First-order Natural Frequency Research Articles

Investigation on the variations of dynamic characteristics of anchor bolts considering transverse inertia effects under tensile loads

Abstract In the case where tunnel anchor bolts are located in strata with limited surrounding rock boundaries, the response signals of the anchor bolts are affected by the tensile load and the transverse inertia effect, resulting in a decrease in the reliability of the non-destructive testing (NDT) results. To accurately assess the anchorage quality under these disturbances, a vibration energy loss model for anchor bolts after excitation was proposed. NDT experiments and numerical simulation studies were conducted on intact and defective anchor bolts under different conditions, analyzing the variation patterns of structural dynamic characteristics such as the the first-order natural frequency, the first-order damping ratio, and the vibration energy loss under the influence of tensile load and transverse inertia effect. The results show that during the gradual increase of the tensile load, the first-order natural frequency and the first-order damping ratio exhibit an overall trend of first increasing and then decreasing, while the rate of the energy loss initially decreases and then increases. The presence of anchorage defects leads to a reduction in the first-order natural frequency, the first-order damping ratio, and the energy loss of the anchor bolt. As the transverse inertia effect intensifies, the first-order natural frequency initially increases and then decreases, the first-order damping ratio decreases, and the energy loss initially decreases slightly before increasing. The numerical simulation verifies the applicability of the theoretical model and explores the influence of defect location on energy loss. The results indicate that the closer the defect location is to the free end, the less the vibration energy loss of the anchor bolt.

Rapid Assessment Method of Buckling Stability of Bridge Pier–Cap–Pile System Under Scour Effect

A novel analytical method for evaluating the buckling stability of the pier–cap–pile system under scour effect is proposed, and furthermore, the concept of rapid assessment of bridge buckling stability based on natural frequency is innovatively introduced in this paper. First, the total potential energy function of the bridge pier–cap–pile system is established, and the closed-form solution of structural system critical buckling load under scouring is solved according to the principle of stationary potential energy. Second, the sensitivity analyses of pier height, pier width, bending stiffness reduction in pier, pile slenderness ratio, pile bending stiffness reduction, m-value of soil and structural gravity to the buckling load are carried out. On this basis, 60 sets of sensitive parameter sample combinations are extracted by the Latin Hypercube Sampling algorithm, and a proxy model relating the critical buckling load to scour depth and the sensitive parameters are then developed using the McQuarter global optimization algorithm. Finally, the regression relationship model between the critical buckling load and the natural frequency is formed by combining the proxy model and the existing relationship between the scour depth and the first-order natural frequency. The feasibility of the proposed assessment method is demonstrated by the finite element method using a bridge case study, which provides an insight and a new means of quantitatively evaluating the safety of bridges under scour effect.

Modal analysis and optimization design of ultra-high acceleration platform rail frame

The ultra-high acceleration macro and micro motion platform has the advantages of high positioning accuracy and small error, and the key mechanism rail frame of the ultra-high acceleration macro and micro motion platform is optimized based on modal analysis to achieve the performance optimization of the platform. SolidWorks software was used to build the rail frame model, and ANSYS Workbench software was used to carry out modal analysis, topology optimization and response surface optimization, etc., so as to reduce the quality of the rail frame as much as possible under the premise of maintaining the stability of the first-order natural frequency. The results show that the optimization of the response surface meets the expected goal, the first-order natural frequency of the guide rail frame increases by 0.7 %, the mass decreases from 6.165 kg to 5.592 kg, and the change rate is 9.2 %, which achieves the purpose of lightweight.

