First-order Modal Frequency Research Articles

Multi-objective optimization of structural parameters for the monorail sled connecting plate

Abstract Addressing the multi-objective optimization of structural parameters for the monorail sled connecting plate, the static strength and modal characteristics were computed using the finite element method. The optimization objectives were set to minimize the total mass of the structure, reduce maximum equivalent stress, and maximize the first-order modal frequency. A proxy model for the finite element analysis and calculation of connecting plates was constructed based on a BP neural network, and the trained model exhibits strong predictive capabilities. During the optimization process, an improved MOPSO is introduced, merging the external archive maintenance strategy from CDMOPSO with the dynamic mutation strategy from ASMOPSO. The Pareto solution set produced by this refined MOPSO exhibits a lower IGD value. A mathematical model for multi-objective optimization of connecting plate structural parameters was established, and the Pareto solution set was calculated. Compared to the initial structure, the optimized one showed a reduction of 8.41% in overall mass, a decrease of 40.47% in maximum equivalent stress, and an increase of 34.29% in the first-order modal frequency, thereby verifying the optimization algorithm’s feasibility.

Modal Analysis and Optimization of Fluid-Structure Coupling for Rotor and Inner Cylinder of Vertical Condensate Pump

Background: Low-frequency resonance is one of the common issues encountered during the variable-frequency operation of condensate water pumps. There have been numerous patents and papers proposing solutions to address the low-frequency resonance problem in condensate water pumps. However, the solutions for resonance problems often need to be tailored to specific circumstances. Methods: Based on the acoustic method, the dynamic model of the rotor and inner cylinder of Jiangsu Guohua Chenjiagang Power Plant 2B condensate pump is established to compare the difference between dry modal and fluid-structure coupling modal, the influence of perpendicularity, concentricity and bearing wear on the natural frequency of rotor is studied. Results: The rotor is rigid under normal conditions. When the bearing is worn, the frequency of the rotor will be greatly reduced and may fall into the frequency conversion operation range to excite resonance. The deviation of perpendicularity and concentricity will not directly lead to the decrease of rotor modal but will lead to the increase of bearing stress, aggravate bearing wear, and then affect the rotor modal. As the inner cylinder only relies on the fixed support at the top, the structure stiffness is low, which may lead to low-frequency resonance. By adding two support structures at the guide vane, the first-order modal frequency of the inner cylinder can be increased from 3.29 Hz to 28.88 Hz, effectively avoiding the operating frequency range of the system. Conclusion: This study can guide the optimization of similar pump structures.

Horizontal shaking table tests on a four-story prototype structure using multi-dimensional earthquake isolation and mitigation devices

Three-dimensional isolation system (3DIS) has been increasingly applied to civil structures with small height-width ratios, but is rarely employed in the multistory and high-rise buildings due to the lack of efficient control strategy for the rocking effect. In this paper, a simplified analysis model of 3DIS was established firstly to bring insights into the coupled motion mode caused by the rocking effect, and the influence of damping ratio and height-width ratio on the modal frequency was revealed. Then, aimed at weakening rocking motion and improving the seismic isolation efficiency, a novel multi-dimensional earthquake isolation and mitigation device (MEIMD) was proposed, and both the design composition and design principle were given in detail. To validate the effectiveness of MEIMDs, a full-scale four-story frame with a height of 13.05 m and a weight of 70 tons was produced for horizontal shaking table tests. The experimental results indicated that after adopting MEIMDs, the first-order modal frequency was 1.7 Hz, with 68% decrease compared with that of the prototype structure, and the first-order modal damping ratio was above 0.23, about eight times that of the prototype structure. Moreover, the horizontal peak acceleration was significantly decreased for each floor with a maximum reduction of 49%, while the maximum horizontal displacement and rocking response were obviously lower than the limit value specified by building codes. Therefore, the MEIMDs can not only efficiently isolate the earthquake energy, but also ensure the sufficient dynamic stability of the system. This study sheds light on the real coupled horizontal-rocking response of the base isolation system with MEIMDs, and can promote the development and application of 3DIS in multistory and high-rise buildings.

