Order Of Natural Frequency Research Articles

Free vibration properties of beetle elytron plate: Composite material, stacked structure and boundary conditions

Beetle elytron plate (BEP), which is derived from the bionics of Trypoxylus dichotomus's elytra, is a typical lightweight and high-strength structure with superior and comprehensive mechanical properties. To promote the engineering application of BEPs, this paper explores the vibration characteristics of foam-filled fiber composite BEPs. Through the finite element method (FEM), structural parameters such as the length-to-width ratio, core height-to-thickness ratio, skin thickness and foam density influence the natural frequency and mode. Furthermore, the influence pattern of parameters (such as boundary conditions and the number of stacked layers) toward the first two orders of natural frequencies and modes of the BEP were investigated under controlled total height and controlled single layer height. The results indicate that 1) the ranking of structural parameters on the 1st order frequency from a strong to weak sequence is as follows: length-to-width ratio, core height-to-thickness ratio, foam density and skin thickness; for the 2nd order natural frequency: length-to-width ratio, skin thickness, foam density and core height-to-thickness ratio. 2) Generally, an increase in the length-to-width ratio will reduce the frequency of the BEP, and increases in the core height-to-thickness ratio and skin thickness will raise its frequency. Additionally, foam filling plays a decisive role in local deformation. 3) When the total height of the sandwich plate is controlled, the improvement of the boundary conditions can effectively boost its 2nd-order frequency (approximately 200%), but the 1st-order frequency can be significantly increased (approximately 140%) only when all four sides are improved. 4) In the case of controlling the height of the single layer of the sandwich plate, its frequency gradually increases with the increase in the number of stacked layers. However, when the constraints are weak or there are few stacked layers, increasing the number of stacked layers can effectively boost the vibration frequency. This paper provides references and suggestions for the design and application of sandwich structures, enriching the research on the mechanical properties of BEPs and establishing groundwork for promoting BEPs in engineering practices.

Bionics structural modification and collaborative optimization design of a waste crossbeam based on an RBF neural network and NSGA-II

ABSTRACT In this work, a bionic structure was redesigned for a specific type of crossbeam and the corresponding modification strategies were formulated. Three modification schemes were put forward and the corresponding parameterized analysis models established. Sensitivity analysis results guided the variable parameter selection and the total design of an orthogonal test. Data obtained were utilized to establish a neural network model that reflects the dynamic nonlinear mapping relation. Then, a collaborative optimization design method was proposed that was based on the neural network and the genetic algorithm for secondary design of the rib thickness. Through optimizing the neural network model by NSGA-II, Pareto optimal results were obtained. The results showed that the mass of the newly designed crossbeam had been reduced by 3.74%, while the first three orders of natural frequency had been increased by 6.67%, 3.47% and 14.20%, respectively. The bionic modification structure and the collaborative optimization design method were proved to be valuable for redesign in the remanufacturing field.

An experimental study of the centrifugal hardening effect on rotating cantilever beams

As one of the most important dynamic characteristic of the widely-used rotating cantilever beams, the centrifugal hardening effect has been extensively studied through theoretical and Finite Element Method (FEM) modeling, but rarely through operational experiments due to the lack of proper measurement techniques. As a result, the previous studies have not been verified convincingly. With the help of Digital Image Correlation and the newly proposed Phase Mapping Method, direct measurements under operational conditions were carried out on three rotating blade-like cantilever beams under 20 different rotating speeds (0–16.25 rps). With the abundant data, full-field displacement responses of the beams were presented and several orders of natural frequencies under different speeds were obtained and compared to results from simulations based on a typical theoretical model and a FEM model. The test results show centrifugal hardening behaviors of different cantilever beams on the flap-wise direction in detail and proved the applied models to be accurate in the prediction of frequency hardening with an average error of 0.401 Hz for the theoretical model or 0.404 Hz for the FEM model. In addition, the mode shapes with dense measurement points (up to 168 points on one beam) are presented and found to be coincided with the result from simulation.

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.

Design Optimization of the Driving Shaft of a Hammer Feed Grinder Base on the Response Surface Method

Abstract. Taking the driving shaft of a hammer feed grinder rotor system as the research object, the static calculation and modal analysis were carried out by ANSYS Workbench software. The results show that under actual working conditions, the maximum deformation of the driving shaft is 0.437 mm, which occurs at the end of the pulley-mounted shaft section. The maximum stress on the driving shaft is 210.91 MPa, and the stress is mainly concentrated on the shoulder of the left shaft section matched with the bearing. The stress values at most other positions on the driving shaft are below 23.435 MPa. The first-order natural frequency of the driving shaft is 504.98 Hz, and the first six orders of natural frequencies are much higher than the excitation frequency of the hammer feed grinder (58.33 Hz). The driving shaft has small deformation and good dynamic performance, but there is a problem of local stress concentration. Therefore, the response surface method was used to optimize the parameters of the driving shaft. The diameter and length of the pulley-mounted shaft section on the driving shaft were selected as design variables, and the maximum stress value was taken as the optimization target. After the optimization, the diameter and length of the pulley-mounted shaft section are reduced from 30 to 28 mm and from 199 to 170 mm, respectively, and the maximum stress value on the driving shaft is reduced from 210.91 to 174.41 MPa. Finally, static calculation and modal analysis were performed on the driving shaft after the parameter optimization. The results demonstrate that both the strength and stiffness of the driving shaft are sufficient, and it does not cause resonance in the working process, indicating the successful optimization of the driving shaft parameters. Keywords: ANSYS Workbench, Grinder driving shaft, Model analysis, Parameter optimization, Response surface method, Static calculation.