Research on the transient dynamic characteristics of the low-density polyethylene compressors shaft system with operating pressure exceeding 180 MPa

The safe and stable function of hyper-compressors with operating pressures exceeding 180 MPa is a guarantee for the low-density polyethylene production process, and the transient dynamics of the compressor shaft system under stable operating conditions are an important concern for the design, maintenance, and fault detection of such compressors. Therefore, this paper presents a finite-element model of the hyper-compressor shaft system and analyzes the dynamic stress and fatigue life of the crankshaft, the connecting rod, the crosshead, and the plunger. In order to verify the accuracy of the model, all stages of the compressor's plunger stress and the torque of the crankshaft–motor connection end were tested in the field. The dynamic gas pressure of each stage cylinder was obtained by the tested stress of the corresponding plunger, then it was set as the load input of the finite-element model. The results show that: the average errors of the simulated plunger stress at two stages are 0.14% and 0.21%, respectively; the mean, peak, valley, and range errors of the torque at the crankshaft–motor connection end are 3.80%, 12.37%, and 3.49%, respectively; the simulated first-order torsional natural frequency of the shaft system is 78 Hz with an error of 8.3%. In the occurrence of the first-order torsional resonance, the maximum torsional stress appears at the crankshaft–motor connection end. The maximum dynamic stress alternating amplitude of the hyper-compressor shaft system under stable operating conditions is 103.7 MPa with a minimum life of 3.309 × 109, which occurs at the crankshaft–motor connection end and is converted into 31.48 years. The finite-element model, test, and simulation data presented in this paper can provide a reference for the fault detection and optimization design of hyper-compressors.

Analytical approach for lateral dynamic responses of offshore wind turbines supported by cement-soil composite steel pipe pile embedded in gassy marine sediment layer

This study aims to clarify and gain an insight into the lateral dynamic response of offshore wind turbines (OWTs) supported by cement-soil composite steel (CCS) pipe pile embedded in gassy marine sediment layer by developing an analytical approach. In the proposed approach, the CCS pipe pile-supported OWT system is divided into three parts including the tower part, the seawater-immersed steel pipe pile part, and the embedded CCS pipe pile part. The lateral dynamic behaviours of the CCS pipe pile-supported OWT system have been determined and then validated by solving the analytical solution of lateral displacement for the above three parts. Numerical discussions are finally conducted to analysis the influence of some physical parameters on the lateral displacement and the first-order natural frequency of the CCS pipe pile-supported OWT system. The main findings can be summarized as: (i) the offshore deep cement-soil mixing (ODCM) pile is an effective reinforcement method to reduce the lateral vibration of conventional steel pipe pile-supported OWTs; (ii) the increase in tower height and seawater layer thickness will have a serious negative impact on the lateral dynamic response of CCS pipe pile-supported OWTs; (iii) the increase in gas saturation of gassy marine soil will lead to a negative influence on the maximum lateral displacement of CCS pipe pile-supported OWTs.

Dynamic response of OWT tripod pile foundation in clay considering scour

Tripod-supported offshore wind turbine (OWT) foundation must withstand wind, wave, and seismic loads. In addition, it may be threatened by scouring during its service life, which could affect its bearing capacity and the overall OWT dynamic response. This study develops a three-dimensional numerical model of OWT tripod pile foundation to investigate scour effects. The numerical model incorporates a simplified single bounding surface model to simulate the dynamic stress–strain response of clay soil. The results revealed that scouring can reduce the first-order natural frequency of tripod pile-OWT system; however, the reduction usually does not lead to resonance within the 1P frequency range. Nonetheless, as the scour depth increases under wind and wave loads, the horizontal displacement of the wind turbine structure increases monotonously; however, its peak acceleration increases initially then decreases slightly as the scour depth continues to increase. Under seismic loading only, the OWT response exhibits complex evolution pattern as the scour depth increases. On the other hand, the foundation horizontal displacement and rotation angle increase significantly under combined wind-wave-seismic loads when the scouring depth reaches three times the pile diameter. Finally, the scouring depth has a relatively small impact on the foundation vertical displacement.

