Natural Frequency Coefficients Research Articles

Research on Electro-Hydraulic Servo Resonance Technology.

In this paper, an electro-hydraulic servo resonance technology is proposed to meet the loading requirements of a high-frequency sound fatigue test for large tonnage. First of all, we analyze the static and dynamic loading structure of electro-hydraulic servo vibration and establish the vibration equation of the system. Additionally, the modal and vibration characteristics of the system are analyzed by simulation, which verified the feasibility of the proposed electro-hydraulic servo resonant loading technology. Finally, the influence of various factors such as sample stiffness, lead screw stiffness, class II spring stiffness, class II weight mass, lower beam mass, and upper beam mass on the natural frequency and amplification coefficient of the system is analyzed. In this paper, a new technology is proposed to provide theoretical support for the research and development of large-tonnage high-frequency noise fatigue testing equipment.

Vibration characteristics of eccentric annular plates

An effective theoretical method for investigating the vibration characteristics of eccentric annular plates is developed. The vibration equation of eccentric annular plates is solved by utilizing the Bessel function as the vibration mode function and combining it with the translational addition theorem for cylindrical vector wave functions. Substituting the boundary conditions into the vibration mode function yields the frequency equation. The natural frequencies and corresponding vibration modes of the plate are obtained by determining the natural frequency coefficients. Compared with the results obtained from the finite element method (FEM) and vibration experiment, the correctness of the mode shapes and natural frequencies of the plate obtained by the present method are validated. The influences of several parameters such as the eccentric distance, the structural parameters, and various boundary conditions on the vibration characteristics of the plates are discussed. An analysis on the mode composition of the eccentric annular plates is also presented. The research results are useful for the practical engineering applications of the eccentric annular plates.

Numerical simulation and analysis of fluid-structure interaction on 3D MHKF-180 and NACA4418 cavitating hydrofoils

A numerical investigation of structural and hydrodynamic performance of 3D stainless steel MHKF-180 and NACA4418 cavitating hydrofoils has been carried out using one-way fluid-structure interaction (FSI). Under the application of hydrodynamic load, the structural performance of MHKF-180 is compared with NACA4418 in terms of natural frequency, maximum tip deformation, and von Mises stress, whereas hydrodynamic performance is compared in terms of lift coefficient, drag coefficient, lift to drag ratio, pressure coefficient, and Strouhal number. The simulation is performed at a chord-based Reynolds number, Re = 750000, for different cavitation numbers and angles of attack using ANSYS software. The present result is validated by comparing the natural frequency and pressure coefficient curve of the non-cavitating NACA66 hydrofoil and lift coefficient and drag coefficient of cavitating NACA4412 hydrofoil with the available experimental data. The fluid flow is simulated using the unsteady-Reynolds-averaged-Navier-Stokes (URANS) equations and Realizable k −ε turbulence model. The cavitation effect on the hydrofoil is studied using the Zwart-Gerber-Belamri cavitation model. Comparing the maximum tip deformation under cavitation, the MHKF-180 shows larger tip deformation than NACA4418 hydrofoil. However, the hydrodynamic performance, assessed in terms of lift coefficient, MHKF-180 gives a better than NACA4418 under the cavitating condition at different angles of attack and for different cavitation numbers.

Modeling and experimental investigation of asymmetric distance with magnetic coupling based on galloping piezoelectric energy harvester

This paper presents an asymmetric magnetic coupling piezoelectric energy harvester (PEH) based on galloping to scavenge low-speed wind. The piezoelectric beam of energy harvester undergoes bending and torsional vibration simultaneously due to the eccentric distance. By analyzing the kinetic energy, potential energy, and virtual work of the energy harvesting system, the mathematical model of harvester is constructed and verified by experiments. The optimal external load resistance is confirmed at different eccentric distances and wind speeds by experiments. Compared with traditional galloping piezoelectric energy harvester (GPEH), the asymmetric with magnetically coupling GPEH has a lower threshold wind speed, i.e. 2 m s−1. And the asymmetric configuration contributes to a lower natural frequency and electromechanical coupling coefficient, which results in a lower power and voltage output. The potential energy of harvesting systems at different distances between two magnets are respectively numerical analyzed in detail. The theoretical results illustrate that the energy harvester operates in monostable and bistable at different magnet distances. And the threshold wind speed of energy harvester increases when the energy harvester works at bistable. According to the above analysis, this work provides a detailed guideline for mathematical modeling and performance improvement of asymmetric PEH based on galloping.

