel and rail. Subsequently, within the vehicle–track coupled system, track random irregularities are introduced as input excitations for the coupled model, and the dynamic response of the system is simulated and solved. Then, the obtained wheel–rail forces are applied to the bridge–catenary coupled system finite element model in the form of time-varying moving load forces. Finally, the dynamic response characteristics of the catenary portal structure under different conditions are determined. Meanwhile, a study on the vibration characteristics of the truss-type pillar portal structure was conducted, and the results were compared with those of existing models. The results indicate that the vertical and lateral forces between the vehicle and track are positively correlated with the speed and irregularity amplitude. Response values such as the derailment coefficient and wheel load reduction rate are within the specified range of relevant standards. The low-order natural resonant frequency of the truss-type pillar structure has, on average, increased by 0.86 compared to the existing pillar structure, which signifies improved stability. Furthermore, under various conditions, the average reductions in maximum displacement and stress response of this pillar structure are 13.2% and 14.19%, respectively, in comparison to the existing pillar structure, rendering it more suitable for practical engineering applications.

Mechanics mode characteristics analysis and numerical analytical optimization study of a three-stage centrifugal pump

To increase the accuracy of an analytic method based on the concentrated-mass approach for solving the mechanical operating modal characteristics of complete impellers and impellers with balancing holes in a centrifugal-pump rotor system, we establish a mathematical model and a three-dimensional simulation model for a double-supported three-stage centrifugal-pump rotor system. By comparing the modal results obtained from the two models, we propose a mathematical model that integrates the optimization of mass-distribution methods and bending stiffness correction coefficients, and we derive an optimized mathematical model for rotors with balancing holes. The effectiveness of the optimized mathematical model is validated via three-dimensional simulation, and the influence of balancing holes on the wet modes is analyzed. The results show that the wet natural frequencies are lower than the dry ones and that the wet natural frequencies obtained from analytical calculations are consistently higher than those obtained from three-dimensional simulation results. The optimized mathematical model significantly improves the accuracy of the wet modal characteristics for both complete impellers and impellers with balancing holes, with the errors in the low-order natural frequencies reduced by more than 50%. Under the same hole spacing, the natural frequencies of the three-stage centrifugal pump rotor system decrease with increasing hole diameter slightly. Under the same hole diameter, the natural frequencies of the rotor system increase slightly with the hole spacing. The effect of stiffness changes caused by balancing holes on the natural frequencies is larger than the effect of mass changes.

Effects of Vehicle Speed on Vehicle-Induced Dynamic Behaviors of a Concrete Bridge with Smooth and Rough Road Surfaces

According to a previous study, a concrete bridge bearing vehicles traveling at lower speeds suffers from more severe apparent damage compared to one bearing vehicles traveling at higher speeds. The authors of the study subjectively inferred that the observed phenomenon is due to different vehicle load-holding durations for different vehicle speeds. However, this interpretation is not true for bridges with a smooth road surface. Based on an engineering case study of Renyihe Bridge (a concrete rigid-frame continuous highway bridge with spans of 80 m + 4 × 145 m + 80 m), this article reveals via numerical simulations that with the increase in road surface roughness, the resonant responses of the bridge are significantly amplified for cases of low vehicle speed, which can well explain the phenomenon observed by the aforementioned study. Field experiments undertaken on Renyihe Bridge further reveal the related mechanism. These experiments reveal that the frequency of the vehicle excitation for a bridge with sufficient road surface roughness might be closer to the low-order natural frequencies of a bridge with a decrease in vehicle speed. Therefore, the resonant responses are supposed to be more significantly amplified in cases of low vehicle speed after an increase in road surface roughness.

An optimization neural network model for bridge cable force identification

Accurate determination of cable force values is the most important technical means to avoid damage to the cable bridge. In order to avoid the influence of the difficulty in distinguishing the boundary conditions and the lack of low-order natural frequency on the cable force determination results, an intelligent method for determining the bridge cable force based on the vibration method is proposed. With the cable length, linear density, flexural stiffness and input frequency as input units and the cable force as output unit, a neural network is established to identify the cable force by combining the finite element simulation data, and the model is optimized using the intelligent swarm optimization algorithm. The results show that compared with the cable force prediction models using generalized regression neural network (GRNN) and GRNN optimized using particle swarm optimization (PSO-GRNN) and canonical identification methods, the GRNN optimized using sparrow search algorithm (SSA-GRNN) proposed in this paper has a better identification effect. The prediction error of short cables is essentially within 10%, and that of long cables is within 5%. It can not only realize the accurate identification of bridge cable force by ignoring the boundary conditions and vibration frequency order of cables, but also has a wide range of applications.