An XYZ parallel nanopositioning stage with hybrid damping

It is well known that lightly damping linear dynamics of a piezo-hysteresis-compensated flexure-based stage severely limits its motion control bandwidth. To address it, a novel damped XYZ parallel flexure-based nanopositioning stage (3⊥(P⊥K∥K), P for prismatic, K for Cardan or Universal) with hybrid passive damping, which is composed of shearing–squeezing hinge damping and in-band damping by graded local resonators (GLRs), is presented. The dynamic modeling and optimization design are implemented based on the maximization of motion amplification ratio, first-order natural frequency, and inverse in-band H2 norm of frequency response function (FRF). The optimized GLR module has distributed dynamic characteristics. The approximate motion decoupling is verified by Jacobin matrix analysis and experiments. The static/scanning-frequency dynamic experiments and step/triangular trajectory tracking control with the low-order controllers for all-hinge damping and hybrid damping stages are implemented. The experimental results indicate the small crosstalks due to hybrid passive damping, as the static crosstalks in X-to-Z and Y-to-Z are 0.293% and 0.276%, respectively, and the dynamic crosstalks in X-to-Z and Y-to-Z are 0.922% and 0.910%, respectively. The capability of improving positioning precision and expanding control bandwidth by hybrid damping only with a low-order controller is also validated experimentally.

Investigation of structural parameters influencing vibration characteristics of heavy-duty truck diesel tanks.

The working conditions of heavy-duty trucks are very complicated as the diesel shaking and resonance problems, which causes weld tears, separators to fall off, and other failures occur. Through experiments and finite element simulation, the natural frequency and vibration mode of a given 400 L diesel tank were calculated to study the influences of structural parameters such as the fill ratio (0.1-0.9), the number of baffle plates (0, 1, 2), the spacing of the plates (240 mm, 400 mm, 560 mm) and the aperture (38 mm, 78 mm, 118 mm) on the modal parameters with the wet mode method. The results of the hammering mode test and the simulation modal analysis agree well with the maximum error is 4.8%; the natural frequency of the diesel tank will increase with fill ratio decrease; the increase of the baffle plate number (0, 1, 2) can effectively increase the first-order natural frequency of the diesel tank, but the change of the natural frequency is not obvious on the higher order; the higher plates spacing has a smaller natural frequency; increasing the aperture will highly increase the natural frequency, 188 mm has better vibration safety.

Optimization Design of Straw-Crushing Residual Film Recycling Machine Frame Based on Sensitivity and Grey Correlation Degree

This paper takes the frame as the research object and explores the vibration characteristics of the frame to address the vibration problem of a 1-MSD straw-crushing and residual film recycling machine in the field operation process, and an accurate identification of the modal parameters of the frame is carried out to solve the resonance problem of the machine, which can achieve cost reduction and increase income to a certain extent. The first six natural frequencies of the frame are extracted by finite element modal identification and modal tests, respectively. The rationality of the modal test results is verified using the comprehensive modal and frequency response confidences. The maximum frequency error of modal frequency results of the two methods is only 6.61%, which provides a theoretical basis for the optimal design of the frame. In order to further analyze the resonance problem of the machine, the external excitation frequency of the machine during normal operation in the field is solved and compared with the first six natural frequencies of the frame. The results show that the first natural frequency of the frame (18.89 Hz) is close to the external excitation generated by the stripping roller (16.67 Hz). The first natural frequency and the volume of the frame are set as the optimization objectives, and the optimal optimization scheme is obtained by using the Optistruct solver, sensitivity method, and grey correlation method. The results indicate the first-order natural frequency of the optimized frame is 21.89 Hz, an increase of 15.882%, which is much higher than the excitation frequency of 16.67 Hz, and resonance can be avoided. The corresponding frame volume is 9.975 × 107 mm3, and the volume reduction is 3.46%; the optimized frame has good dynamic performance, which avoids the resonance of the machine and conforms to the lightweight design criteria of agricultural machinery structures. The research results can provide some theoretical reference for this kind of machine in solving the resonance problem and carrying out related vibration characteristics research.