Quasi-3D theory for the vibration of a magnetostrictive laminated plate on elastic medium with viscoelastic core and faces

The vibration of a magnetostrictive laminated composite sandwich plate with a viscoelastic core and faces rested on the two-parameter elastic medium is analyzed in the present article. The laminated sandwich plates are designed wherein consist of three kinds of composite materials: magnetostrictive material, fiber-reinforced material, and viscoelastic material in the core and faces. The viscoelastic core and faces are modeled as a Kelvin-Voigt viscoelastic model. The partial differential equations of motion are derived by implementing Hamilton’s principle. The analytical Navier’s solution type is obtained to analyze the behavior of the damping coefficient and the damped natural frequency coefficient. The influence of significant parameters is examined on vibration characteristics of the plate and discussed in detail, especially, location of smart layers, lamination schemes, elastic foundation coefficients, modes, the magnitude of the feedback coefficient, viscoelastic structural damping, thickness ratio, the aspect ratio, and viscoelastic layer thickness-to-magnetostrictive layer thickness ratio. Numerical results illustrate that the location of smart layers is an important element in the design of the plate to be more stable. It is anticipated that the findings reported in the study can be utilized to develop the adaptive structural applications and the solutions to future smart structure problems.

Simulation Analysis on Quasistatic Characteristics of Multistage Face Gears with Double Crown Surface

The multistage face gears are the core component of the planetary gear train, which is symmetrically meshed by multiple single-stage face gear and multiple cylindrical gears. However, it is difficult to synchronize the contact between face gears and cylindrical gear due to the tooth number differences. Thus, the interference problems between two stages and big stress concentration are obvious. The crown surface configuration technology and structure design were introduced to optimize the meshing condition. To improve the double crown design feasibility and meshing stability, it is necessary to establish a reasonable multistage face gears pair simulation model to evaluate various influence factors on the contact condition and quasi-static characteristics of multistage face gears structure. The relevant scatter plots are fitted by comparing the contact results with different crown quantities and friction coefficients to intuitively obtain the variation regularity of maximum deformation, maximum strain, maximum stress and maximum strain energy. The natural frequency and mode coefficient are also determined by modal analysis under these two conditions. All the above mentioned studies verified the contact conjugate properties of double crown surface configuration were suitable. The results can provide a foundation for structure optimization and transmission reliability of multistage face gears.

A new solution to enhance cuttings transport in mining drilling by using pulse jet mill technique

In horizontal drilling, the cuttings bed is frequently formed to result in severe problems such as backing pressure, binding of bottom hole assembly (BHA) and even sticking of tool. Practice and research show that the smaller particle size is, the more favorable to carry out from bottom of hole in extended reach well or horizontal well. This paper presented a new solution to enhance cuttings transport in mining drilling through a new type of bit called pulsed mill bit (PMB) by using pulse jet mill technique. It provides a promising solution to enhance the efficiencies of rock breaking and cuttings carrying for pulsed jet, sucking cuttings to decrease the chip hold down effect, and reducing cuttings’ diameter to eliminate cuttings bed. The design was supported by the calculation models of Helmholtz resonator natural frequency, optimal drilling fluid flow rate of resonator, drilling fluid flow velocity in forward jet channel, critical impact velocity of cuttings and minimum length of the accelerating cavity. Meanwhile, factors affecting optimal drilling fluid flow rate, critical impact velocity of cuttings and minimum length of accelerating cavity were investigated. Case study showed a good consistency between the calculation results and the related theories. It is concluded that optimal drilling fluid flow rate increases with the increase of inlet and outlet cavity’s diameter, and decreases with the increase of the diameter of the resonant cavity. Critical impact velocity of cuttings increases with the energy conversion factor (β) and ROP, while decreasing with the final size of the cuttings (dt). This effect is obvious when β<0.2, ROP <3.048 m h−1 and dt<0.3 mm. Minimum length of the accelerating cavity decreases with the increase of the resonator’s natural frequency and separation coefficient (α) of drilling fluid flow rate. This study provides a promising solution to remove cuttings bed in horizontal well.