Comparison of tensioning effect between roll and multi-spot pressure tensioning process of circular sawblade

ABSTRACT Tensioning is an important manufacturing process of circular sawblade, which can effectively improve the critical rotation speed of the sawblade. With the development of tensioning technology, the comprehensive research of each technology is of great significance. In this paper, the elastic-plastic numerical simulation models of roll and multi-spot pressure tensionings were established. The natural frequency and critical rotation speed of the tensioned sawblade were obtained through modal analysis and analytical calculation, using no buckling of the sawblade as the limiting condition. The results show that with the increase of the mold reduction, the anti-plane displacement, critical rotation speed, and high-order natural frequency of the sawblade increased, while the low-order natural frequency decreased. After the multi-spot pressure tensioning process, the critical rotation speed was higher, and the tensile tangential stress at the edge of the sawblade was greater. The post buckling forms of the roll tensioned and multi-spot pressure tensioned sawblades were a dish and saddle, respectively. Through this study, the upper limit critical rotation speed of the sawblade under different tensioning methods could be found, which could be used for the selection of tensioning methods and parametric optimization.

Evaluation of gravity effects on the vibration of fluid-conveying pipes

Gravity effects are generally ignored in the study on the pipe vibration. However, in this paper, the effect of gravity on the nonlinear vibration of a pipe conveying fluid has been evaluated. The nonlinear vibration of the pipe with an intermediate elastic support is investigated, and the equilibrium configuration of the pipe caused by gravity is calculated. The governing equation of the nonlinear vibration near the equilibrium configuration is established. Then, the natural frequencies and modes of the transverse vibration of the pipe are obtained. The vibration characteristics of the pipe around the equilibrium configuration are studied. In addition, the effects of gravity on the vibration characteristics of the pipe are illustrated by comparing the same system without gravity effects considered. The influence of pipe parameters on the gravity effects is also investigated. The results show that there are some different trends in the natural frequencies with and without considering gravity effects. The lower-order natural frequencies are more affected by gravity. Moreover, the contribution of this paper is to propose an impact factor of gravity to evaluate the relative difference caused by gravity. Furthermore, the critical impact factors of the gravity of three metal pipes are proposed. In short, this paper evaluates the effects of gravity on the vibration of the pipe conveying fluid and provides an effective strategy for engineering design.

Dynamic and Static Multiobjective Topology Optimization for Gears of Directional Drill Transmission System

Aiming at the multiobjective topology optimization design of the structure, this paper proposes a method to establish the comprehensive objective function based on the normalized subobjective of the compromise programming method and to determine the weight coefficient of the subobjective of the comprehensive objective function by the analytic hierarchy process (AHP). By using statistical analysis and modal analysis, the static and dynamic characteristics of the gear can be obtained. The single objective topology optimization is used to reduce the compliance of the gear and elevate the low-order natural frequency, and the frequency weighting method is used to suppress the oscillation phenomenon in the frequency-single-objective optimization. AHP was used to determine the weight coefficient of each subtarget. The compromise programming method is used for multiobjective topology optimization, and the gear design is improved according to the optimization results. By analyzing the improved gear structure, the weight of the optimized gear is reduced by 25.3%. The overall stiffness performance and strength performance are enhanced, and the natural frequencies of each order are improved to different degrees.

Modal Analysis of Main Structure of Substation Post-switchgear

The main structure of the substation post-equipment is a typical wind-sensitive structure, which is high and flexible. In order to ensure the safety and stability of the structure, it is necessary to conduct a modal analysis of the main structure of the substation post equipment, which in turn provides a basis for the analysis of wind vibration characteristics of the structural system. This paper analyzes the self-oscillation frequency and vibration pattern of the main structure of a substation in Inner Mongolia based on ABAQUS, compares them with the measured wind response modal results to verify the reliability of the numerical simulation results and finds that the low-order natural frequency of the main structure of the substation pillar-type equipment is between 0-2 Hz, and the frequency in the opening state is lower than the state of closing soon.

Analysis and experimental study on vibration response characteristics of mechanical harvesting of jujube

To explore the vibration energy transmission characteristics of mechanical harvesting of jujube and improve the effectiveness of vibration harvesting, the vibration response characteristics of small and densely planted Jun jujube branches were experimentally studied and evaluated. According to the agronomic requirements of mechanical harvesting of jujube, first, this paper analyzes the vibration harvesting mechanism of jujube, establishes the transverse bending vibration mechanical model of jujube branches, and obtains the sixth-order natural frequency of jujube branches through vibration frequency sweep experiments. Based on the slope scoring principle and response surface method, the impact of different excitation parameters on the jujube branch vibration effect evaluation index Pz was characterized through field experiments, and an optimized vibration effect score was obtained. The results showed that the low-order natural frequencies of small and densely planted jujube branches were mainly concentrated in the range of 6 ∼ 22 Hz, and the vibration response was the most intense at 17.5, 18.0 and 22.5 Hz, which was more conducive to vibration harvesting. By optimizing the relationship between the excitation parameters and evaluation index Pz, a better jujube branch vibration effect score of Pz = 85.63 is obtained, which provides a reference for the design and development of high-efficiency jujube vibration harvesting devices.

