A cylindrical standing wave ultrasonic motor using bending vibration transducer

A cylindrical standing wave ultrasonic motor using bending vibration transducer was proposed in this paper. The proposed stator contains a cylinder and a bending vibration transducer. The two combining sites between the cylinder and the transducer locate at the adjacent wave loops of bending vibration of the transducer and have a distance that equal to the half wave length of bending standing wave excited in the cylinder. Thus, the bending mode of the cylinder can be excited by the bending vibration of the transducer. Two circular cone type rotors are pressed in contact to the end rims of the teeth, and the preload between the rotors and stator is accomplished by a spring and nut system. The working principle of the proposed motor was analyzed. The motion trajectories of teeth were deduced. The stator was designed and analyzed with FEM. A prototype motor was fabricated and measured. Typical output of the prototype is no-load speed of 165 rpm and maximum torque of 0.45 N m at an exciting voltage of 200 V_rms.     

FEM dynamic model for active vibration control of flexible linkages and its application to a planar parallel manipulator

Development of dynamic models of flexible linkages, with flexible motion caused by rigid body motion and electromechanical coupling of transduction devices and the host linkage, is very important for the design of active vibration control laws for flexible-link mechanisms. In the first part of this paper, the Lagrange finite element (FE) formulation is used to derive such a dynamic model for a flexible planar linkage with two translational and one rotational degrees of freedom. Linear electromechanical coupling of surface-bonded lead zirconate titanate (PZT) patches with the host linkage is incorporated into the model. In the second part of this paper, this dynamic model is applied to a flexible-link planar parallel manipulator. Based on standard kineto-elastodynamic assumptions, the linkage dynamic model is simplified and simulation of strain rate feedback control using PZT sensors and actuators is performed. Numerical results show that PZT actuators effectively damp vibration of the flexible linkages.     

Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

新型指挥仪模拟器的分析与研究

针对美国6S04指挥仪模拟器中几种运动方式的输出波形,研究和分析了新型模拟器关于正弦、等速、方波、等速 方波以及阶跃等运动方式的数学模型和实现方法。对于新型模拟器中正弦运动的函数计算,采用建立正弦快速查表和定时中断程序结合的方法实现。并以建立的正弦和等速运动的数学模型为例,对模拟器中正弦和等速运动曲线图进行分析和验证。在某模拟器的设计中,该数学模型结合虚拟仪器技术,得到很好的应用,避免了模拟器中复杂的电子线路设计。     

多级阻振质量阻隔振动波的传递特性研究

利用波动理论的分析、处理方法,分析了多级平行阻振质量阻隔振动波传递的特性,给出了多级阻振质量对平面弯曲波传递的阻抑公式,讨论了平面弯曲波传递时形成的穿透频段和堵塞频段,并进行了相应的算例分析,采用有限元法对多级阻振质量的隔振性能进行了数值计算,结果表明:阻振质量对偏离法向角的弯曲波分量的阻抑较强,传递能量的损失较大;多级阻振质量能够较好地阻抑结构声的传递,且阻抑效果随着阻振级数的增加而增大;在有几个阻振质量的情况下,通过改变它们的平行性,可以提高其隔振效果;且如果将不同质量、不同横截面形状的阻振质量前后交错配置,同样可以使总的隔振效果提高,这对于多级阻振质量在船体结构减振降噪中的应用具有重要的参考意义。     

Wormlike chain theory and bending of short DNA

The probability distributions for bending angles in double helical DNA obtained in all-atom molecular dynamics simulations are compared with theoretical predictions. The computed distributions remarkably agree with the wormlike chain theory and qualitatively differ from predictions of the subelastic chain model. The computed data exhibit only small anomalies in the apparent flexibility of short DNA and cannot account for the recently reported AFM data. It is possible that the current atomistic DNA models miss some essential mechanisms of DNA bending on intermediate length scales. Analysis of bent DNA structures reveal, however, that the bending motion is structurally heterogeneous and directionally anisotropic on the length scales where the experimental anomalies were detected. These effects are essential for interpretation of the experimental data and they also can be responsible for the apparent discrepancy.     

Robust visual tracking based on multi-cue integration

Traditional color-based mean shift tracking algorithm is unable to accurately track the object. To address this problem, we present an improved tracking algorithm. The improved tracker integrates the color and motion cues which characterize the appearance and motion information of the object, respectively. These two visual cues can complement each other and make for more precise target localization. Experiments show that the proposed tracking algorithm has better performance than the traditional mean shift tracker.     

An actuator for the n=2 circumferential mode of a pipe

The axial propagating wave of the n=2 circumferential mode in a pipe can cause large vibration when the wave cuts on and may cause fatigue damage or transmit structure-borne noise along the pipe. For this reason, a control system (passive or active) is desirable. In this paper, a PZT modal actuator for the n=2 mode, which could be used in an active control system, is described. It is constructed from a set of PZT elements bonded to the pipe. By arranging them in form of the n=2 mode, only the motion of that particular mode is generated and is proportional to the applied voltage. With two PZT modal actuators, which are in forms of sine and cosine functions, the orientation of the propagating wave of the n=2 mode can be modified to any angle. In this paper a theoretical model for the actuator is developed and is validated by some experimental work.     