Structural design and experimental research of a micro-feed tool holder based on topology optimization

Abstract. In the present study, a new configuration for a micro-feed tool rest driven by piezoelectric ceramics with a rigid–flexible phase is designed. The flexible driving part of the micro-feed tool rest is optimized using the topology optimization method, which not only improves the driving stiffness, resolution and structural stability but also increases the maximum displacement. The structural stiffness achieved in finite element simulation analysis is 16.28 N µm−1, and the first natural frequency reaches 2521 Hz. A prototype of a piezoelectrically driven micro-feed tool holder and a testing platform are constructed, and the structural stiffness of the prototype is determined to be 15.53 N µm−1 via analysis and testing, resulting in an error of 4.8 % compared with the finite element simulation results. The first-order natural frequency is 2636 Hz given a resolution of 12 nm and a maximum output displacement of 12.983 µm. Compared with the double-parallel flexible hinge, the maximum stroke of the micro-feed tool holder increases by about 5.4 µm and the resolution is improved by about 50 %. The new micro-feed tool holder developed in this paper features a cross-plate-type flexible mobile guiding mechanism. Combining stiffness, maximum travel and displacement resolution, it is applicable to precision and ultra-precision machining.

The study of the natural frequency evolution and numerical simulation of retrogressive landslides

A retrogressive landslide is influenced by the cyclical fluctuations in reservoir water levels is considered a common natural disaster. Tension cracks are important indicators for assessing landslide status in the case of retrogressive landslides. Displacement monitoring is a commonly used method and provides an intuitive reflection of the landslide deformation; however, it does not directly indicate the depth of the tension cracks. Based on the principles of vibrational dynamics, a retrogressive landslide is proposed to be initially classified as a single-mass spring oscillator model before the development of cracks. Following the development of tension cracks, the model can be classified as a double-mass spring oscillator model. The model patterns are verified through numerical simulations using ABAQUS. Based on the numerical simulations, with an increase in the number of reservoir water cycle fluctuations, the displacement and stress of the landslide exhibit periodic growth. However, during displacement growth, the tension cracks do not necessarily increase. As the tension cracks deepen, the landslide transitions from a single-mass spring oscillator model to a double-mass spring oscillator model, with the appearance of a second-order natural frequency. Moreover, as the tension cracks deepen, the numerical values of the natural frequency change. The maximum change in first-order natural frequency is 3.5 Hz. The maximum change in second-order natural frequency is 4.5 Hz. The variation in the natural frequency can reflect the depth of development of the landslide's tension cracks and, consequently, indicate changes in the stability state of the landslide.

Topology optimization of gradient lattice structure filling with damping material under harmonic frequency band excitation

With the rapid development of 3D printing technology, lattice structures have been widely utilized in structural designs aimed at vibration resistance due to their excellent performance. In this study, considering the moderate improvement of vibration suppression property of existing graded lattice, we introduce high-damping material into the optimization framework and further enhance the vibration resistance ability of gradient lattices. This framework extends the existing framework of stiffness and mass distribution to incorporate the distribution of stiffness, mass, and damping, which allows us to consider the damping changes with the cell configuration. Initially, the lattice cells are assigned with two different constitutive materials, one with high stiffness and the other with excellent damping properties. Different from traditional lattice units, we can obtain a series of lattice units with adjustable stiffness , mass and damping in a certain range. Via the homogenization method on the frequency domain, the complex elastic matrices about distribution of these lattice cells controlled by three parameters are obtained. In the meantime, the loss factor of these lattice cells is also obtained. A polynomial-based interpolation technique is employed to characterize the graded lattice units, which is integrated into an optimization process aimed at minimizing the lattice structures’ vibration responses. Several numerical examples are presented to illustrate this framework’s effectiveness, and experimental tests on 3D printed specimens are conducted to validate the numerical results. It’s worth noting that under the condition that the total weight of the structure remains unchanged, this weakens the overall stiffness of the structure (the reduction of first-order natural frequency), but greatly increases the damping of the structure (with a widened resonance peak) to resist the vibration of the structure. For the lattice structures induced by damping materials, the average loss factor is 0.114, which is almost doubled to the average value of those not including the damping material. When comparing the results of the mean displacement amplitude with and without damping materials, the reduction of displacement amplitude of lattice structures is above 25 %. The methodology expands the scope of optimization design for lattice structures, moving beyond stiffness maximization to include vibration mitigation by determining the appropriate distribution of stiff and damping materials, showcasing the practical applicability of the presented methods in engineering practice.