Study for Dynamic Stability Behavior of I-Section Cantilever Beam under Axis Compressive Load

By mean of the energy functional variational principle and considering shear lag effect of flange, the dynamic governing differential equation for the I-section cantilever beam in the action of compressive loadPat the member end is obtained. The equation is solved by the separation variable method. According to the weigh residual method, the relation between natural frequency coefficient and critical load coefficient as well as the flutter critical load coefficient are made, the influence of shear lag effect on natural frequency coefficient and critical load coefficient is discussed.

Seismic Behaviour and Seismic Design of Single-Layer Reticulated Shells with Semi-Rigid Joint System

An investigation of the seismic behaviour and a design method for single-layer reticulated shells with semi-rigid joints is described in this paper. A semi-rigid joint system has some bending and rotational rigidity that lying between that of a rigid-joint and a pin-joint. The seismic capacity of Kiewit reticulated shells with bolt-ball joints is analyzed in detail on the basis of the bending rigidity of the bolt-ball joint reported by others. The change rules of natural frequency and seismic internal force coefficient are reviewed by analyzing of large-scale shells with different span, depth-to-span ratio, bending rigidity, roof load, section size of members and seismic wave parameters. The seismic internal force coefficient (under the influence of bending moment) for shells with a semi-rigid joint system is summarized statistically to provide the maximal seismic response envelop.

Analysis of Multiple Degrees of Freedom Vibration Isolation System Using the State Space Method

This papers deals with fast solving method of natural frequency and vibration isolation coefficient of multiple degrees of freedom vibration isolation system. In the foundation of a mathematical model of vibration motion differential equation, a new state space method is derived and presented. Through transforming the vibration isolation differential equations into the state space equations, it is convenient to facilitate the solution of vibration isolation coefficient of vibration isolation system of multiple degrees of freedom with damping, by using the state space method and the MATLAB/Simulink module. Simulation results showed the result is consistent with the theory result. Simulation results also showed that with the help of damping, the maximal vibration isolation coefficient of x direction is lowered from 90 to 3.2 in the 5.31Hz, which eliminate the resonance phenomenon. In y and z direction, the maximal vibration isolation coefficient is also decreased from 78 to 2.4 and from 210 to 2.35. The state space method can find further applications on the selection of vibration isolation system and the evaluation of vibration isolation efficiency.

The influence of natural frequency of the experimental set-up on the friction coefficient of copper

The present article investigates experimentally the effect of natural frequency of the experimental set-up on the friction property of copper. To do so, a pin-on-disc apparatus having the facility of vibrating the test samples at different directions, amplitudes, and frequencies was designed and fabricated. The natural frequency of the set-up was varied by adding dead loads of the set-up from 0 kg to 490.33 N. At each added load the friction coefficient has been measured. Results show that both the natural frequency and friction coefficient decrease with the increase of added loads. It has also been observed that the coefficient of friction increases with the increase of natural frequency of the experimental set-up. The experimental results are also compared with those available in literature and simple physical explanations are provided.

실험계획법을 이용한 복합재 경통 적층각의 최적 설계에 관한 연구

복합재는 인공위성 카메라 경통의 재료로 많이 사용되는 재료이다. 하지만 적층된 복합재는 층간응력에 의한 층간분리 현상으로 약화된다 이러한 파괴모드는 경통의 구조적 불안정을 유발하며, 카메라의 광학적 성능도 저하시킨다. 따라서 경통은 층간분리에 대해서 강건해야하며, 또한 고강성, 충분히 높은 고유진동수 및 작은 열 팽창 계수 등을 가져야한다. 본 연구에서는 실험계획법을 바탕으로 설계를 진행하였다. 각 실험과정은 직교배열표를 기준으로 설계되었으며, 여러 속성을 고려하기 위해서 MADM 방법을 사용하였다. 그리고 분산분석과 F-검정을 통해서 영향력 인자를 결정하여 경통의 최종 적층각을 결정하였다. Composite has become one of the most frequently used material for a tube of satellite camera due to its attractive characteristics. However, laminated composites can be weakened by delamination which comes from interlaminar stress. Such failure mode cause structural instability of the camera as well as degradation of optical quality. Therefore composite tube should be robust in delamination. Also, composite tube should have high stiffness, sufficient high natural frequency and small coefficient of thermal expansion. The design procedures presented in this paper are based on design of experiments. The experiments for mechanical analysis are designed by the tables of orthogonal arrays. In order to manipulate the various mechanical properties systematically, multiple-attribute decision making(MADM) is employed. Through analysis of variance and F-test, the critical design variables which have dominant influences on mechanical performance are determined. Finally improved ply angles for composite tube are determined.

