Minimum Natural Frequency Research Articles

Structural Dynamics Analysis of 3-U CubeSat

The development of CubeSats has been advanced significantly during the past two decades for both scientific research and industrial purposes. During the manufacturing process, every CubeSat must satisfy various system requirements in which the structural analysis is one of the most vital necessity in order to assure a normal operation of the CubeSat during its working time in space. In the conceptual design phase, structural dynamics is a mandatory step to determine the natural frequencies of individual bodies, the deformation and stress induced at the corresponding vibration modes to prevent structural failure. In this work, IGOSat, a 3-Unit CubeSat, which was developed at the Paris Diderot University is exanimated in term of modal, harmonic response, and random vibration analysis at the time of ground testing as well as the launching phase using ANSYS software. These numerical simulations conducted according to the CubeSat Design Specification and the system requirements of QB50 project. The minimum natural frequency of the CubSat obtained to be 363.17 (Hz), which passed the required frequency of 90 (Hz). Moreover, the Harmonic and Random vibration analyses indicate that the peak response of normal stress, as well as deformation values obtained, are far lesser compared to the yield strength of the frame structure and subsystem materials. Hence, our numerical analysis found that the CubeSat remains intact during the launch environment.

Experimental study on the natural frequency of tunable piezoelectric cantilever plate

PEH (piezoelectric energy harvester) outputs a higher voltage when the natural frequency matches ambient vibration frequency. How to widen working frequency band is a hot issue in study of PEH. In this paper, an auto-tuning PEH is presented by attaching a box to each corner of its free sides and a ball is placed in each box. Change of the balls position makes natural frequency of PEH variable, which expands working bandwidth of the device to accommodate complex ambient vibration. Fixing the equipment on experimental platform by designing fixture, hammering experiments are carried out to measure natural frequency of the structure when balls are in different positions. It is found that the maximum and minimum natural frequencies exist in the auto-tuning PEH, which form a resonance bandwidth. Moreover, there are multiple position combinations of two balls at the same natural frequency in the range of resonance bandwidth. Fixed the apparatus on exciter by the fixture, and a constant excitation frequency is selected in the bandwidth to perform auto-tuning experiments on the instrument. It is observed that location of balls is automatically changed to make natural frequency of the system coincide with the excitation, and the law of variation in balls position is obtained. The converter is subjected to sweeping experiments through an exciter and an oscilloscope. Using voltage-frequency diagrams, it is shown that the auto-tuning PEH outputs a higher voltage and its frequency band is wider when the ball rolls freely compared to two cases where balls are fixed.

Optimization of concrete cable-stayed bridges under seismic action

A computational tool is presented for the optimum design of concrete cable-stayed bridges under seismic action. The finite element method is used for the three-dimensional analysis of the structure under dead and live loads, time-dependent effects and geometrical nonlinearities are considered. The dynamic analysis is solved by the modal/spectral approach. The design problem is posed as a multi-criteria optimization. The design variables are the cable forces and the cross-sectional dimensions of cables, deck and towers. Design objectives of minimum cost, deflections, natural frequencies and stresses considering both, serviceability and ultimate limit states are considered. Given that a gradient-based algorithm is applied for the optimization the discrete direct method is used for sensitivity analysis. An entropy-based algorithm finds economically and structurally efficient solutions by rearranging the stiffness and mass distribution to enhance the structural response. Numerical examples illustrate the features of the proposed computational tool.