LOCALIZED FAMILIES OF BENDING WAVES IN A THIN MEDIUM-LENGTH CYLINDRICAL SHELL UNDER PRESSURE

The initial-boundary-value problem for the equations describing motion of a thin, medium-length, non-circular cylindrical shell is examined. The shell edges are not necessarily plane curves, with the conditions of a joint support, a rigid clamp or a free edge being considered as the boundary conditions. The shell is supposed to experience normal internal (or external) dynamic pressure which may be non-uniform in the circumferential direction. It is assumed that the initial displacements and velocities of the points at the shell middle surface are functions decreasing rapidly away from some generatrix. Using the complex WKB method the asymptotic solution of the governing equations is constructed by superimposing localized families (wave packets) of bending waves running in the circumferential direction. The dependence of frequencies, group velocities, amplitudes and other dynamic characteristics upon variable pressure and geometrical parameters of the shell are studied. As an example, the wave forms of motion of a circular cylindrical shell with sloping edges under growing dynamic pressure are considered. The effect of localization of bending vibrations near the longest generator as well as the effects of reflection, focusing and increasing amplitude in the running wave packets are revealed.     

Active control of sound radiated by a submarine in bending vibration

This paper theoretically investigates the use of inertial actuators to reduce the sound radiated by a submarine hull in bending vibration under harmonic excitation from the propeller. The radial forces from the propeller are tonal at the blade passing frequency and are transmitted to the hull through the stern end cone. The hull is modelled as a fluid loaded cylindrical shell with ring stiffeners and two equally spaced bulkheads. The cylinder is closed by end-plates and conical end caps. The actuators are arranged in circumferential arrays and attached to the prow end cone. Both Active Vibration Control and Active Structural Acoustic Control are analysed. The inertial actuators can provide control forces with a magnitude large enough to reduce the sound radiated by the vibrations of the hull in some frequency ranges.     

Piezoelectric linear motor concepts based on coupling of longitudinal vibrations

Classically, rotary motors with gears and spindle mechanisms are used to achieve translatory motion. In means of miniaturization and weight reduction piezoelectric linear motors are of interest. Several ultrasonic linear motors found in literature base on the use of two different vibration modes. Most often flexural and longitudinal modes are combined to achieve an elliptic micro-motion of surface points. This micro-motion is converted to direct linear (or translatory) motion of a driven slider. To gain high amplitudes of the micro-motion and thus having a powerful motor, the ultrasonic vibrator should be driven near the eigenfrequency of its modes. Additionally, low mechanical and electrical losses lead to increased efficiency and large amplitude magnification in resonance. This demands a geometrical design that fits the eigenfrequencies of the two different modes. A frequency-deviation of only a few percent leads to non-acceptable disturbance of the elliptical motion. Thus, the mechanical design of the vibrators has to be done very carefully. Within this contribution we discuss different motor designs based on the coupling of two the same longitudinal vibrations within one structure to generate an elliptic motion of surface points. Different concepts based on piezoelectric plates and Langevin transducers are compared. Benefits and drawbacks against the combination of longitudinal and bending modes will be discussed. Numerical results of the stator vibration as well as motor characteristics are validated by measurements on different prototypes.     

Analysis of flexural wave velocity and vibration mode in thin cylindrical shell

The relationship between the flexural wave velocity and the excited vibration mode of a thin cylindrical shell is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, all of these vibration modes are not excited actually. To estimate the excited vibration mode, the concept of "modified bending stiffness" is introduced, and the influence of each stress component upon the modified bending stiffness is analyzed. The excited mode is theoretically discriminated from the nonexcited mode based on the smallness of this modified bending stiffness. The validity of our theory is confirmed by an excellent agreement between theoretical and experimental results on flexural wave velocity.     

铝棒振动波动实验的理论分析

结合实际从理论上分析和解释了铝棒振动波动的实验，并揭示出两端自由的金属棒内部的振动传播规律。     

The benefit of practice for sound localization without sight

An experiment was designed to determine whether normally sighted human subjects would be able to adapt to the handicapping effects of sudden deprivation of visual cues on horizontal plane sound localization. Two groups of sighted normal-hearing young adults participated. One group was allowed the benefit of sight. The other group was blindfolded. Measurements of accuracy and the time to respond were made daily over the course of five consecutive days, in a semi-reverberant sound proof booth that modeled listening in a small office. Sound localization was assessed using an array of eight speakers that surrounded the subject in space. Each day, one block of 120 trials was presented for each of three stimuli, two one-third octave noise bands, centred at 0.5 and 4 kHz, and broadband noise, to assess the utilization of interaural temporal difference cues, interaural level difference cues and binaural and spectral cues in combination. Blindfolded subjects were relatively less accurate than sighted subjects. Both groups showed gains with practice, the blindfolded group to a greater degree, largely due to improvements in the use of spectral cues. The blindfolded group took longer to respond than the sighted group, but showed greater decrements in response time with practice.     