Multi-objective optimization design for the table of a CNC machine tool based on bionic structures

To improve the static and dynamic performance of CNC machine tool tables, a multi-objective optimization design method based on bionic structures is proposed, which involves bionic design and size optimization design. Based on the bionics, four types of bionic structure tables for the original XK5032 machine tool were designed, namely bamboo cross-section bionic structure table, spider web bionic structure table, honeycomb bionic structure table, and prairie rushes bionic structure table. Static and modal analysis of the original and four types of bionic tables were conducted using finite element simulation methods validated through modal experiments. The results show that the overall mechanics of the four bionic tables have been improved compared to the original table. Using the entropy weight TOPSIS method, the prairie rushes bionic structure table was selected from four types of bionic tables. Conducting multi-objective optimization design on the prairie rushes bionic structure table, three optimization candidate schemes were obtained. The entropy-weighted TOPSIS method was used again to select the optimal solution from these three schemes, resulting in a 0.8% reduction in mass, an increase in first-order natural frequency by 2.8%, a decrease in maximum displacement by 3.2%, and a significant 21.6% reduction in maximum equivalent stress compared to the original table.

Experimental and numerical investigations on non-synchronous vibration and frequency lock-in of transonic compressor rotor blades

Non-synchronous vibration (NSV) problems in axial compressors are challenging and frequently result in high vibration stress or structural failure within the frequency lock-in region. A deeper understanding of the lock-in phenomenon in NSV is necessary to improve blade reliability and safety. In this study, an experiment was conducted on a multistage transonic axial compressor to obtain frequency lock-in characteristics. The enforced motion of the flexible blade simulation method was used to study the frequency lock-in mechanism between blade vibration and tip unstable flow. The results showed that the aerodynamic frequency characteristic changed from a broadband spectrum to a distinct frequency peak as the NSV onset. The nonlinear vibration pattern could maintain the limited cycle oscillation for 26 s. The vibration stress of the frequency locked-in case was approximately 19 times that of the frequency unlocked one. The pressure fluctuations generated by the large-scale radial separation vortex structures were stronger than those of the tip leakage flow, and the third-order harmonic frequency of the circumferential instability flow was close to the first-order bending model natural frequency. The periodic shedding and reattachment process of flow separation provided the initial non-synchronous aerodynamic excitation source. The frequency lock-in phenomenon occurred at a maximum vibration amplitude of 2 % and 3 % tip chord length. The tip unstable flow characteristics were consistent and entirely dominated by blade vibration.

Design of a Shock-Protected Structure for MEMS Gyroscopes over a Full Temperature Range.

Impact is the most important factor affecting the reliability of Micro-Electro-Mechanical System (MEMS) gyroscopes, therefore corresponding reliability design is very essential. This paper proposes a shock-protected structure (SPS) capable of withstanding a full temperature range from -40 °C to 80 °C to enhance the shock resistance of MEMS gyroscopes. Firstly, the shock transfer functions of the gyroscope and the SPS are derived using Single Degree-of-Freedom and Two Degree-of-Freedom models. The U-folded beam stiffness and maximum positive stress are deduced to evaluate the shock resistance of the silicon beam. Subsequently, the frequency responses of acceleration of the gyroscope and the SPS are simulated and analyzed in Matlab utilizing the theoretical models. Simulation results demonstrate that when the first-order natural frequency of the SPS is approximately one-fourth of the gyroscope's resonant frequency, the impact protection effect is best, and the SPS does not affect the original performance of the gyroscope. The acceleration peak of the MEMS gyroscope is reduced by approximately 23.5 dB when equipped with the SPS in comparison to its counterpart without the SPS. The anti-shock capability of the gyroscope with the SPS is enhanced by approximately 13 times over the full-temperature range. After the shock tests under the worst case, the gyroscope without the SPS experiences a beam fracture failure, while the performance of the gyroscope with the SPS remains normal, validating the effectiveness of the SPS in improving the shock reliability of MEMS gyroscopes.

