A Method of Determing Dynamic Stability Critical Length of Construction Member

2012 ◽  
Vol 166-169 ◽  
pp. 3306-3310
Author(s):  
Qiang Sun ◽  
Cong Cong Guan

Based on the theory of elastic stability of structure,the calculating formula for dynamic stability critical length of construction member being in lateral resonance under the axial dynamic load is derived in this paper. The influence of different parameters, such as end conditions; rod size; damp force and excitation frequency, natural frequency, rod material, on dynamic stability critical length of rod is analyzed. The paper puts forward some related measures for reducing vibration of rod, and may provide reference values for the design and analysis of engineering.

2011 ◽  
Vol 261-263 ◽  
pp. 1434-1438
Author(s):  
Qiang Sun ◽  
Qiu Yi Lin ◽  
Jing Wei Wu

Based on the principle of elastic stability, this paper deduces the calculating formulas for dynamic stability critical length of foundation piles when lateral syntony occurs under the axial dynamic loads, and analyzes the effects on dynamic stability critical length of foundation piles from the aspects of parameters such as section dimensions of piles, horizontal resistance forces of foundation soil and excitation frequency etc. Study shows that different soil stratum has the bigger effects on the critical length of piles, while damping coefficient smaller. It also puts forward some related measures for reducing vibration of foundation piles, and can provide reference values to the practical engineering.


Author(s):  
Tae Ho Kim ◽  
Moon Sung Park ◽  
Jongsung Lee ◽  
Young Min Kim ◽  
Kyoung-Ku Ha ◽  
...  

Gas foil bearings (GFBs) have clear advantages over oil-lubricated and rolling element bearings, by virtue of low power loss, oil-free operation in compact units, and rotordynamic stability at high speeds. However, because of the inherent low gas viscosity, GFBs have lower load capacity than the other bearings. In particular, accurate measurement of load capacity and dynamic characteristics of gas foil thrust bearings (GFTBs) is utmost important to widening their applications to high performance turbomachinery. In this study, a series of excitation tests were performed on a small oil-free turbomachinery with base excitations in the rotor axial direction to measure the dynamic load characteristics of a pair of six-pad, bump-type GFTBs, which support the thrust collar. An electromagnetic shaker provided dynamic sine sweep loads to the test bench (shaking table), which held rigidly the turbomachinery test rig for increasing excitation frequency from 10 Hz to 200 Hz. The magnitude of the shaker dynamic load, represented as an acceleration measured on the test rig, was increased up to 9 G (gravity). An eddy current sensor installed on the test rig housing measured the axial displacement (or vibrational amplitude) of the rotor thrust collar during the excitation tests. The axial acceleration of the rotor relative to the test rig was calculated using the measured displacement. A single degree-of-freedom base excitation model identified the frequency-dependent dynamic load capacity, stiffness, damping, and loss factor of the test GFTB for increasing shaker dynamic loads and increasing bearing clearances. The test results show that, for a constant shaker force and the test GFTB with a clearance of 155 μm, an increasing excitation frequency increases the dynamic load carried by the test GFTB, i.e., bearing reaction force, until a certain value of the frequency where it jumps down suddenly because of the influence from Duffing’s vibrations of the rotor. The bearing stiffness increases and the damping decreases dramatically as the excitation frequency increases. Generally, the bearing loss factor ranges from 0.5 to 1.5 independent of the frequency. As the shaker force increases, the bearing dynamic load, stiffness, damping, and loss factor increase depending on the excitation frequency. Interestingly, the agreements between the measured GFTB dynamic load versus the thrust runner displacement, the measured GFTB static load versus the structural deflection, and the predicted static load versus the thrust runner displacement are remarkable. Further tests with increasing GFTB clearances of 155, 180, 205, and 225 μm revealed that the vibrational amplitude increases and the jump-down frequency decreases with increasing clearances. The bearing load increases, but the bearing stiffness, damping, and loss factor decrease slightly as the clearance increases. The test results after a modification of the GFTB by rotating one side bearing plate by 30° relative to the other side bearing plate revealed insignificant changes in the dynamic characteristics. The present dynamic performance measurements provide a useful database of GFTBs for use in microturbomachinery.