Application of improved morphological filter to the extraction of impulsive attenuation signals

Rotating machinery response is often characterized by the presence of periodic impulses modulated by high-frequency harmonic components. It can be defined with three parameters, which are natural frequency, fault frequency and decay coefficient. In this paper, we propose an improved morphological filter for feature extraction of the above signals in the time domain. Firstly, an average weighted combination of open-closing and close-opening morphological operator, which eliminates statistical deflection of amplitude, is utilized to extract impulsive component from the original signal. Then, according to the geometric characteristic of impulsive attenuation component, the structure element is constructed with an impulsive attenuation function, and a new criterion is put forward to optimize the structure element. The proposed method is evaluated by simulated impulsive attenuation signals with different natural frequencies and vibration signals measured on defective bearings with outer race fault and inner race fault, respectively. Results show that the background noise can be fully restrained and the entire impulsive attenuation signal is well extracted, which demonstrates that the method is an efficient tool to extract impulsive attenuation component from mechanical signals.

Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

AbstractThe excessive lateral vibrations of Londons Millenium Bridge and the Toda Park Bridge in Japan due to a large number of crossing pedestrians have raised an unexpected problem in footbridge constructions. Secondary tuned structures, like the conventional tuned mass damper (TMD) or the tuned liquid damper (TLD) were installed to the bridge in order to suppress these vibrations. In the present investigation it is proposed to apply the more efficient and more economic tuned liquid column damper (TLCD), which relies on the motion of a liquid mass in a sealed tube to counteract the external motion, while a built‐in orifice plate induces turbulent damping forces that dissipate kinetic energy. For optimal tuning of TLCDs the natural frequency and equivalent linear damping coefficient have to be chosen suitable, likewise to the conventional TMDs, as given in Den Hartog [1]. The advantages of TLCDs are: simple tuning of natural frequency and damping, low cost of design and maintenance and a simple construction. A mathematical model of a three degree‐of‐freedom (DOF) bridge coupled with an optimal tuned TLCD is derived and analyzed numerically. Furthermore, a small scale experimental model set‐up has been constructed in the laboratory of the TU‐Insitute. The experimental results are in good agreement with the theoretical predictions and indicate that TLCDs are effective damping devices for the undesired pedestrian induced footbridge vibrations. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Experimental Determination of Dynamic Characteristics of the VentrAssist Implantable Rotary Blood Pump

The VentrAssist implantable rotary blood pump, intended for long-term ventricular assist, is under development and is currently being tested for its rotor-dynamic stability. The pump consists of a shaftless impeller, which also acts as the rotor of the brushless DC motor. The impeller remains passively suspended in the pump cavity by hydrodynamic forces, which result from the small clearances between the outside surfaces of the impeller and the pump cavity. These small clearances range from approximately 50 microm to 230 microm in size in the version of pump reported here. This article presents experimental investigation into the dynamic characteristics of the impeller-bearing-pump housing system of the rotary blood pump for increasing pump speeds at different flow rates. The pump was mounted on a suspension system consisting of a platform and springs, where the natural frequency and damping ratio for the suspension system were determined. Real-time measurements of the impeller's displacement were performed using Hall effect sensors. A vertical disturbance force was exerted onto the pump housing, causing the impeller to be displaced in vertical direction from its dynamic equilibrium position within the pump cavity. The impeller displacement was represented by a decaying sine wave, which indicated the impeller restoring to its equilibrium position. From the decaying sine wave the natural frequency and stiffness coefficient of the system were determined. Furthermore, the logarithmic decrement method was used to determine the damping ratio and eventually the damping coefficient of the system. Results indicate that stiffness and damping coefficients increased as flow rate and pump speed increased, representing an increase in stability with these changing conditions. However, pump speed had a greater influence on the stiffness and damping coefficients than flow rate did, which was evident through dynamic analysis. Overall the experimental method presented in this article was successful in determining the dynamic characteristics of the system.