An Application of Genetic programming for Lithium-ion Battery Pack Enclosure Design: Modelling of Mass, Minimum Natural Frequency and Maximum Deformation Case

For ensuring the safety of battery pack and its enclosure, the mechanical design is crucial for generating lower deformation, lower stresses and vibrations during its actual operation. In addition, the minimum mass of battery pack is needed for lower energy consumption of pack. Therefore, the problem to be solved can be formulated as multi-objective optimization and much desire one for electric vehicle industry application. In this paper, the application of evolutionary approach of Genetic programming (GP) is illustrated for battery pack casing design considering the design requirements having higher mechanical performance. Data generated from finite element simulation was used as input in GP. The analysis concluded that the GP perform satisfactorily. GP models for three design outputs predicted the values in compare to actual values with errors RMSE and MAPE of .00154 and .00715, .000033 and 1.16, .52 and .48, respectively. These results can be used to design the battery pack enclosures. The similar models can be applied to different independent parameters to find out the possible relation in between them to correlate the results, find out the criticality of the individual parameter and then optimize the design accordingly.

딸기 고설 재배 베드에서 양액 코코피트 분쇄를 위한 미니 로터리 장치의 개발 및 설계에 관한 연구

In the agriculture of strawberry cultivation, it is necessary to loosening and breaking up of the intertwined coco peat and strawberry root in order to cultivate strawberry again. The main objective of this study is to design and analyze the structure of strawberry rotary device for using breaking up of coco peat and strawberry root. In order to perform crushing coco peat on the bed, the rotary device was designed under the weigh 20kg with the speed 11.75m/min, and it can operate on bed width from 250~310mm. Due to different depth of bed, the body of device also was designed screw holder to adjust the hight from 0~120mm. To evaluate the safety of structure, body device was analyzed in static and free vibration state by using Abaqus program. The device was applied maximum load 1177.2N, and the maximum equivalent stress was reached 41.9MPa. The free vibration analysis of two rotating cutter showed minimum natural frequency mode 338.58Hz and 339.9Hz. The results indicate that the designed rotary device was satisfied and has enough strength under design and simulation conditions.

Convergence of the finite element algorithm for the determination of the minimum natural frequency of the strip-plate with the use of some models of deformation

Free linear vibrations of plates-strips in two cases of fixing of elongated ends are considered. The efficiency of the model based on the quadratic approximation of displacements along the normal coordinate to the median plane at determining the minimal natural frequency in comparison with the generalized plate theory on the basis of the shift S. P. Timoshenko model in the case of using the finite element method is shown. Cite as: T. V. Goriachko, V. S. Pakosh, O. F. Lesyk, “Convergence of the finite element algorithm for the determination of the minimum natural frequency of the strip-plate with the use of some models of deformation,” Prykl. Probl. Mekh. Mat. , Issue 16, 154–157 (2018) (in Ukrainian), http://doi.org/10.15407/apmm2018.16.154-157

Natural Characteristic of Thin-Wall Pipe under Uniformly Distributed Pressure

Natural characteristics of thin-wall pipe of the compressor under uniformly distributed pressure were presented in this paper based on a cylindrical shell model. In the traditional method, the beam model was usually used to analyze the pipe system. In actual fact, the pipe segment of the compressor was always broken in the form of a long crack or a partial hole and the phenomenon was hardly explained by beam model. According to the structure characteristic of compressor pipe segment, whose radius is large and thickness is little, shell model shows the advantage in this kind of pipe problem. Based on Sanders’ shell theory, the vibration differential equation of pipe was established by applying the energy method. The influences of length to radius ratio (L/R), thickness to radius ratio (h/R), circumferential wave number (n) and pressure (q) on the natural frequencies of pipe were analyzed. The study shows: Pressure and structural parameters have a great effect on the natural characteristics of the pipe. Natural frequency increases as the pressure increases, especially for the higher mode. The sensitivity of natural frequency on pressure becomes stronger with h/R ratio increases; when L/R ratio is greater than a certain critical value, the influence of the pressure on natural frequency will no longer be obvious. The value of n corresponding to the minimum natural frequency also depends on the value of pressure. In the end, analysis of the forced vibration of a specific pipeline model was given and the modal shapes were illustrated to understand the break of the pipe. The research here will provide the theory support for the dynamic design of related pressure pipe and further experiment study should be employed.

A Fiber Bragg Grating Based Torsional Vibration Sensor for Rotating Machinery.