Research on the influence of geometric parameters on the natural frequency of the lattice sandwich structure

The lattice sandwich structure has the advantages of lightweight and high specific stiffness, and the natural frequency is an important index to characterize the quality and stiffness of the structure. Therefore, studying the changing law of the natural frequency can guide the engineering design of the lattice sandwich structure to exert its excellent performance. Since the multilayer lattice sandwich structure has good designability, the natural frequency can vary by changing the relevant geometric parameters of the multilayer lattice sandwich structure. Therefore, this article carries out specific work from the above perspective. This article first takes the two-layer lattice sandwich structure sample as the object, and conducts finite element modal analysis and experimental modal analysis to verify the accuracy of the finite element model. On this basis, the finite element software is used to study the influence of panel thickness, lattice sandwich rod diameter and the number of lattice sandwich layers on the low-order natural frequencies of the multilayer lattice sandwich structure. The results show that the natural frequency of the multilayer lattice sandwich structure is variable due to the different geometric parameters. Therefore, the lattice sandwich structure can obtain higher specific stiffness and better load-bearing capacity by selecting the geometric parameters reasonably. The above will bring new ideas and inspirations for the lightweight applications of lattice sandwich structures in aerospace, weaponry, automotive industry and other related fields.

Research on the effects of raft on vibration isolation

The floating raft vibration isolation system includes upper and lower isolators and middle raft. As one of the most important parts that affect the performance of vibration isolation, the raft is usually assumed to be an undamped or viscous damping structure in the analysis, which is different from the actual situation. To study the effects of raft with hysteresis damping characteristics, a three-freedom complex stiffness mechanical model was built, and an approach for calculating the raft's force transmission rate was derived from impedance methods. Based on the mechanical model and a large-sized floating raft, we analysed the effects of raft mass, stiffness and damping on vibration isolation through numerical calculation. Results show that increasing raft mass improved vibration isolation over most frequency ranges; increase in raft stiffness contributed to improved isolation performance over frequency ranges near its low-order natural frequencies, while reduced the performance over higher frequency ranges; and greater raft damping led to enhanced vibration isolation at its natural frequencies and higher frequency ranges.

Simulation study and field experiments on the optimal canopy shaking action for harvesting Camellia oleifera fruits

With the increasing cultivation scale of Camellia oleifera in China, the demand on the mechanical harvesting machinery is very urgent. Inefficient fruit harvesting has become a bottleneck hindering the development of Camellia oleifera industry. In order to achieve high fruit harvesting percentage and low detachment percentage of the flower buds, a canopy shaking mechanism is proposed for massively harvesting Camellia oleifera fruits which applies the reciprocating linear motion of multiple beating-bar arrays to the tree canopy. The multiple beating-bar arrays driven by the eccentric disk can generate comb-brushing effects on the tree canopy. Three kinds of Camellia oleifera tree architecture were modelled and their dynamics were simulated by finite element analysis. Their modal analysis results show that the low-order natural frequencies of the Camellia oleifera trees with different canopy shapes are very close. According to harmonic response analysis, the low-frequency excitation is used to harvest Camellia oleifera fruit. The orthogonal experiments were carried out on the canopy shaker prototype with the motor speed, reciprocating stroke and duration of vibration as the influencing factors, and the fruit harvesting percentage and the detachment percentage of the flower buds as the evaluation indices. The results show that the same optimal parameter combination can be used for three kinds of Camellia oleifera tree architecture, in which the motor speed is 360 r/min, the reciprocating stroke is 80 mm and the duration of vibration is 8 s. The average fruit harvesting percentage is 72.3% and the average detachment percentage of the flower buds is 13.9%.