A Frequency Identification Approach for Damaged Heavy-Haul Railway Bridge with Bogie Accelerations

Bridge structural health monitoring (BSHM) is extensively employed to assess whether bridge damage exceeds maintenance limits and helps maintenance decision-making. Frequency identification is an essential part of BSHM, which utilizes the first-order modal frequency as an evaluation indicator of bridge health status. This paper proposes a method for bridge damage identification based on extracting the first-order modal frequency of the bridge from dynamic responses of vehicle bogies. Firstly, the feasibility of extracting bridge modal frequency from bogie accelerations is theoretically deduced via a vehicle–bridge interaction model. The result indicates that the bogie accelerations encompass three frequency components, namely vehicle driving frequency, vehicle pitching frequency and bridge first-order modal frequency. Then, a multi-domain conjoint analysis method incorporating the time domain, frequency domain and time–frequency domain is proposed to extract the first-order frequency of damaged bridge from bogie accelerations. By defining a damage sensitivity index of the sliding window, the time-domain sensitive boundaries of bogie acceleration to bridge damage are pinpointed. Leveraging prior knowledge of the bridge modal frequency range, the frequency-domain sensitive boundaries bogie acceleration to bridge frequency are determined. On this basis, the sensitive region of bogie acceleration to bridge frequency can be precisely localized in the Hilbert Huang transform spectrum, ultimately identifying bridge frequency through searching local maximum instantaneous energy points within this region. Finally, comprehensive experiments, considering different vehicle speeds and track spectra scenarios, are carried out to investigate the effectiveness and robustness of the proposed method. The results affirm the performance of the method to accurately identify the first-order modal frequency of the damaged bridge, further underscoring the promising prospect of on-board BSHM.

Anti-vibration Design of the Civil Aircraft’s Horizontal Tail Trailing Edge Compartment

The horizontal tail trailing edge compartment is a vital component of civil aircraft, situated between the horizontal tail beam and elevator. Its primary function is to connect the elevator and meet the aerodynamic sealing requirements of the unflapped elevator, and to transfer the aerodynamic and inertial load of the elevator to the outboard wing box of the horizontal tail in concentrated form. Under aerodynamic or other excitation, the horizontal tail trailing edge compartment may experience vibration, increasing the risk of structural damage. This study aims to enhance the anti-vibration capability of the horizontal tail trailing edge compartment via parametric finite element analysis. This analysis examines various design elements of the horizontal tail end cabin and compares the first-order modal frequency to deduce the influence of factors on the stiffness. The results provide a reference for the anti-vibration design of the horizontal tail trailing edge compartment in civil aircraft.

Research on Scheme Design and Structure Optimization of High Speed and High Precision Vehicle Contour Detection Platform

To improve road traffic safety and reduce the incidence of unauthorized vehicle modifications, overloading, and oversizing, this study proposed a detection platform structure to support the quick measurement of key dimensions and high-precision reconstruction of local features using the automotive contour size system. Using CAE technology, static and dynamic characteristic analysis was performed on the platform structure, and optimization design was conducted on the column frame and gantry frame separately. The optimized column frame's first-order modal frequency increased by 243% from 5.16 Hz to 17.65 Hz, with an average optimization ratio of 187% for the first six modal frequencies. For the optimized gantry frame, the average optimization ratio of the key node displacement exceeded 46%, with the first-order modal frequency increasing by 13% from 36.43 Hz to 41.33 Hz, and an average optimization ratio of 21% for the first six modal frequencies. Ultimately, the optimized detection platform's key nodes achieved an average optimization ratio of nearly 60%, with the first-order modal frequency increasing by 240% from 5.16 Hz to 17.57 Hz and an average optimization ratio of 185% for the first six modal frequencies. The optimized platform structure provides robust support for the high-speed and high-precision vehicle contour detection system's implementation.

Study on dynamic characteristics and wide temperature range modification of elastic pad of high-speed railway fastener

The operation line of China’s high-speed railway has exceeded 40,000 km. The performance decay and even failure to some fastener systems could be caused by complex terrain (mountain and plain), variable environment (−50 °C to 50 °C), high speed (300–350 km/h) and high frequency (500–700 Hz). Herein, the W300-1 fastener is taken as the research object to test and conclude the service performance and online track modal recognition. The comprehensive test system is used to obtain the dynamic characteristics of fasteners with the preload under the temperature-dependent (−70 °C to 50 °C) and frequency-dependent (10–1250 Hz) coupling conditions. It is found that the elastic pad stiffness in fastener system is sensitive to the low temperature and high frequency. In order to study the influences of temperature- and frequency-dependent dynamic characteristics of fasteners on track system, the dynamics analysis model of track system is constructed. The rail receptance curve under constant working condition is verified by the online track recognition. Simultaneously, the dynamic characteristics of the rail under constant working condition (4 Hz) and temperature-/frequency-dependent conditions are contrastively analyzed. The results indicate that the frequency-dependent characteristics of elastic pad enable the first-order modal frequency to shift toward a higher frequency, accompanied by the amplitude increase. The temperature-dependent characteristics of elastic pad make the medium- and high-frequency decay rate of rail wider but smaller. Due to the adverse effects of above conclusions, the polymer materials of elastic pad in fastener system are modified and optimized from two perspectives of polyol type and crosslinking agent type. Based on the standard requirements of Q/CR7-2014, it is certain that the dynamic performances of PUEP samples prepared by PTMG1000 and NDI together can meet the requirements of safety and stability of high-speed railway.