Effect of the Aero-Engine Mounting Stiffness on the Whole Engine Coupling Vibration

A finite element (FE) model of the rotor tester of an aero-engine, having a thin-walled casing structure, mounted with the way of an actual engine, is developed to simulate the intrinsic vibration characteristics under actual engine-mounting condition. First, a modal experiment of the rotor tester for the whole aero-engine is conducted, and the FE model is modified and validated based on the modal experimental results. Second, the first three orders of natural frequencies and the modal shapes are evaluated using the modified FE model under three different types of mounting stiffness, namely, a fixed mounting boundary, a free mounting boundary, and a flexible mounting boundary. Subsequently, the influences of the mounting stiffness on the coupling vibration of the rotor and stator are studied via a new rotor–stator coupling factor, which is proposed in this study. The results show that the higher the rotor–stator coupling degree of the modal shape, the greater the influence of the mounting condition on the modal shape. Moreover, the influence of the mounting stiffness on the rotor–stator coupling degree is nonlinear. The coupling phenomena of the rotor and stator exist in many modal shapes of actual large turbofan engines, and the effect of mounting stiffness on the rotor–stator coupling cannot be ignored. Hence, the mounting stiffness needs to be considered carefully while modeling the whole aero-engine and simulating the dynamic characteristics of the whole aero-engine.

Design and Analysis of a Kind of Centralized Forced Flip-Flow Screen

During the dry screening, the hole plugging is a serious problem for most traditional screening equipment sieving the moist fine coal. It would lead to the low preparation efficiency and the low screening efficiency. The flip-flow screen is a new kind of screening equipment by using flip-flow motion of elastic screen surfaces to implement the separation of material. With the remarkable advantages of the extraordinary vibration intensity of screen surface, the hole is difficult to be plugged, and the screening efficiency is improved. In this paper, a kind of centralized forced flip-flow screen (CFFS) was proposed based on the crank rocker mechanism. The flip-flow motion of elastic screen surfaces is achieved by the periodical reversed motion of inner and outer screen boxes driven by crank. The advantages of the CFFS include considerable deformation of the screen surface, stable flip-flow quantity, low working noise, low vibration influence on environment, etc. The principle and construction of the CFFS were introduced, and the modal analysis and harmonic response analysis of key components (the crank and the linkage) were implemented based on finite element method (FEM), respectively. The first six orders of natural frequency and vibration modes were obtained. The maximum equivalent stress and strain under working and resonance frequency were achieved. The results illustrate that the resonance frequency is much higher than the working frequency, and the stress and strain are all within the safe limit of the material. The prototype was manufactured, and the sieving experiment demonstrates that the CFFS perform steadily, and screening efficiency is over 80%. The new feasible method of the dry screening was proposed by the CFFS. The corresponding numerical simulation and the experiment provided a reliable basis for the future promotion of similar product design and research.

Basic dynamic characteristics and seismic design of anchorage system

Based on some assumptions, the dynamic governing equation of anchorage system is established. The calculation formula of natural frequency and the corresponding vibration mode are deduced. Besides, the feasibility of the theoretical method is verified by using a specific example combined with other methods. It is found that the low-order natural frequency corresponds to the first mode of vibration, and the high-order natural frequency corresponds to the second mode of vibration, while the third mode happens only when the physical and mechanical parameters of anchorage system meet certain conditions. With the increasing of the order of natural frequency, the influence on the dynamic mechanical response of anchorage system decreases gradually. Additionally, a calculating method, which can find the dangerous area of anchorage engineering in different construction sites and avoid the unreasonable design of anchor that may cause resonance, is proposed to meet the seismic precautionary requirements. This method is verified to be feasible and effective by being applied to an actual project. The study of basic dynamic features of anchorage system can provide a theoretical guidance for anchor seismic design and fast evaluation of anchor design scheme.

Wind Turbine Gearbox Transmission Chain Forced Vibration Analysis Exerted by Random Actuator

The reason for the gearbox high failure rate is mainly its poor working environment, especially the vibration due to random actuator. Consequently, its necessary to study the gearbox vibration characteristics under random actuators to prevent from serious damage caused by a resonance. In order to follow the actual working condition, random input speed and random torque actuators are inputted with power spectrum density method (PSD). 64 orders of natural frequencies, displacement frequency response and modal participation factor are obtained after computation and simulation. The analysis results indicate transmission system resonance occurs likely. In addition, displacement vibration responses of planet gears and high speed shaft are the largest, which are the easiest to cause vibration fatigue damage. Keywords: wind turbine gearbox, transmission chain, vibration analysis, random actuator

A layer-wise analysis for free vibration of thick composite cylindrical shells

A semi-analytical, three-dimensional, layer-wise theory is proposed, to solve for various orders of natural frequencies, and mode shapes of thick, arbitrarily laminated, composite cylindrical panels with three-dimensional boundary conditions at the four edges being any combination of free, simply supported, clamped and guided, for each layer. The displacement field is modelled by finite element interpolation shape functions along the thickness direction and by beam functions in the two in-plane directions. Numerical results from the present work are compared with those from first order transverse shear deformation theory (FSDT) and higher order shear deformation theory (HSDT). Results indicate that the present method predicts the frequencies more accurately than either FSDT or HSDT. The present study represents a significant improvement in the capability for modelling complex three-dimensional boundary conditions.