Simulation Analysis of Vibration Characteristics of the Submerged-propeller Shaft Coupling System

The vibration characteristics of the submerged-propeller shaft coupling system are studied in this paper. Firstly, Based on the fluid structure interaction theory on acoustics wave equation, the vibration analysis model of the propeller-shaft system under water is established and computed. And the vibration characteristics of coupling system is analysed by comparing the shaft system and the submerged-propeller system. The results show that the natural vibration of the coupling system presents complicated propeller-shaft strong or weak coupling characteristics. Comparing the natural vibration and frequencies of the shaft system and the submerged-propeller system, all of the coupling system modes are corresponding to the shaft system or the submerged-propeller system in low frequency range. And there is strong transverse coupled vibration of coupling system near the propeller’s 1st-order transverse vibration frequency, which appears as propeller’s 1st-order transverse vibration coupling shaft’s 2nd-order transverse vibration. That indicates the strong transverse coupled natural vibration of the coupling system is easy to be excited near the low order natural frequency of propeller. Which may cause propeller’s transverse excitation force to be easily transmitted to the hull through the bearings under non-uniform flow, resulting in the severe vibration of the hull stern.

Research on Abnormal Vibration and Vibration Reduction Measures of a Natural Gas Compressor Station: A Case Study of the JYG Compressor Station

As an important medium transmission element, the pipeline has a very important application in the chemical industry, electric power industry, and petroleum industry. However, the pipeline vibration problem has seriously restricted the large-scale development of equipment, reduced the reliability of equipment operation, and even caused serious accidents. Therefore, it is very important to analyze the dynamic characteristics of these vibrations and to reduce the impact of vibrations within pipelines. We focus on the problem of abnormal vibrations within the JYG compressor station pipeline and use a 3D calculation model of the launcher pipeline of west–east gas pipeline III to perform simulation analysis using Fluent to find the cause of the abnormal vibrations. Our results show that the fluid pressure fluctuation in the pipeline is the main factor for the abnormal vibration of the launcher pipeline in the JYG compressor station. The main causes of the vibrations are excessive fluid flow and high flow velocity. Also, by comparing and analyzing the natural frequency of the pipeline system and the pressure fluctuation frequency of the vortex core in the pipeline, we found that the pressure fluctuation frequency is close to the low-order natural frequency of the pipeline system, which is prone to resonance. In this paper, three vibration reduction schemes of the JYG compressor station are suggested and verified. The efficiency of vibration reduction is 68–94%, which can be effectively applied to the outgoing pipeline of the west–east gas pipeline III to solve the abnormal vibration problem of the pipeline.

Optimization design of titanium alloy connecting rod based on structural topology optimization

Purpose The purpose of this paper is to realize the lightweight of connecting rod and meet the requirements of low energy consumption and vibration. Based on the structural design of the original connecting rod, the finite element analysis was conducted to reduce the weight and increase the natural frequencies, so as to reduce materials consumption and improve the energy efficiency of internal combustion engine. Design/methodology/approach The finite element analysis, structural optimization design and topology optimization of the connecting rod are applied. Efficient hybrid method is deployed: static and modal analysis; and structure re-design of the connecting rod based on topology optimization. Findings After the optimization of the connecting rod, the weight is reduced from 1.7907 to 1.4875 kg, with a reduction of 16.93%. The maximum equivalent stress of the optimized connecting rod is 183.97 MPa and that of the original structure is 217.18 MPa, with the reduction of 15.62%. The first, second and third natural frequencies of the optimized connecting rod are increased by 8.89%, 8.85% and 11.09%, respectively. Through the finite element analysis and based on the lightweight, the maximum equivalent stress is reduced and the low-order natural frequency is increased. Originality/value This paper presents an optimization method on the connecting rod structure. Based on the statics and modal analysis of the connecting rod and combined with the topology optimization, the size of the connecting rod is improved, and the static and dynamic characteristics of the optimized connecting rod are improved.

An improved concentrated mass method for analysis of the mechanics modes of a four-stage pump rotor system

To improve the calculation accuracy for the mechanics mode of a double-support four-stage centrifugal pump rotor system (FCPRS), a simplified mathematical model derived from “four segments-four concentrations” and an ANSYS model were used to solve the model of a D-type FCPRS with balanced mass. Based on ourresults, we present an improved mathematical model combining "five segments-four concentrations" and the modal resistance-bending stiffness (RBS) correction coefficient. Moreover, the calculation results of the impeller mass eccentricity from the optimized model were compared with those from ANSYS simulations. The natural frequencies (NF) from the concentrated mass method (CMM) are slightly lower than those obtained from ANSYS. After optimization, the errors of the first four orders of NFs decreased from 1.13%, 1.24%, 7.62%, and 7.96% to 0.79%, 0.90%, 4.17%, and 4.51%, respectively. The NFs of each order increase slightly in the case of impeller mass eccentricity. The low-order NF increases slightly and the high-order NF decreases when the impeller in the middle is eccentric. The NF error obtained via the optimized CMM for the impeller with eccentric mass is slightly larger than that for the impeller without eccentricity.