Author(s):  
Kai Feng ◽  
Xueyuan Zhao ◽  
Zhiyang Guo

With increasing need for high-speed, high-temperature, and oil-free turbomachinery, gas foil bearings (GFBs) have been considered to be the best substitutes for traditional oil-lubricated bearings. A multi-cantilever foil bearing (MCFB), a novel GFB with multi-cantilever foil strips serving as the compliant underlying structure, was designed, fabricated, and tested. A series of static and dynamic load tests were conducted to measure the structural stiffness and equivalent viscous damping of the prototype MCFB. Experiments of static load versus deflection showed that the proposed bearing has a large mechanical energy dissipation capability and a pronounced nonlinear static stiffness that can prevents overly large motion amplitude of journal. Dynamic load tests evaluated the influence of motion amplitude, loading orientation and misalignment on the dynamic stiffness and equivalent viscous damping with respect to excitation frequency. The test results demonstrated that the dynamic stiffness and damping are strongly dependent on the excitation frequency. Three motion amplitudes were applied to the bearing housing to investigate the effects of motion amplitude on the dynamic characteristics. It is noted that the bearing dynamic stiffness and damping decreases with incrementally increasing motion amplitudes. A high level of misalignment can lead to larger static and dynamic bearing stiffness as well as to larger equivalent viscous damping. With dynamic loads applied to two orientations in the bearing midplane separately, the dynamic stiffness increases rapidly and the equivalent viscous damping declines slightly. These results indicate that the loading orientation is a non-negligible factor on the dynamic characteristics of MCFBs.


Author(s):  
Takashi Ikeda

Abstract The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a rectangular tank, partially filled with liquid, are investigated. The structure containing the tank is vertically subjected to a sinusoidal excitation. In the theoretical analysis, the resonance curves for the responses of the structure and liquid surface are presented by the harmonic balance method, when the natural frequency of the structure is equal to twice the natural frequency of one of the sloshing modes. From the theoretical analysis, the following predictions have been obtained: (a) Due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface, (b) the shapes of the resonance curves markedly change depending on the liquid depth, and (c) when the detuning condition is slightly deviated, almost periodic oscillations and chaotic oscillations appear at certain intervals of the excitation frequency. These were qualitatively in good agreement with the experimental results.


Author(s):  
Jiawei Gu ◽  
Zhijiang Xie ◽  
Jian Zhang ◽  
Yangjun Pi

When a parallel robot is equipped with kinematic redundancy, it has sufficient capabilities of natural frequency modulation through adjusting geometric configuration. To reduce resonance of a mechanism, this paper investigates the natural frequency modulation of a kinematically redundant planar parallel robot. A double-threshold searching method is proposed for controlling the inverse kinematics solution and keeping the natural frequencies away from the excitation frequency. The effectiveness of modulating the natural frequencies is demonstrated by comparing it with a non-modulation method. The simulation results indicate that, in all directions, the responses are coupled, and every order should be taken into consideration during natural frequency modulation. Compared to the non-modulation method, the proposed method can reduce the resonance amplitude to a certain extent, and the effect of vibration suppression is remarkable.


2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Siqi Li ◽  
Shenglei Tian ◽  
Wei Li ◽  
Tie Yan ◽  
Fuqing Bi

In order to study the resonance characteristics of rock under harmonic excitation, two vibration models have been presented to estimate the natural frequency of rock encountered during the drilling. The first one is a developed single-DOF model which considers the properties and dimensions of the rock. The second one is a multi-DOF model based on the principle of least action. Subsequently, the modal characteristics, as well as the influence of excitation frequency, the mechanical properties, and dimensions of the rock on its resonance frequency, are analyzed by using FEM. Finally, the ultrasonic test on artificial sandstones and materials of drill tools are carried out indoor, and the FFT transform method is adopted to obtain their resonance frequencies. Based on the analysis undertaken, it can be concluded that the natural frequency of the rock increases with the change of vibration mode. For the same kind of rock, the resonance frequency is inversely proportional to mass, while for the different kinds of rocks, the mechanical parameters, such as density, elastic modulus, and Poisson’s ratio, determine the resonance frequency of the rock together. Besides, the shape of the rock is also one of the main factors affecting its resonance frequency. At last, the theoretical research results are further verified by ultrasonic tests.