Research on the Reliability of a Core Control Unit of Highway Electromechanical Equipment Based on Virtual Sensor Data.

The printed circuit board (PCB) is the core control unit of electromechanical equipment. In order to determine the influence of the coupling vibration caused by vehicle–road interaction on the PCB reliability of roadside electromechanical equipment, first, the dynamic load of the vehicle tire is solved by establishing the dynamic model of a vehicle road. Then, the acceleration response data generated by road vibration are obtained by solving the road finite element model. Finally, the power density spectrum of the acceleration response is taken as input excitation, and the deformation response of the PCB under vehicle–road coupling vibration is analyzed. The experimental results show that when the vehicle is driving close to the roadside, the vibration caused by vehicle–road coupling will lead to a large deformation of the PCB, and the deformation value reaches 0.170 mm, which can cause structural damage to the PCB. This shows that the vehicle–road coupling vibration can affect the reliability of the roadside electromechanical equipment; thus, the optimal design of the PCB layout is created. After optimization, the first-order modal frequency of the PCB is increase by 5.4%, which reduces the risk of the components breaking away from the PCB substrate.

Bayesian Regularization Algorithm Based Recurrent Neural Network Method and NSGA-II for the Optimal Design of the Reflector

The optical-mechanical system of a space camera is composed of several complex components, and the effects of several factors (weight, gravity, modal frequency, temperature, etc.) on its system performance need to be considered during ground tests, launch, and in-orbit operation. In order to meet the system specifications of the optical camera system, the dimensional parameters of the optical camera structure need to be optimized. There is a highly nonlinear functional relationship between the dimensional parameters of the optical machine structure and the design indexes. The traditional method takes a significant amount of time for finite element calculation and is less efficient. In order to improve the optimization efficiency, a recurrent neural network prediction model based on the Bayesian regularization algorithm is proposed in this paper, and the NSGA-II is used to globally optimize multiple prediction objectives of the prediction model. The reflector of the space camera is used as an example to predict the weight, first-order modal frequency, and gravitational mirror deformation root mean square of the reflector, and to complete the lightweight design. The results show that the prediction model established by BR-RNN-NSGA-II offers high prediction accuracy for the design indexes of the reflector, which all reach over 99.6%, and BR-RNN-NSGA-II can complete the multi-objective optimization search efficiently and accurately. This paper provides a new idea of optimization of optical machine structure, which enriches the theory of complex structure design.

Optimization of Optical Machine Structure by Backpropagation Neural Network Based on Particle Swarm Optimization and Bayesian Regularization Algorithms.

Fit of the highly nonlinear functional relationship between input variables and output response is important and challenging for the optical machine structure optimization design process. The backpropagation neural network method based on particle swarm optimization and Bayesian regularization algorithms (called BMPB) is proposed to solve this problem. A prediction model of the mass and first-order modal frequency of the supporting structure is developed using the supporting structure as an example. The first-order modal frequency is used as the constraint condition to optimize the lightweight design of the supporting structure’s mass. Results show that the prediction model has more than 99% accuracy in predicting the mass and the first-order modal frequency of the supporting structure, and converges quickly in the supporting structure’s mass-optimization process. The supporting structure results demonstrate the advantages of the method proposed in the article in terms of high accuracy and efficiency. The study in this paper provides an effective method for the optimized design of optical machine structures.

Multi-objective optimization of CFRP engine hood considering dynamic performance based on surrogate model

This paper uses a steel engine hood as a prototype to design a carbon fiber reinforced plastic (CFRP) engine hood, analyzes the dynamic performance of the engine hood and optimizes the dynamic stiffness index while considering lightweight of the structure. Taking the layer thickness of each ply orientation of the CFRP engine hood as the design variable, the optimal Latin hypercube design (Opt-LHD) method is applied for uniform sampling. Moreover, the Kriging model method and response surface model (RSM) method are used to construct the surrogate model of the total mass, equivalent dynamic stiffness of critical points, and the first-order modal frequency. Then the Non-dominated Sorting Genetic Algorithm NSGA-II is used for multi-objective optimization with the equivalent dynamic stiffness and mass of the CFRP engine hood as the optimization objective. Finally, the optimized CFRP engine hood was trial-produced and compared with the original steel engine hood. The results indicate that the optimized CFRP engine hood has better dynamic stiffness performance; furthermore, the lightweight effect reaches 24.4 %.

