Inverse Frequency Problem of Discrete System of Symmerty Beam with Two Fixed Ends

2013 ◽  
Vol 328 ◽  
pp. 564-569
Author(s):  
Min He ◽  
Quan Jin Liu ◽  
Qi Shen Wang
Keyword(s):  
Natural Frequency ◽  
Frequency Spectrum ◽  
Discrete System ◽  
Physical Parameters

This paper discussed some properties of the discrete system of the Eulers beam in vibration, which geometrical, physical parameters and supporting forms at both ends are symmetry about the midpoint of the span. On this foundation the inverse frequency problem based on the beam with both fixed-ends is raised and solved, i.e. given a set of frequency spectrum of the beam with both fixed-ends and other n positive number satisfying the interlace relation as following: the discrete system of the above symmetry beam fixed at both ends could be constructed, and would be the natural frequency of the fixed-free half-beam which is cut off from the midpoint of the beam fixed at both ends.

scholarly journals Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo

Actuators ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 28
Author(s):  
Imran Hussain ◽  
Wei Xia ◽  
Dongpo Zhao ◽  
Peng Huang ◽  
Zhiwei Zhu
Keyword(s):  
Natural Frequency ◽  
Trajectory Tracking ◽  
Voice Coil Motor ◽  
Diamond Turning ◽  
Analytical Models ◽  
Physical Parameters ◽  
Fast Tool Servo ◽  
Element Analysis ◽  
Loop Control ◽  
Resonant Controller

In this paper, a voice coil motor (VCM) actuated fast tool servo (FTS) system is developed for diamond turning. To guide motions of the VCM actuator, a crossed double parallelogram flexure mechanism is selected featuring totally symmetric structure with high lateral stiffness. To facilitate the determination of the multi-physical parameters, analytical models of both electromagnetic and mechanical systems are developed. The designed FTS with balanced stroke and natural frequency is then verified through the finite element analysis. Finally, the prototype of the VCM actuated FTS is fabricated and experimentally demonstrated to achieve a stroke of ±59.02 μm and a first natural frequency of 253 Hz. By constructing a closed-loop control using proportional–integral–derivative (PID) controller with the internal-model based resonant controller, the error for tracking a harmonic trajectory with ±10 μm amplitude and 120 Hz frequency is obtained to be ±0.2 μm, demonstrating the capability of the FTS for high accuracy trajectory tracking.

Natural frequency spectrum of a flat superconducting cable

1999 ◽  
Vol 25 (7) ◽  
pp. 524-526
Author(s):  
A. A. Akhmetov ◽  
S. S. Ivanov ◽  
I. O. Shchegolev
Keyword(s):  
Natural Frequency ◽  
Frequency Spectrum ◽  
Natural Frequency Spectrum

Analysis of Vibrating Natural Frequency of Pressure Pipeline

2011 ◽  
Vol 421 ◽  
pp. 98-101
Author(s):  
Ting Yue Hao
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Flow ◽  
Physical Parameters ◽  
Beam Model ◽  
Instability Condition ◽  
Coupling Vibration ◽  
Critical Flow Velocity ◽  
Pressure Pipeline ◽  
The Mathematical Model

The pressure pipeline is simplified as the beam model with two simple supported ends. The mathematical model is established, considering influence of the fluid-solid coupling vibration. Then the critical flow velocity is obtained by calculation and solving. By analyzing the practical numerical example，the influence of physical parameters on the first three-order natural frequency is discussed. Using Matlab software for programming, the instability condition of pressure pipeline is obtained, which is consistent with the result of numerical calculation.

scholarly journals Simulasi Getaran Sistem Diskrit Satu Derajat Kebebasan

MESIN ◽  
2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Vega Amalia Eka Rizky ◽  
Muhammad Ganesha ◽  
Tono Sukarnoto ◽  
Soeharsono Soeharsono
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Forced Vibration ◽  
Discrete System ◽  
Mechanical Vibration ◽  
Degree Of Freedom ◽  
Rigid Object ◽  
Resonance Frequencies ◽  
Vibration Experiment ◽  
Rigid Rod

<em>Equipment has been made to simulate a discrete system vibration of one degree of freedom. The aim is to obtain equipment for learning for students in the field of mechanical vibration. Vibration simulation includes free vibration and forced vibration of discrete system in one degree of freedom. The main parts of this equipment are rigid rods with mass of 2.6 kg, vibrators with mass of  3.385 kg, spring with stiffness of 3738 N/m and loading masses. A rigid rod of 0.775 m in length is supported by a hinge on one end and hung on a spring in another position. The vibrator is rotated by an electric motor and the rotation can be adjusted from 90-1600 rpm. The vibrator is mounted on a rigid object at the position of 0.285 m, 0.385 m, 0.485 m and 0.585 m from the hinge. A spring with stiffness of 3738 N/m is placed on a rigid object at the position of the hinge. The loading masses of 1.08 kg and 2.08 kg are mounted on a rigid beam in a row at the position of 0.685 m from the hinge. For the free vibration experiments, the natural frequency for each position of vibrator is searched experimentally and theoretically. It is found that the results of the two are similar. For the forced vibration experiments, graphs of vibrational responses are constructed in the frequency domain, then the resonance frequencies are compared to the natural frequency results from the free vibration experiment. Apparently the results are very close. This shows that the research equipment made is reliable and can be used as a student learning tool.</em>

scholarly journals Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo

2020 ◽  
Author(s):  
Imran Hussain ◽  
Wei Xia ◽  
Dongpo Zhao ◽  
Peng Huang ◽  
Zhiwei Zhu
Keyword(s):  
Natural Frequency ◽  
Trajectory Tracking ◽  
Voice Coil Motor ◽  
Diamond Turning ◽  
Analytical Models ◽  
Physical Parameters ◽  
Fast Tool Servo ◽  
Element Analysis ◽  
Loop Control ◽  
Resonant Controller

In this paper, a voice coil motor (VCM) actuated fast tool servo (FTS) system is developed for diamond turning. To guide motions of the VCM actuator, a crossed double parallelogram flexure mechanism is selected featuring totally symmetric structure with high lateral stiffness. To facilitate the determination of the multi-physical parameters, analytical models of both electromagnetic and mechanical systems are developed. The designed FTS with balanced stroke and natural frequency is then verified through the finite element analysis. Finally, the prototype of the VCM actuated FTS is fabricated and experimentally demonstrated to have a stroke of &plusmn;59.02 &mu;m and a first natural frequency of 253 Hz. By constructing a closed-loop control using PID controller with the internal-model based resonant controller, the error for tracking a harmonic trajectory with &plusmn;10 &mu;m amplitude and 120 Hz frequency is obtained to be &plusmn;0.2 &mu;m, demonstrating the capability of the FTS for high accuracy trajectory tracking.

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