This paper proposes a new type of torsional vibration sensor based on fiber Bragg grating (FBG). The sensor has two mass ball optical fiber systems. The optical fiber is directly treated as an elastomer and a mass ball is fixed in the middle of the fiber in each mass ball fiber system, which is advantageously small, lightweight, and has anti-electromagnetic interference properties. The torsional vibration signal can be calculated by the four FBGs’ wavelength shifts, which are caused by mass balls. The difference in the two sets of mass ball optical fiber systems achieves anti-horizontal vibration and anti-temperature interference. The principle and model of the sensor, as well as numerical analysis and structural parameter design, are introduced. The experimental conclusions show that the minimum torsional natural frequency of the sensor is 27.35 Hz and the torsional vibration measurement sensitivity is 0.3603 pm/(rad/s2).

A MODIFICATION OF AN ESTIMATION METHOD OF THE NATURAL FREQUENCY OF A CUBE FORM MICRO SATELLITE

Micro satellites must survive severe mechanical conditions during their launch phase. One design requirement for rockets is the stiffness requirement, i.e. the natural frequencies requirement. In the early stages of satellite development, presumption of the natural frequency of a satellite may be difficult. The material used for the structure of many micro satellites is an aluminum alloy. The structure subsystem occupies a large portion of the satellite mass, and the elastic modulus of this aluminum alloy is larger than that of other subsystems. Therefore, the mechanical property of the aluminum alloy cannot be used to represent the mechanical property of the whole satellite. The density of an actual satellite differs from the density of the aluminum alloy. Therefore, when estimating the minimum natural frequency, the size and the elastic modules of an actual satellite structure must be used. When using an actual satellite structure, the estimated minimum natural frequencies of the lateral direction and the longitudinal direction during the ascent phase are in agreement with the measured values acquired by the vibration tests. In order to shorten a process of satellite development, this paper describes a practical method for estimating the natural frequency of a cube-shaped micro satellite This paper is a modified version of the previous paper [1] using new measurement results.

AN ESTIMATION METHOD OF THE NATURAL FREQUENCY OF A CUBE FORM MICRO SATELLITE

Micro satellites must survive severe mechanical conditions during their launch phase. One design requirement for rockets is the stiffness requirement, i.e. the natural frequencies requirement. In the early stages of satellite development, presumption of the natural frequency of a satellite may be difficult.
 The material used for the structure of many micro satellites is an aluminum alloy. The structure subsystem occupies a large portion of the satellite mass, and the elastic modulus of this aluminum alloy is larger than that of other subsystems. Therefore, the mechanical property of the aluminum alloy cannot be used to represent the mechanical property of the whole satellite. The density of an actual satellite differs from the density of the aluminum alloy. Therefore, when estimating the minimum natural frequency, the size and the elastic modules of an actual satellite structure must be used. When using an actual satellite structure, the estimated minimum natural frequencies of the lateral direction and the longitudinal direction during the ascent phase are in agreement with the measured values acquired by the vibration tests.
 In order to shorten a process of satellite development, this paper describes a practical method for estimating the natural frequency of a micro satellite.

Investigation of notch effect on vibration behavior of filled and unfilled composite beam

In this study, the effect of the notches on natural frequencies of ceramic particles filled and unfilled unidirectional composite beams are investigated numerically. Shape, number, size and location of the notch are examined for unfilled unidirectional composite beam. Moreover, the effect of the particle additives on the natural frequency of the composite beam with V notch is also examined. Three types of notch shape are considered: U, V and square (S). SiC, Al2O3 and B4C are used as the additive particles. According to the results, minimum natural frequency is found in the S notch. Furthermore, it can be seen from the results that natural frequency of S notch is the most affected by increase in the number, size and location of notch. As for the effect of the particle additives, maximum natural frequency is found in the beam with filled B4C and V notch as compared with the others.

