Flapwise Bending Vibration Analysis of Rotating Tapered Rayleigh Beams for the Application of Offshore Wind Turbine Blades

The flapwise bending vibrational equations of tapered Rayleigh beam are derived based on Hamilton’s principle.The corresponding vibrational characteristics of rotating tapered Rayleigh beams are investigated via variational iteration method(VIM).Natural frequencies and corresponding mode shapes are examined under various rotation speed,taper ratio and slenderness ratio focusing on two types of tapered beam.The convergence of VIM is examined as part of the paper.Validation of VIM solution is made by referring to results available in other literature and corresponding results show that VIM is capable of yielding precise results in a very efficient way.

THE FREE BENDING VIBRATION OF CYLINDRICAL TANK PARTIALLY FILLED WITH-LIQUID AND SUBMERGED IN WATER

This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.

Bending vibration analysis of rotating machineries using multibody dynamics technology — development of computer program RotB

This paper examines a computer program developed to analyze the vibration of rotating machineries based on theories of vibration and multibody dynamics （MBD）. Bending vibration problems of rotating machineries have generally been categorized as either linear or nonlinear. Linear problems can be formulated by standard methods and nonlinear problems can be formulated by MBD methods. In our study, nonlinear problems are treated by the use of a general-purpose computer program, RecurDyn （RD）. In the program we developed, rotor bending vibration analysis （RotB） structural properties such as shafts, rotating rotary disks, unbalanced masses and foundation structures are modeled as multibody elements. Also, nonlinearities such as contact, non-symmetrical shaft effects, bearing characteristics, nonlinear restoring and damping characteristics in the bearings are taken into account. The computational results demonstrate the validity of RotB.

Improvement for design of beam structures in large vibrating screen considering bending and random vibration

Demand for large vibrating screen is huge in the mineral processing industry. As bending and random vibration are not considered in a traditional design method for beam structures of a large vibrating screen, fatigue damage occurs frequently to affect the screening performance. This work aims to conduct a systematic mechanics analysis of the beam structures and improve the design method. Total motion of a beam structure in screening process can be decomposed into the traditional followed rigid translation(FRT), bending vibration(BV) and axial linear-distributed random rigid translation(ALRRT) excited by the side-plates. When treated as a generalized single-degree-of-freedom(SDOF) elastic system analytically, the BV can be solved by the Rayleigh's method. Stochastic analysis for random process is conducted for the detailed ALRRT calculation. Expressions for the mechanics property, namely, the shearing force and bending-moment with respect to BV and ALRRT, are derived, respectively. Experimental and numerical investigations demonstrate that the largest BV exists at the beam center and can be nearly ignored in comparison with the FRT during a simplified engineering design. With the BV and FRT considered, the mechanics property accords well with the practical situation with the maximum error of 6.33%, which is less than that obtained by traditional method.

Dynamic modeling and analysis on rigid-flexible coupling between vertical chatter and transverse bending vibration in process of cold rolling

Considering the dynamic variation of roll gap and the transverse distribution of dynamic rolling force along the work roll width direction, the movement and deformation of rolls system, influenced by the coupling of vertical chatter and transverse bending vibration, may cause instability and also bring product defect of thickness difference. Therefore, a rigid-flexible coupling vibration model of the rolls system was presented. The influence of dynamic characteristics on the rolling process stability and strip thickness distribution was investigated. Firstly, assuming the symmetry of upper and lower structures of six-high rolling mill, a transverse bending vibration model of three-beam system under simply supported boundary conditions was established, and a semi-analytical solution method was proposed to deal with this model. Then, considering both variation and change rate of the roll gap, a roll vertical chatter model with structure and process coupled was constructed, and the critical rolling speed for self-excited instability was determined by Routh stability criterion. Furthermore, a rigid-flexible coupling vibration model of the rolls system was built by connecting the vertical chatter model and transverse bending vibration model through the distribution of dynamic rolling force, and the dynamic characteristics of rolls system were analyzed. Finally, the strip exit thickness distributions under the stable and unstable rolling process were compared, and the product shape and thickness distribution characteristics were quantitatively evaluated by the crown and maximum longitudinal thickness difference.

High-order harmonic generation of CO_2 with different vibrational modes in an intense laser field

We apply the strong-field Lewenstein model to demonstrate the high-order harmonic generation of CO2 with three vibrational modes（balance vibration,bending vibration,and stretching vibration） driven by an intense laser field.The results show that the intensity of harmonic spectra is sensitive to molecular vibrational modes,and the high harmonic efficiency with stretching vibrational mode is the strongest.The underlying physical mechanism of the harmonic emission can be well explained by the corresponding ionization yield and the time-frequency analysis.Finally,we demonstrate the attosecond pulse generation with different vibrational modes and an isolated attosecond pulse with a duration of about 112 as is generated.

Photodissociation Spectra of OCS＋ via B2∑＋←X2П Transitions

In the wavelength range of 231-275 nm, we have studied the mass-resolved dissociation spectra of OCS＋ via B2∑＋←X2П3/2（000） and B2∑＋←X2П1/2（000, 001） transitions by preparing OCS＋ ions in the well-defined spin-orbit states. The spectroscopic constants of v1 （CS stretch）=828.9 （810.4） cm-1, u2 （bend）=491.3 cm-1 and v3（CO stretch）=1887.2 cm-1 for OCS＋（B2∑＋） are deduced. The observed dependence of the v2（bend） mode excitation of B2∑＋ on the spin-orbit splitting of X2П（Ω=1/2, 3/2） in the B2∑＋←-X2П transition can be attributed to the K coupling between the （000）2П1/2 and （010）2∑＋/2 vibronic levels of X2П state, which makes the B2∑＋（010）←X2П1/2（000） transition possible.