Author(s):  
Wenlung Li ◽  
S. P. Tseng

The main objective of the report is to present a new identification method has been derived for single-degree, base-excited systems. The system is actually to mimic a probe of cantilever type of AFMs. In fact, the idea of the present report was initiated by needs for in situ spring constant calibration for such probe systems. Calibration processes can be treated as parameter identification for the stiffness of the probe before it is used. However, sine a real probe is too small to be seen by bare eyes and too costly to verify, a cantilever beam was adopted to replace it during the study. The present method starts with giving a chirp excitation to the target system, and to lock the damped natural frequency. Once the damped natural frequency is obtained, it is possible to locate the frequency at which the phase lag is equal to π/2. From which, the excitation frequency is then purposely changed to that frequency and the corresponding steady-state responses are measured. In the meantime, the system dissipative energy or power may also need to be stored. In fact, the present identification formulation is to express the spring constant of the target systems in terms of two measurable parameters: the phase angle and the system damping. The former can be computed from the damped natural frequency while the latter can be identified along with measuring the input power. The novel formulation is then numerically simulated using the Simulink toolbox of MATLAB. The simulation results clearly showed the current identification method can work with good accuracy. Following the numerical simulation, experimental measurements were also carried out by a cantilever beam that its free end was immersed to viscid fluids. The fluids of different viscosity were used to mimic the environments of a probe in use. The experimental results again substantiated the correctness of the present method. Thus it is accordingly concluded that the new recognition algorithm can be applied with confidence.


Author(s):  
Francesco Pellicano

In the present paper the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature.


Author(s):  
Katsuhide Fujita ◽  
Takashi Saito ◽  
Mitsugu Kaneko

When agricultural machines are operated on pavements, the vibration and noise caused by the interaction between the tire lugs and the road surface are inevitable. In conventional studies, it is considered that the dynamic behavior of a rolling agricultural tire is influenced by the vibration characteristics of the tire. Resonance occurs when the lug excitation frequency of the tire, which is defined as the lug number multiplied by the number of revolutions of the tire, becomes equal to the natural frequency of the tire. In other words, the rolling tire shows large vibrations in the direction of the natural mode corresponding to the natural frequency of the tire. However, in the conventional equipment, the diameter of the drum is smaller than that of the tire. Therefore, the real running condition on the road was not realized by the rolling test using the conventional equipment. In this study, a new equipment is produced to realize the running condition in the rolling test. The dynamic and vibratory characteristics of operating agricultural machine are investigated by using this new equipment. The obtained results are compared to the conventional ones and the influence of the running condition on dynamic characteristics of rolling tire is investigated.


Author(s):  
Katsuhide Fujita ◽  
Takashi Saito ◽  
Toru Yamazaki

When agricultural machines are operated on pavements, the vibration and noise caused by the interaction between the tire lugs and the road surface are inevitable. In conventional studies, it is considered that the dynamic behavior of a rolling agricultural tire is influenced by the vibration characteristics of the tire. Resonance occurs when the lug excitation frequency of the tire, which is defined as the lug number multiplied by the number of revolutions of the tire, becomes equal to the natural frequency of the tire. In other words, the rolling tire shows large vibrations in the direction of the natural mode corresponding to the natural frequency of the tire. However, the vibration mode of the rolling tire in resonance state has not yet been clarified. In this study, it is confirmed that the dynamic behavior of the rolling tire can be evaluated by performing sound pressure measurements using closely located microphones to the tire. Further, the vibration mode in the resonance state is identified by performing simultaneous measurements of the sound pressure, and the vibration mode corresponds to the natural mode of the tire is confirmed as well.


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