Improvement of the Critical Speed of the Ball Screw Mechanism by Using Flexible Supported Nut

The ball screw with a long stroke has small rigidity in radial direction and is very liable to resonate dramatically during operation at high speed. For improving the critical speed of the ball screw, this paper investigates the influence of the supporting stiffness of the screw shaft at the nut on the resonance frequency of the screw shaft in the radial direction. The screw shaft is modeled as an Euler-Bernoulli beam with elastic supports at both ends and the position of the nut. According to the established model, the relationship between the natural frequencies and the supporting stiffness of the shaft at the nut can be obtained. The simulation results show that the flexible support at the position of the nut can effectively increase the minimum natural frequencies and reduce the variation range of the natural frequencies over the travel range of the nut. It is conducive to the vibration suppression and the critical speed improvement of the ball strew.

A low-cost acceleration monitoring system based on dual fiber Bragg gratings

In this paper, we constructed a low-cost acceleration monitoring system based on a rectangle cantilever beam (RCB), two fiber Bragg gratings and the light intensity measurement method. To do this, we investigated the minimum natural frequency of RCB and the dependence relationship of the strain of the measurement point and its change rate with respect to the acceleration amplitude upon the inclination angle of the sensor, and given the quantitative relationship between the amplitude of AC voltage of monitoring system versus the acceleration amplitude and the inclination angle of the sensor. Finally, we have finished a series of vibration monitoring experiments, and the experiment data are consistent with the theoretical equations.

Assessment of Thermal Effects on the Free Vibration Characteristics of Composite Beams

Abstract In this study, thermal effects on the free vibration characteristics of composite beams are studied for different temperatures and boundary conditions by using numerical and experimental techniques. Different ply angles, stacking sequences and specimen thickness are also considered. The comparison revealed a good agreement between numerical and experimental results. It is also concluded that regardless of the type of boundary condition and thickness, natural frequencies are decreased with increasing temperature. In addition, a minimum natural frequency value occurs in the natural frequency-ply angle graph at 60° ply angle for all considered temperatures. It can also be stated that the natural frequencies of the composite beams can be adjusted by controlling the temperature as well as the stacking sequences.

Vibration Analysis of Tendon-Based Parallel Robot for Processing

The vibration characteristics of the tendon-based parallel robot for processing are presented. Firstly, the free vibration equations of the robot on the stable position and orientation were modeled, and secondly the natural frequencies were deduced from the transformation of principal coordinates into modal coordinates. Next, cutting-force model was introduced and the solutions of the forced vibration equations were obtained from the Runge-Kutta method, where the minimum natural frequency was taken as basis of the time step that was important for computation convergence. Lastly, the algorithm was verified by simulations, also including solution transformation of time domain into frequency domain by Fast Fourier Transformation (FFT). The vibration properties could be manifested clearly by the solutions in frequency domain. The results show that the eccentricity and the mass of the moving platform are the important factors to make system instable in certain excitation frequency.

The Numerical Method for Natural Frequencies Analysis of Simply Supported Ring-Stiffened Cylinder

Based on frequency equation of simply supported ring-stiffened cylinder, an alternative approach for calculating natural frequencies of ring-stiffened cylinder is proposed. Using some transformation techniques, the frequency equation is converted to determinant form of matrix pencil. Thus, solving frequency equation is equivalent to calculating generalized eigenvalues of matrix pencil. Then the natural frequencies of ring-stiffened cylinder are acquired with QR method. The result of QR method agrees well with that of bisection method and finite element method. By reducing order of the determinant, a simplified formula for calculating the minimum natural frequency of ring-stiffened cylinder is given. It proves that the simplified formula meets accuracy requirements when rings have small stiffness through comparing results from QR method and simplified formula. Using the approach of this paper, natural frequency’s curves of ring-stiffened shell are compared with that of unstiffened cylinder, while the effects of ring’s number and stiffness on natural frequencies are investigated.