WELL－POSEDNESS AND CONTROLLABILITY AND OBSERVABILITY OF A COUPLED VIBRATING SYSTEM

In this paper, we derive a new description form of coupled bending and torsionalvibrating system with boundary control and observation through Green's formula and provethat it is equivalent to the original form. On the basis of this. we prove the control system iswell-posed in time and frequency domain and completely controllable and observable.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

High-frequency vibration analysis of thin plate based on wavelet-based FEM using B-spline wavelet on interval

The wavelet finite element methods （WFEMs） own higher calculation accuracy and efficiency for structure analysis. Unfortunately, the existing WFEMs are still limited in low-frequency domain when capturing dynamic characteristics of thin plate. This paper proposes the wavelet multi-elements method based on C1 type B-spline Kirchhoff plate （CIBKP） element to break up this limitation. The validity, numerical stability and convergence respectively are investigated systematically in numerical study. The corresponding results show that the calculation accuracy and numerical stability are very excellent when predicting the high-order natural frequency. The maximum relative errors can be rapidly reduced to 0.4% within the first 1000 modes of thin plate under simply supported. Besides, the method is suitable for predicting the dynamic characteristics of thin plate under various boundary conditions.

Evaluation of vibration stress of TA11 titanium alloy blade by quantitative fractography

Vibration fatigue is the main failure mode of compressor blade. Evaluating the vibration stress of blade that leads to cracking is very useful for analysis of vibration fatigue. In this paper, fatigue stress estimation methods by quantitative fractography were studied through experimental blade and in-service first-stage compressor blade in order to evaluate the initiation vibration stress of in-service blade. The analysis process of initiation vibration stress was established. The evaluating result of vibration stress of in-service blade subjected to centrifugal force and bending vibration stress agrees with aero engine test result. It is shown that the evaluation method can not only evaluate the equivalent fatigue stresses of different crack depths but also yield the initiation equivalent fatigue stress.

FINITE ELEMENT MODELING AND ROBUST VIBRATION CONTROL OF TWO-HINGED PLATE USING BONDED PIEZOELECTRIC SENSORS AND ACTUATORS

Active vibration control for a kind of two-hinged plate is developed in this paper. A finite element model for the hinged plate integrated with distributed piezoelectric sensors and actuators is derived, including bending and torsional modes of vibration. In this model, the hinges are simplified as regular plate elements to facilitate operation. The state space representations for bending and torsional vibrations are obtained. Based on two low-order models of the bending and torsional motion, two H∞ robust controllers are designed for suppressing the vibrations of the bending and torsional modes, respectively. The simulation results indicate the effectiveness and feasibility of the designed H~~ controllers. The vibration magnitudes of the low-order modes can be reduced without affecting the high frequency modes.

Design and experiments of a small resonant inchworm piezoelectric robot

A small resonant inchworm piezoelectric robot with six driving feet which are set evenly along the circumference is proposed and tested.A bonded-type structure is adopted to realize a small size.The radial bending vibration mode and longitudinal vibration mode are excited at the same frequency.The superposition of these two vibration modes makes the driving feet produce elliptical motions.And the driving force can be generated by friction coupling between the driving foot and the operating plane.The structure of the robot is designed by finite element simulation.The geometric parameters are adjusted to make the resonant frequencies of the vibration modes as close as possible.The elliptical trajectories generated at the driving feet are discussed in detail.The vibration and motion characteristics of the prototype are tested,and the resonant frequencies of the radial bending mode and the longitudinal vibration mode are degenerated successfully.The optimal working frequency of the prototype is 21.5 kHz.The maximum speed of the prototype is 200 mm/s,and the displacement resolution is 0.71μm.The measured results show that the resonant inchworm piezoelectric robot can be used for fast and high-precision transportation in narrow space.

One-step and Continuous Fabrication of Coaxial Piezoelectric Fiber for Sensing Application

Although there has been rapid advancement in piezoelectric sensors,challenges still remain in developing wearable piezoelectric sensors by a one-step,continuous and environmentally friendly method.In this work,a 1D flexible coaxial piezoelectric fiber was directly fabricated by melt extrusion molding,whose core and sheath layer are respectively slender steel wire(i.e.,electrode)and PVDF(i.e.,piezoelectric layer).Moreover,such 1D flexible coaxial piezoelectric fiber possesses short response time and high sensitivity,which can be used as a selfpowered sensor for bending and vibration sensing.More interestingly,such 1D flexible coaxial piezoelectric fiber(1D-PFs)can be further endowed with 3D helical structure.Moreover,a wearable and washable motion monitoring system can be constructed via braiding such 3D helical piezoelectric fiber(3D-PF)into commercial textiles.This work paves a new way for developing 1D and 3D piezoelectric fibers through a one-step,continuous and environmentally friendly method,showing potential applications in the field of sensing and wearable electronics.