Frequencies Of Other Modes Research Articles

The axisymmetric oscillations of a cylindrical bubble in a liquid bounded volume with free deformable interface

The eigen axisymmetric oscillations of a cylindrical gas bubble surrounded by an incompressible fluid with free deformable interface are considered. The bubble has an equilibrium cylindrical shape and is bounded axially by two parallel solid surfaces. Dynamics of contact lines is taken into account by an effective boundary condition: velocity of the contact line is assumed to be proportional to contact angle deviation from the equilibrium value. The equilibrium contact angle is right. Eigen frequency decreases with liquid outer free surface radius decreasing and increases with the radius-to-height ratio increasing. It’s found that the eigen frequency can vanish in some wetting parameter interval for the volume mode of natural oscillations (which describes the radial compression of the bubble). The length of this interval increases with increasing ratio of the equilibrium bubble radius to the height. The eigen frequencies of other modes decrease with increasing Hocking’s constant. The lowest natural frequency is observed for the freely sliding bubble.

Multi-parameter sensing with a single magnetoelastic sensor by applying loads on the null locations of multiple resonant modes

Magnetoelastic sensors are mass sensitive sensors commonly used for stress and pressure measurement, as well as chemical and biological monitoring when combined with a functionalized coating. Magnetoelastic sensors are typically made of free-standing, rectangular strips of magnetoelastic materials that exhibit longitudinal, extensional vibrations due to the excitation of magnetic fields. A single magnetoelastic sensor is generally used to monitor one parameter since only the fundamental resonant frequency is measured. Multiple-parameter sensing in close proximity has previously been achieved by using multiple magnetoelastic sensors of different dimensions and tracking their resonant frequencies independently. However, this requires a large surface area and inconvenient layout of dissimilarly shaped sensors. This paper presents a technique for monitoring multiple parameters with a single magnetoelastic sensor by applying separate mass loads at the null points (points of zero vibration) of multiple resonant modes. Applying a load at a null location does not affect the corresponding resonant mode but alters the resonant frequencies of other modes. Therefore, by isolating the variables of interest to multiple null points and simultaneously measuring the resonant frequency shifts of related resonant modes, the masses at each null location can be calculated. Results showed that changing the coverage at a null location along the width of the sensor can be used to minimize the loading effect on the corresponding resonant mode. In contrast, changing the lengthwise coverage can maximize the loading effect on other resonant modes, thus increasing the mass sensitivity of the sensor. Furthermore, simultaneously applying loads to null points of multiple resonant modes had a nearly additive effect, allowing detection of multiple parameters with a single magnetoelastic sensor.

A study of the influence of cooling water on the structural modes and vibro-acoustic characteristics of a gasoline engine

The influence of the cooling water on the vibration mode and damping characteristics of an engine was evaluated through experimental and simulation methods. The wet mode method of the fluid–structure interaction field was applied in numerical analysis, which led to several significant conclusions. Several additional fluid related modes were present when the effect of cooling water was considered. Meanwhile, the frequencies of other modes were almost the same. On the other hand, the damping characteristics of an engine were changed while the cooling water was used. For Rayleigh damping, the cooling water effect has made the mass matrix scale factor α nearly double and the stiffness matrix scale factor β almost unchanged. The engine surface vibration acceleration magnitude was calculated by means of the multi-body dynamic analysis. It was shown that the calculated vibration acceleration magnitude was close to the measured one when the cooling water was taken into account. Furthermore, acoustic simulation results were estimated by Boundary Element Method, which revealed that the sound power level of the radiation noise of most engine components was lower than that with the fluid structure interaction model being applied in the engine block modeling. The overall sound power level of the whole engine radiation noise was increased by 3.6dB when the effect of the cooling water was considered, which demonstrated that the effect of the cooling water on the engine vibro-acoustic characteristics should not be neglected during the computation. This paper has disclosed the influences of the cooling water on the engine structural modes, damping, sound power level of the engine radiation noise and a systematic approach for evaluation of the influences.

Transient wave motion analysis for modal suppression of a circular cylindrical wedge wave ultrasonic motor

This paper describes a modal suppression method for improving the transient wave motion responses of a wedge wave ultrasonic motor (WW-USM). Typically, an ultrasonic motor operates near the resonant frequency of a specific vibration mode that must be adequately separated from the resonant frequencies of other modes. In the developed prototype, longitudinal modes accompany a transient response to the designed flexural mode, because electrodes are placed at the half-wavelength around the piezoelectric lead zirconate titanate tube (PZT tube). An uncertain disturbance can be easily induced at the instant in which the motor is switched on or off, or when the direction of the motor is changed. This study proposes a modification of the electrode arrangement for suppressing these unexpected modes. The simulation and experimental results indicated that performance improved when the electrodes were placed over the entire-wavelength around the PZT tube. When the longitudinal mode produced by exciting the WW-USM was suppressed, the transient response of the revolution speed became quicker and smoother than that obtained using the previous design. The proposed modification increased the maximal output power and efficiency of the mechanical–electrical transformation by 21%.