The Utilization of a Damping Structure in the Development of Self-Adaptive Water-Lubricated Stern Bearings

A novel water-lubricated stern bearing damping structure with self-adaptive performance is proposed to meet the load-balancing and vibration-damping requirements of water-lubricated bearings. This innovative damping structure comprises an elastic element and a damping alloy layer. The elastic element facilitates the static and dynamic load sharing of the stern bearing, mitigates the edge effects, ensures even distribution of the contact pressure along the axial direction, and enhances the overall bearing performance. Consequently, it prolongs the service life of the bearing and minimizes friction-induced stimulation. The damping alloy layer effectively attenuates the transmission of shafting vibrations to the foundation through the bearing, optimizing the vibration transmission characteristics. Leveraging the finite element model, an in-depth analysis of the compensation capability of the turning angle and damping performance of the adaptive stern bearing was conducted. The findings reveal that when the thickness of the elastic element is increased from 10 mm to 40 mm, the maximum contact pressure can be reduced by 12.53%. When the length ratio of the elastic element is reduced from 0.7 to 0.4, the maximum contact pressure is reduced by 12.42%. Therefore, increasing the thickness and decreasing the length of the elastic element in the adaptive damping device enhance the load performance, improve the compensation capabilities, and reduce the bearing wear, thereby promoting greater bearing uniformity. Furthermore, the adaptive vibration-damping device optimizes the vibration transmission characteristics from the propeller stimulation to the bearing node. The computational results demonstrate a noteworthy reduction in the speed, acceleration, and displacement responses at the first-order natural frequency, decreasing by 58.82%, 58.90%, and 58.86%, respectively. This substantial reduction in the vibration response at the first-order natural frequency signifies the effective mitigation of vibrations in the system.

Research on the vibration mechanism of compressor complex exhaust pipeline based on transient flow

The periodic exhaust of the compressor often induces gas flow fluctuations within the pipeline, leading to vibrations. Excessive vibration can lead to fatigue, cracks, loosening of components, and resulting in local leakage, which may easily lead to fire, explosion, and secondary hazards. Therefore, in this paper, a computational model for the transient flow field of the compressor exhaust pipeline was established, using the pulse excitation method and Fluent software, the natural frequencies of the gas column in the pipeline were calculated, and the patterns of oscillation decay of the gas column wave propagating back and forth within three exhaust pipes were researched. The mechanism behind the pipeline pressure pulsation and the influence of pipeline structural parameters on the natural frequencies of the gas column were explored. The calculation results show that the first-order natural frequency of the gas column is very close to the double frequency of the compressor excitation frequency at 3.33Hz, and the second-order natural frequency of the gas column is very close to the quadruple frequency of the compressor excitation frequency at 3.33Hz, which may cause significant pipeline vibrations. Altering the pipeline structure, especially when influenced by airflow branching after a tee junction, results in complex changes in the natural frequencies of the gas column. Furthermore, the structural natural frequencies of the pipeline were obtained through the finite element. It has been observed that resonance phenomena exist among the structural natural frequencies and their harmonics of the pipeline and the natural frequencies of the gas column and their harmonics, as well as multiples of the excitation frequency. These results lay the foundation for understanding the vibration mechanism of the pipeline and finding ways to reduce vibration.