Natural frequencies of a vibrating repaired panel in an ocean structure

The present work arose from the need of repairing steel plates badly damaged by corrosion in a portion of the structural element of the naval vehicle. The possibility of removing the portion and replacing it by a patch of a composite material was considered. Its dynamic behavior is altered by the introduction of the patch and the prediction of its new behavior is of great interest in many situations. This condition would appear in other real-life situations like as a localized orthotropic effect caused in the panel by a welding procedure or a metallurgical process. The first four natural frequency coefficients of the composite repaired panel with different types of boundary conditions are determined by means of a variational approach. The displacement function is approximated making use of complete sets of beam functions. The eigenvalues have been computed from (225×225) secular determinants. An independent solution is obtained using the finite element method and a reasonably good agreement with the analytical solution is encountered.

Natural frequencies of edge restrained tapered isotropic and orthotropic rectangular plates with a central free hole

Natural frequencies of tapered orthotropic rectangular plates with a central free hole and edges restrained against rotation and translation are studied by using orthogonal polynomials in the Rayleigh–Ritz method and applying a generalization of the Rayleigh–Schmidt method. The two methods are quite general and can be used to study plates with any combinations of boundary conditions, taper and geometric parameters. To demonstrate the accuracy of the present approach natural frequency coefficients are given for isotropic plates with a central free hole, from which comparison results are available. New results are also given for orthotropic plates with several complicating effects. The studied problems are of interest in several field of engineering, since holes are present in plates due to operational conditions.

A general algorithm for the study of the dynamical behaviour of beams

This paper presents a simple, accurate and flexible general algorithm for the study of a great number of beams vibration problems. The approach is developed based on the Rayleigh–Ritz method with characteristic orthogonal polynomial shape functions. It allows the inclusion of a number of complicating effects such as varying cross-sections, presence of an arbitrarily placed concentrated mass, ends elastically restrained against rotation and translation and presence of an axial, tensile force. Several cases are treated to show the simplicity and great flexibility of this approach, in the determination of frequencies. To demonstrate the accuracy of the present approach natural frequency coefficients are given for beams, from which comparison results are available. New results are also given for tapered beams with several complicating effects.

Free vibration analysis of penta, hepta-gonal shaped plates

Lagrange's equations of motion coupled with the finite element technique are applied to analyze the free vibration of pentagonal and heptagonal plates. Firstly, it is assumed that the elastic deformation of the plates is due to bending only. A high-precision 18 degrees of freedom triangular plate bending element, T18, is used. Results for isotropic, as well as orthotropic, plates, which have combinations of clamped, simply-supported and free edge conditions, are presented. Comparisons indicate that the results are in good agreement with those available in the literature. The effects of the composite filament angle for orthotropic and laminated plates are discussed. In the second part, the transverse shear effect is accounted for and a higher-order T36 finite element is employed. Results for isotropic and orthotropic plates which have fully clamped and fully simply supported edges are obtained. The effects of the plate thickness-to-length ratio on the natural frequency coefficients are discussed.

On-Line Identification of Modal Parameters Using Artificial Neural Networks

Using a neural network concept, an algorithm has been developed that can be employed to conduct on-line identification of modal parameters of a structure such as natural frequency, damping ratio, and mode shape coefficients at measurement locations. Using a band-pass filter, the algorithm extracts from the measurement signal the frequency contents in the vicinity of a desired mode. The filtered signal is then used to train a neural network which consists of a linear neuron with three weights. The structure of the neural network has been designed to allow direct identification of modal parameters from the weights and to enhance efficiency for on-line implementation. The algorithm has been implemented on a DSP (digital signal processor) system for performance evaluation. Modal parameter identification tests have been conducted for a laboratory circular plate structure. The algorithm runs approximately at a sampling frequency of up to 50 kHz for the DSP system used for the study and correctly identifies modal properties of the first two modes of the circular plate. This high performance on-line identification algorithm is expected to be useful in improving the performance of control systems that require knowledge of time-varying plant dynamic characteristics.