The Effect of Reinforcement Structure on the Modal Parameters for Sandwich Structure Composite Plate

In order to investigate the effect of different reinforcement structure on the dynamic characteristics of sandwich structure composite plates used for manufacturing the high speed reciprocating motion composite components, four kinds of paulownia wood sandwich composite test specimens with dimensions of 350×83.5×9.5mm was designed and made by hand lay-up performing and press molding technology. The woven and 2D braiding fabric prepreg were both selected as top face and inner face materials , respectively, and the carbon fiber woven fabric prepreg was chosen as inner part materials. According to the impulse response modal test method, a modal test system was established. It was found that this kind of sandwich structure composite plate has bigger natural frequency value, it’s minimum natural frequency was about 609.77Hz that could meet the requirement for high speed reciprocating motion parts. The dynamic test results shown that the natural frequency of F2BAF-IUC-CPW sample is higher t about 11.17% at least, selecting 2D integral braiding pipe fabric as top face and inner face reinforced materials could effectively improve the dynamic properties of sandwich composite rectangular plates. The modal experiments indicated that the modal shapes of sandwich composite plate specimen with four kind reinforcement structures were identical, it’s 1st modal shape, 2nd modal shape and 3rd modal shape presented torsional vibration shape, flexural vibration shape and torsional flexural vibration shape, separately, the modal shapes of sandwich composite plate specimen were not obviously affected by reinforcement structure.

The Theoretical Prediction and Experimental Verification of Modal Parameters for Carbon Fiber Reinforced Composites with Sandwich Structure

A innovative structure of sandwich composite rectangular plate with dimensions of 350 ×83.5×9.5mm was designed, it was made of unidirectional prepreg of carbon fibre and woven fabric prepreg of carbon fiber as face materials and paulownia as core material by hand lay-up performing and press molding technology for investigating the dynamic performance such as natural frequency and modal shapes. Based on testing the in-plane and out-plane mechanical properties of composite samples reinforced by unidirectional carbon fibre and carbon fiber woven fabric, a ANSYS FEA dynamic modeling was developed. According to the impulse response modal test method, a modal test system was established. The natural frequency test results showed that the minimum natural frequency of sandwich composite rectangular plate is about 616.45Hz which is higher about 27.5% than that of aluminum rectangular plate reinforced by carbon. The modal experiment indicated that the 1st modal shape, 2nd modal shape, 3rd modal shape and 4th modal shape of the sandwich composite rectangular plate were torsional vibration, flexural vibration shape, torsional flexural vibration and double-flexural vibration separately. It was found the calculating precision of FEA dynamic predication was very high, the dynamic predicating results by FEA could provide fundamental data to the optimal design high speed reciprocating sandwich composite rectangular parts.

Effect of the stiffness of ribs on the vibrations and stability of open cylindrical shells

The effect of the stiffness of ribs on the minimum natural frequencies and critical stresses of axially compressed open cylindrical shells reinforced with a quasiregular set of longitudinal ribs is analyzed by way of numerical examples. It is shown that the earlier discovered phenomenon of abrupt decrease in the minimum frequencies is independent of rib stiffness for certain modes and a small number of ribs

Slender Monumental Stair Vibration Serviceability

This paper presents the results of an experimental and analytical study of a slender monumental stair. The objective of the study was to gain insight into slender stair vibration issues and provide guidance for the design of such stairs. A slender monumental stair was vibration tested to estimate modal properties and acceleration due to walking. A detailed unadjusted finite-element model was created of the stair using only information that would be available to a designer. The model was used to predict the modal properties and accelerance magnitude. The accelerance magnitude was then used with established harmonic footstep forces to predict the steady-state acceleration due to walking. A factor was developed to account for imperfect resonant buildup, providing reasonable predictions of acceleration due to walking. Design forces were derived based on a set of stair ascent and descent footstep force measurements. An absolute minimum natural frequency is recommended for vertical and horizontal vibrations. Practical aspects of stair vibration analysis are discussed, including the handling of group loading, likely affected occupant locations, and guardrail lateral vibration.