Residual stress dynamic detection and vibration characteristics of wire saw busbar

Diamond wire saw cutting is the primary method for processing single crystal silicon carbide (SiC) and silicon (Si) in the photovoltaic and semiconductor industries, the diamond wire saw is formed by busbar electroplate diamond particles, and the diamond wire saw busbar is drawn from steel wires, and the residual stress generated during the drawing process is a critical factor to determine whether the busbar is easy to break. This paper proposes a method to assess residual stress by measuring the free vibration frequency of the busbar, which detects residual stress of busbars with extremely fine and ultra-long (lengths of up to 250 km and diameters as small as 0.04 mm) for real-time, accurate, non-destructive way. First, the residual stress distribution of the drawn busbar is obtained by Abaqus simulation, according to the simulation results, this paper analyzes the mechanical mechanism underlying different types of free bending in the busbar, and develops the relationship between the free bending circle diameter and the residual stresses; Then, the residual stresses are equated with the axial tensile stresses of the busbar by numerical methods, the equivalent mathematical model of the stresses is developed, and the correctness of the model is verified by experiment. Finally, the dynamic model of the moving busbar with residual stresses is established, the effects of different tensions and velocity on the free vibration characteristics of the busbar under residual stresses are analyzed, and the correctness of the detection method is verified by numerical calculations and experimental comparisons. The results show that the residual stress of busbar drawing can be equivalent to tensile force numerically, and the larger the residual stress, the smaller the circle diameter of the busbar, and the larger the first-order natural frequency of free vibration.

Design and Experimental Evaluation of a Dual-Cantilever Piezoelectric Film Sensor with a Broadband Response and High Sensitivity.

Cantilever-beam-type PVDF (Polyvinylidene Fluoride) piezoelectric film sensors are commonly utilized for vibration signal detection due to their simple structures and ease of processing. Traditional cantilevered PVDF piezoelectric film sensors are susceptible to the influence of the second-order vibration mode and have a low lateral stress distribution at the free end, which limit their measurement bandwidth and sensitivity. This study is on the design of a dual-cantilever PVDF piezoelectric film sensor based on the principle of cantilevered piezoelectric film sensors. The results of the experiments indicate that, compared to a typical single-arm piezoelectric cantilever beam vibration sensor, the developed sensor has a longer second-order natural frequency that ranges from 112 Hz to 453 Hz, while the first-order natural frequency is maintained at around 12 Hz. This leads to a better ratio of the second-order natural frequency to the first-order natural frequency and a wider frequency response range. At the same time, the sensitivity is increased by a factor of 3.48.

Wind-Induced Vibrations and Gust Response Factors of the Cabin–Cable–Tower System

A large-scale radio astronomical telescope is a typical complex coupled system, consisting of a feed cabin, cables, and supporting structures. The system is extremely sensitive to wind loads, especially the feed cabin, which has high requirements for vibration displacement during operation, and excessive vibration may affect normal operation. To investigate the wind-induced vibration characteristics of such coupled systems, this study takes the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) as an example to conduct research. First, a refined finite element model of FAST is established, and a dynamic analysis using simulated random wind loads is conducted. The influence of the cable boundary on the time–frequency domain responses of the feed cabin is particularly considered. Then, the gust response factor (GRF) for different structural components within the coupled system is calculated. Finally, the evolution law of the GRF under various wind speeds and directions is revealed by parametric analysis. The parameter analysis only considers the wind directions ranging from 0° to 60°, because FAST is a symmetric structure. The results indicate that obvious differences are observed in both the rotational and translational displacements of the feed cabin under northward wind, especially the results along the east–west axis. When the supporting towers are considered, there is no change in the power spectral density (PSD) of the feed cabin in the low-frequency range. However, in the high-frequency range, taking the supporting towers into account leads to an increase in PSD and a resonance near the first-order natural frequency of the supporting tower. The GRF based on the dynamic response exhibits substantial deviations compared to those obtained from design codes, highlighting the need for an independent analysis when determining GRF for such coupled systems.