Bi-dimensional finite element analysis for modal separation of a circular cylindrical WW-USM

This paper describes a modal separation model that improves the performance of wedge wave ultrasonic motors (WW-USMs) using the bi-dimensional finite element analysis (Bi-d FEA) method. Most USMs operate near the resonant frequency of a specific vibration mode, which must be well separated from the resonant frequencies of other modes. In the current prototype, unexpected disturbance induced at the instant of switching on/off or changing direction of the motor appeared in simulations and actual measurements. These fluctuations are due to vibration modes other than the driving mode occurring around the operating frequency. Bi-d FEA numerical simulation results indicate that selecting an appropriate height for the upper base under the piezoelectric tube achieves excellent modal separation. Measurements of the traveling wave taken by modal sensors show that the proposed motor performs better than traditional motors, offering a faster transient response in revolution speed and a more stable design. Suppressing the unexpected modes in excitation of the WW-USM increased the maximum output torque by 50% and the efficiency of mechanical/electrical transformation by 50%.

Coupled bending, longitudinal and torsional vibrations of a cracked rotor

The coupling between longitudinal, lateral and torsional vibrations is studied together for a rotating cracked shaft. These coupling mechanisms have been studied here with a response-dependent non-linear breathing crack model. Most of the earlier work on coupled vibrations due to crack has been either on stationary shaft or on rotating shaft with open crack model. The stiffness matrix of a Timoshenko beam element is modified to account for the effect of a crack and all the six degrees of freedom per node are considered. Coupled torsional–longitudinal vibrations for a cracked rotor that has not been reported earlier and coupled torsional–bending vibrations with a breathing crack model have been studied. An attempt has been made to reveal crack specific signatures by using additional external excitations. Since all the couplings are accounted, the excitation in one mode leads to an interaction between all the modes. This, coupled with the rotational effect of a cracked rotor and the non-linearities due to a breathing crack model introduces sum and difference frequencies in the response of cracked rotor. The co-existence of frequencies of other modes in the frequency spectra of a particular mode and the presence of sum and difference frequencies around the excitation frequencies and its harmonics could be useful indicators for crack diagnosis.

Microwave resonators with internal structure

AbstractIf it is possible to divide a resonator in such a way that its specific modal electromagnetic fields are not disturbed, the resonant frequency of such a mode should change very little. On the other hand, the frequencies of other modes should change significantly. Hence, by using this approach, the spurious characteristics of the resonator can be controlled. Also, this division can be used as a means of improving the Q characteristic and the temperature behavior. In addition, it is possible to form a resonator by collecting many small particles. This is a concept for artificial media. By selection of particles and their assembly configuration, various resonant characteristics should become possible. In this paper, a method for improving the resonator characteristics by the above two dual methods is proposed. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(12): 38–48, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10058

Simultaneous optimum design method of dynamic absorbers for controlling multimodes.

This paper proposes a new method of simultaneous optimum design of dynamic absorbers for controlling multi-degree-of-freedom systems when each mode interacts dynamically. This method is based on the sensitivity analysis which examines the affect of variation in natural frequencies of other modes after mounting a dynamic absorber on the controlled mode. Resonance peaks of all modes are adequately controlled by mounting the corresponding dynamic absorbers, which were designed through iterative calculation using this method. The effectiveness of this method is demonstrated theoretically and experimentally, using a seven-degrees-of-freedom system, a Γ-shaped structure and a rectangular plate.

Temperature dependent properties of the dynamics of a two-level system interacting with a radiation field

A system of two-level atoms interacting with one mode of a quantized radiation field is considered by the quantum field theory. The existence of a phase transition to the spontaneous coherent state (SCS) is shown. This state arises from the Bose-Einstein condensation of the photons of the radiation field. The spectrum of the collective excitations of the system is found for all temperatures. In the disordered phase there are two modes of transverse collective excitations when the sizes of an atomic sample are much less than the wavelength and three modes of excitations when the sizes of an atomic sample can be compared with the wavelength of the radiation field. One of the modes is a soft mode provided that the threshold condition is fulfilled. In the SCS there are six transverse collective modes. One of them has zero frequency and the frequencies of other modes increase with decreasing temperature. Moreover, in the SCS three longitudinal collective excitations arise. The photon Green's function has a pole at the origin in the condensed phase which shows that the radiation field is in a coherent state.

Some perturbation effects in cavity resonators

An investigation, partly theoretical and partly experimental, has been made of some effects which occur when the boundary of a cavity is deformed slightly. First, the theory of natural electromagnetic oscillations inside lossless cavities is summarized. Then a general theory, following along the lines of conventional first-order perturbation theory, is given. The theory has been applied to the perturbation of a right-circular cylindrical cavity. Two cases have been considered: the E010 mode, a non-degenerate case; and the H011 and E111 modes, a triply degenerate case. These two cases have also been investigated experimentally. Theory and experiment are in reasonable agreement, even for quite large deformations, when the deformation is applied gradually over a large area of the cavity wall. For sharp abrupt changes in the geometry of the cavity wall, however, it appears that the first-order perturbation theory can be applied only for very small distortions. The general results, theoretical and experimental, which have been obtained, show that if the frequency of the operating mode is well separated from the frequencies of other modes, a deformation of the boundary changes only the frequency of the operating mode and not its electromagnetic field configuration. If the frequency of the operating mode is near to the frequencies of other modes, a slight deformation of the cavity boundary, as well as changing the frequency of the operating mode, may also change its electromagnetic field configuration. “Lossy” material or resistance wires, introduced into a cavity with a view to damping out unwanted modes, may also affect the desired resonance if certain types of deformation are present.