Structural multi-objective optimization on a MUAV-based pan–tilt for aerial remote sensing applications

To realize both mechatronic properties of light mass and high control precision for a pan–tilt based on the multirotor unmanned aerial vehicle (MUAV) for aerial remote sensing applications, a structural multi-objective optimization approach based on the approximate model and genetic algorithm is proposed. The optimized structural parameters for establishing the approximate model are determined through the sensitivity analysis method, by which the predominant variables affecting mass and modal are selected. The approximate models on mass and first-order modal frequency are built through response surface methodology (RSM) and radial basis function (RBF) to heighten the optimization efficiency and smooth the numerical optimization results. Particularly, the non-dominated sorting genetic algorithm-II (NSGA-II) and Pareto Optimality are combined to acquire the parameters’ optimal solutions. The modal tests based on hammering method and the control experiments are both conducted to validate the performance of the proposed approach. The results indicate that the structural multi-objective optimization approach presented in this paper is effective to reduce the mass meanwhile enhance its first-order modal frequency, hence leading to good stabilizing and tracking performances.

Optimization of Servo Parameters for Enhanced Dynamic Behavior of Direct Feed System with Hybrid FEM and PLS Regression

Optimal servo dynamics of a direct feed system driven by linear motor play an important role in improvement of its dynamic behavior and the precision of its processing products. An optimization method for enhancement of the dynamics of the drive system is proposed with hybrid FEM and PLS regression. Dynamic stiffness spectrogram of the servo system, also as optimization performance evaluation, is applied to obtain its resonance frequency. A force pulse excitation-based dynamic stiffness measurement scheme is introduced to acquire the spectrum diagram. For simulation of the stiffness characteristic, a FE model of the drive mechanism is developed with dynamic conjunctions, which parameters are considered to be related to the servo parameters. A relationship model between the stiffness variables of the conjunctions and the servo parameters is established with PLS regression. Based on the regression equation, the optimization model is constructed for the dynamics enhancement. To validate the feasibility of the scheme, an experiment was conducted on a domestic test rig. The results show that the method can effectively extend non-resonant frequency and improve the dynamics with 10.4 Hz higher in first-order modal frequency and 6.7 Hz higher in second-order than the corresponding results of the samples in the mean value from random tests.

Effect of cutter body geometry in Ti-6Al-4V face-milling process

Tool geometry has a direct impact on workpiece deformation, cutting forces, and tool wear, thereby affecting machinability, surface quality, and tool life. However, the research about the effect of cutter body geometry on cutting performance has rarely been reported. In this paper, the performance of the same series of indexable face-milling cutters with different diameters was investigated. The dynamic characteristic analysis results show that the cutter with diameter of 80 mm is the least susceptible to resonance due to the highest first-order modal frequency of 13,201 Hz. The cutter body geometry has a significant impact on mode shapes. The cutting performance tests show that the milling cutter with a diameter of 125 mm performs the best in terms of static force and maximum dynamic force in the Z direction and wear resistance. In view of the overall situation, the machined surface quality of the cutter with a diameter of 40 mm is the worst, whose abnormalities can be attributed to the vibration caused by the change of cutting depth and the formation and abscission of built-up edge. By the analysis of geometric structure, the center offset and the installation angle of indexable insert, together with the outline dimensions of the cutter body, jointly determine the tool cutting performance. The present work will provide guidance for the design of indexable milling cutters for high-performance machining of titanium alloys.

Modeling and simulation for low-frequency vibration energy harvesting based on piezoelectric unimorph cantilever beam

In order to solve the problem of sustainable energy supply for low-power electronic products used in low-frequency vibration environment, the mathematic model was established based on the theory of piezoelectricity and Euler-Bernoulli beam. Also, the effects of different parameters of PZT unimorph beams such as the length, width, and tip mass on generating capacity were studied by FEM. The results show that the energy harvester with PZT unimorph beam and tip mass is suitable for low-frequency vibration environment. Increasing the length or reducing the width of the beam can significantly lower the first-order modal frequency of energy harvester when other conditions remain the same. Within certain range, the first-order modal frequency of the beam also gradually reduced as the tip mass increasing. When the size of the PZT unimorph beam is 60x60x0.33mm, the tip mass is 8.92g and an exciting force of 0.01N is applied to it along z axis, an output of 8.1V can be obtained. Meanwhile, the PZT unimorph beam is under the first vibration mode and the resonant frequency is 16.296Hz.

