RADIAL VIBRATIONS OF AXISYMMETRICALLY LOADED STEPPED PRESSURE VESSELS

Differential equations of free/forced radial vibrations of axisymmetrically loaded stepped pressure vessels are established by using singular functions. Furthermore, their general solutions are solved, the expression of vibration mode function and frequency equations on usual supports are derived with W operator and the forced response of such vessels are calculated.

Improved Model of Radial Vibration in Switched Reluctance Motor Including Magnetic Saturation

This paper proposes an improved method for the prediction of radial vibration in switched reluctance motor(SRM)considering magnetic saturation.In this paper,the basic modeling principle is briefly introduced,it is based on the derivation that the peak acceleration is dependent on the product of phase current and current gradient idi/dt.However,the derivation may cause errors due to saturation effect.Thus in this paper,the discrete sample data are firstly acquired based on DC pulse measurement method,by which electromagnetic,torque and peak acceleration characteristics can all be acquired.Then the entire peak acceleration characteristics are obtained by improved Least Square Support Vector Machine(LSSVM).Based on the obtained static peak acceleration characteristics,the time-varied radial vibration model is established based on superposition of natural oscillations of dominant vibration modes.Finally,a simulation model is built up using MATLAB/Simulink.The good agreement between simulation and experiment shows that the proposed method for modeling is feasible and accurate,even under saturation.In addition,since LSSVM does not need any prior knowledge,it is much easier for modeling compared with other existing literatures.

Radial vibration of a slit-type annular ultrasonic concentrator

The radial vibration characteristic of an annular ultrasonic concentrator with multi- slits is studied. Based on the electro-mechanical analogy and by introducing an area ratio coef- ficient, the radial vibrational equivalent circuit and the frequency equation of the concentrator are derived. The radial displacement amplitude magnification factor of it is obtained. By nu- merical calculating, the relationship between the radial displacement amplitude magnification factor, the resonance frequency of the concentrator at the first and second resonance and its radius ratio are investigated. Also, the relationship between the radial displacement amplitude magnification factor, the resonance frequency of the concentrator and the length, the angle and the number of the silts are analyzed. It is illustrated that a maximum of displacement ampli- tude magnification factor of the concentrator appears with the increase of the radius ratio, and the amplitude magnification factor increase as the length, the angle and the number of the silts increase, while the radial resonance frequency of the concentrator decreases as the length, the angle and the number of the silts increase. The theoretical resonance frequencies are in good agreement with that of the FEM simulations and measurement.

Theoretical analysis and experimental validation of radial cascaded composite ultrasonic transducer

A radial cascaded composite ultrasonic transducer is analyzed.The transducer consists of three short metal tubes and two radially polarized piezoelectric ceramic short tubes arranged alternately along the radial direction.The short metal tubes and the piezoelectric ceramic short tubes are connected in parallel electrically and in series mechanically,which can multiply the input sound power and sound intensity.Based on the theory of plane stress,the electro-mechanical equivalent circuit of radial vibration of the transducer is derived firstly.The resonance/anti-resonance frequency equation and the expression of the effective electromechanical coupling coefficient are obtained.Excellent electromechanical characteristics are determined by changing the radial geometric dimensions.Two prototypes of the transducers are designed and manufactured to support the analytical theory.It is concluded that the theoretical resonance/anti-resonance frequencies are consistent with the numerical and experimental results.When R_(2) is at certain values,both the anti-resonance frequency and effective electromechanical coupling coefficient corresponding to the second mode have maximal values.The radial cascaded composite ultrasonic transducer is expected to be used in the fields of ultrasonic water treatment and underwater acoustics.