NON-LINEAR FREE VIBRATION ANALYSIS OF A STRING UNDER BENDING MOMENT EFFECTS USING THE PERTURBATION METHOD

In this paper, the non-linear free vibration of a string with large amplitude is considered. The initial tension, lateral vibration amplitude, cross-section diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. Therefore, it is impossible to use the classical equation of transverse motion assuming a small amplitude. On the other hand, by increasing the string cross-sectional diameter, the bending moment effect will increase dramatically, and it will act as an impressive restoring moment. Considering the effects of the bending moments, the non-linear equation governing the large amplitude transverse vibration of a string is derived. The time-dependent portion of the governing equation has the form of the Duffing equation. Due to the complexity and non-linearity of the derived equation and the fact that there is no established exact solution method, the equation is solved using the perturbation method. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration of a string without bending moment effects.     

Flat band localization due to self-localized orbital

We discover a new wave localization mechanism in a periodic wave system, which can produce a novel type of flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band lattices. The first example we give is a designed electron waveguide (EWG) on 2DEG with special periodic confinement potential. Numerical calculations show that, with proper confinement geometry, electrons can be completely localized in an open waveguide. We interpret this flat band localization (FBL) phenomenon by introducing the concept of self-localized orbitals. Essentially, each unit cell of the waveguide is equivalent to an artificial atom, where the self-localized orbital is a special eigenstate with unique spatial distribution. These self-localized orbitals form the flat bands in the waveguide. Such self-localized orbital induced FBL is a general phenomenon of wave motion, which can arise in any wave systems with carefully engineered boundary conditions. We then design a metallic waveguide (MWG) array to illustrate that similar FBL can be readily realized and observed with electromagnetic waves.     

Mode-splitting and quasi-degeneracies in circular plate vibration problems: The example of free vibrations of the stator of a traveling wave ultrasonic motor

In systems with rotational symmetry, bending modes occur in doubly-degenerate pairs with two independent vibration modes for each repeated natural frequency. In circular plates, the standing waves of two such degenerate bending modes can be superposed with a 1/4 period separation in time to yield a traveling wave response. This is the principle of a traveling wave ultrasonic motor (TWUM), in which a traveling bending wave in a stator drives the rotor through a friction contact. The stator contains teeth to increase the speed at the contact region, and these affect the rotational symmetry of the plate. When systems with rotational symmetry are modified either in their geometry, or by spatially varying their properties or boundary conditions, some mode-pairs split into singlet modes having distinct frequencies. In addition, coupling between some pairs of distinct unperturbed modes also causes quasi-degeneracies in the perturbed modes, which leads their frequency curves to approach and veer away in some regions of the parameter space. This paper discusses the effects of tooth geometry on the behavior of plate modes under free vibration. It investigates mode splitting and quasi-degeneracies and derives analytic expressions to predict these phenomena, using variational methods and a degenerate perturbation scheme for the solution to the plate’s discrete eigenvalue problem; these expressions are confirmed by solving the discrete eigenvalue problem of the plate with teeth.     

Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

We study the influence of nonlinearity on wave localization in one-dimensional random media. Using a discrete nonlinear Schrödinger equation with a random on-site energy term, we calculate the localization length in a numerically exact manner. Unlike in many previous works, we fix the intensity of the incident wave and calculate quantities as a function of other parameters. We find that localization is enhanced due to nonlinearity for the focusing and defocusing nonlinearities. For small nonlinearity, the localization length is a decreasing function of nonlinearity. For sufficiently large nonlinearity, however, the localization length is found to approach a saturation value.     

Underwater localization of pure tones by harbor seals (Phoca vitulina)

The underwater sound localization acuity of harbor seals (Phoca vitulina) was measured in the horizontal plane. Minimum audible angles (MAAs) of pure tones were determined as a function of frequency from 0.2 to 16 kHz for two seals. Testing was conducted in a 10-m-diam underwater half circle using a right/left psychophysical procedure. The results indicate that for both harbor seals, MAAs were large at high frequencies (13.5 degrees and 17.4 degrees at 16 kHz), transitional at intermediate frequencies (9.6 degrees and 10.1 degrees at 4 kHz), and particularly small at low frequencies (3.2 degrees and 3.1 degrees at 0.2 kHz). Harbor seals seem to be able to utilize both binaural cues, interaural time differences (ITDs) and interaural intensity differences (IIDs), but a significant decrease in the sound localization acuity with increasing frequency suggests that IID cues may not be as robust as ITD cues under water. These results suggest that the harbor seal can be regarded as a low-frequency specialist. Additionally, to obtain a MAA more representative of the species, the horizontal underwater MAA of six adult harbor seals was measured at 2 kHz under identical conditions. The MAAs of the six animals ranged from 8.8 degrees to 11.7 degrees , resulting in a mean MAA of 10.3 degrees .