FBAR-on-diaphragm type electro-acoustic resonant micro-accelerometer: a theoretical study

We presented a theoretical study of the performance of a novel FBAR-on-diaphragm sensor-head structure for the FBAR-based electro-acoustic resonant micro-accelerometer. This structure overcomes disadvantages in the FBAR-beam structure for its limited cantilever beam thickness, and deficiencies in the embedded-FBAR structure for its complex micro-fabrication process. Its elastic diaphragm is made of silicon dioxide (SiO2)/silicon nitride (Si3N4) bilayer film, which is not only more susceptible to the IC compatible integration process for the Si-based microstructure and the FBAR, but also improves sensitivity and temperature stability of the BAW accelerometer. FBAR-on-diaphragm type BAW accelerometer integrates the acceleration sensing structure, i.e., the SiO2/Si3N4 bilayer diaphragm and the Si proof-mass, with the AlN FBAR electro-acoustic transducer. Preliminary performance analysis on FBAR-on-diaphragm type BAW accelerometer suggests that the FBAR-on-diaphragm structure is feasible. We obtained modal frequencies of the FBAR-on-diaphragm structure and stress distribution of the diaphragm under 0---100 g acceleration loads through the finite element modal analysis and static simulation, Applying the calculated maximum stress to the piezoelectric film in FBAR for qualitative analysis, and combining the dependency of elastic coefficient on stress in the Wurtzite AlN film calculated with the first-principle method, we roughly predicted the maximum elastic coefficient variation in the Wurtzite AlN film under different acceleration load. With the help of the RF simulation software ADS, we changed the longitudinal wave velocity corresponding to the elastic constants with variant acceleration loads. By comparing the resulted resonant frequencies of the sensor head without and with different acceleration loads, we qualitatively characterized its frequency shift and sensitivity. In our study, we gave further analysis of the simulation results. It reveals that the first-order modal frequency of the SiO2/Si3N4 circular diaphragm is quite far away from the higher ones, which means less cross modal coupling. It also reveals that under the acceleration load, its resonant frequency with a quite linear acceleration---frequency shift characteristic will up-shift with the sensitivity of several KHz/g.

Fatigue Crack Mechanism Research on High Speed Train Equipment Cabin Frame

As the load bearing structure, the equipment cabin frames connecting the bottom plates and apron plates are acted on the aerodynamic load and vibration load, which appear the fatigue cracks in service. The crack macro analysis of the frame fracture section and the life mileage statistics of the frames are demonstrated. On the basis of the online pressure test of the equipment cabin on the passenger dedicated railway lines, the inside and outside aerodynamic pressure and differential pressure of the equipment cabin bottom plates and apron plates are executed and analyzed under the conditions of trains running or passing each other in the open air or in the tunnel. The equivalent stress and the first-order frequency of the crack position are gained by the on track dynamic stress test. The first-order modal frequency in the vertical and horizontal direction of the frames is tested using the pulse excitation method. The results show that the exciting frequency from the bottom plate or apron plate aerodynamic differential pressure is mixed with the frame natural frequency and the resonance of the frame happens, which induces the high dynamic stress amplitude. This idea is helpful to improve the equipment cabin frame design and ensure the high speed train running in safety.

Vibro-acoustic analysis and optimization of damping structure with Response Surface Method

In order to reduce sound radiation, the effective ways are to modify the dimension and shape of structure, or cover the damping material. However, these methods base on the knowledge of qualitative and quantitative relationship between sound radiation and design parameters. It is very difficult to get this kind of function because of highly non-linear and complicated properties of vibro-acoustic problems. Therefore, in order to decrease the complexity of the analysis and reduce cost, approximate method is an effective method. In this study, Response Surface Method (RSM) is utilized to analysis and optimize the vibro-acoustic properties of the damping structure. A simple case was illustrated to demonstrate the capabilities of the developed procedure. In details, a structure-born noise problem is approximated by a series of polynomials using RSM. Three main performances are considered, i.e. sound radiation power, first-order modal frequency and system loss factor. In this way, the analysis and optimization of vibro-acoustic problems can be obtained conveniently and effectively.