Dynamic stability of pretwisted columns under periodic axial loads

This paper deals with the parametric instability of pretwisted columns subjected to static and periodic axial loads. The governing equations of the problem are reduced to time domain by applying Galerkin's method. The instability regions are determined with the procedure proposed by Hsu. The analysis includes free vibration and static buckling of the column as special cases. Although the method is quite general, numerical calculations are carried out only for a simply supported column. Free vibration frequencies, static buckling loads and the coefficients of the instability regions are obtained for various values of the pretwisting angle and those of the cross sectional rigidity ratio of the column.     

On the flexural vibration of cylinders under axial loads: Numerical and experimental study

The flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper. Natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the Ritz method with terms of power series in the coordinate directions as approximating functions. The effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory, therefore, geometrically nonlinear strain–displacement relations with second-order terms are considered here. The natural frequencies of free–free, clamped–clamped, and sliding–sliding cylinders subjected to axial loads are calculated using the proposed three-dimensional Ritz approach and are compared with those obtained with the finite element method and the Bernoulli–Euler theory. Different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results. An approach based on the Ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression. The results show that for low compressions the cylinder behaves similarly to a sliding–sliding cylinder, whereas for high compressions the cylinder vibrates as a clamped–clamped one.     

Vibratory source identification by using the Finite Element Model of a subdomain of a flexural beam

This paper proposes the identification of vibration excitations by an inverse method. The use of the local operator of a structure, for which the vibration field is obtained by measurements, is investigated. This method has already been developed on analytically known structures, but there are as yet few applications. The goal of this paper is to adapt the same technique by using an operator obtained with the Finite Element Method rather than a discretised differential motion equation. The first difficulty is the measurement of rotational degrees of freedom. A concept analogous to an observation matrix enabling only the measurement of displacements is then proposed. The method of extracting the operator on a part of the structure is also discussed. Two variants are proposed: an operator with free boundary conditions and a truncated operator without boundary conditions. The first permits identifying internal forces at the boundaries of the subdomain, whereas the second ignores them. In order to regularise the inverse method, a Tikhonov approach is used. An important point of this paper is the discussion of the effect of this regularisation which implies ambiguities between reconstructed forces and moments in the results. The possibility of an a priori “force only” assumption is then demonstrated and recommended. After illustrations obtained from numerical simulations on beams, an experimental validation is provided for a beam excited by a shaker where several signals are used, giving several signal to noise ratios. The results are discussed and compared to the force measured directly by a piezoelectric sensor.     

Propagation of mode shape errors in structural identification

It is of interest to the modal testing and health monitoring community to quantify how an error in any identified mode shape propagates to the identified flexibility matrix. Here this problem is investigated in a probabilistic framework. The approach followed involves deriving analytical expressions to track how errors, due to random deviations between identified and “true” mode shapes, propagate to the Modal Assurance Criterion (MAC) and the Coordinate Modal Assurance Criterion (COMAC) values as well as the estimated flexibility matrix. The comparison of the expected values and variances of these errors identifies the inconsistency between the magnitude of errors in the MAC and COMAC values and the identified flexibility matrix. The analytical results are further validated via Monte Carlo simulations. Finally, two mode shape comparison criteria, termed as the Flexibility Proportional Modal Assurance Criterion (FPMAC) and the Flexibility Proportional Coordinate Modal Assurance Criterion (FPCOMAC), are proposed. These new criteria aim to mimic the expected error in the predicted flexibility matrix in a direct comparison of the identified and “true” mode shapes, and hence they can be used to complement MAC and COMAC in interpreting the analysis results.     

Dynamic axle and wheel loads identification: laboratory studies

Two methods have been reported by Zhu and Law to identify moving loads on the top of a bridge deck. One is based on the exact solution (ESM) and the other is based on the finite element formulation (FEM). Simulation studies on the effect of different influencing factors have been reported previously. This paper comparatively studies the performances of these two methods with experimental measurements obtained from a bridge/vehicle system in the laboratory. The strains of the bridge deck are measured when a model car moves across the bridge deck along different paths. The moving loads on the bridge deck are identified from the measured strains using these two methods, and the responses are reconstructed from the identified loads for comparison with the measured responses to verify the performances of these methods. Studies on the identification accuracy due to the effect of the number of vibration mode used, the number of measuring points and eccentricities of travelling paths are performed. Results show that the ESM could identify the moving loads individually or as axle loads when they are travelling at an eccentricity with the sensors located close to the travelling path of the forces. And the accuracy of the FEM is dependent on the amount of measured information used in the identification.     

考虑弯曲和轴向振动模态的一维梁压电阻抗模型及试验研究

同时考虑一维梁结构的弯曲和轴向振动,对其压电阻抗模型进行建模分析和试验验证。在0.02～42 kHz频段内区分并标记了一维钢梁弯曲振动模态前18阶及轴向振动模态前3阶。结果表明:在0.02～7.5kHz频段内,数值计算和试验结果中谐振峰对应频率的相对误差较大:11.7%～16.5%,其原因可能是低频时振动能量较低且波的传播受结构阻尼、边界条件及环境噪音等因素影响较为明显;在7.5～42kHz范围内,两者谐振峰位置符合良好,相对误差较小:0.11%～2.31%,表明该模型在高频段具有较好的适用性;轴向振动模态对应频率大于弯曲振动模态。本研究为结构健康监测过程中检测频段的选取及损伤信息的提取提供参考。     

Control of flexural waves on a beam using distributed vibration neutralisers

This paper is concerned with the use of distributed vibration neutralisers to control the transmission of flexural waves on a beam. Of particular interest is an array of beam-like neutralisers and a continuous plate-like neutraliser. General expressions for wave transmission and reflection metrics either side of the distributed neutralisers are derived. Based on transmission efficiency, the characteristics of multiple neutralisers are investigated in terms of the minimum transmission efficiency, the normalised bandwidth and the shape factor, allowing optimisation of their performance. Analytical results show that the band-stop property of the neutraliser array depends on various factors, including the neutraliser damping, mass, separation distance in the array and the moment arm of each neutraliser. Moreover, it is found that the particular attachment configuration of an uncoupled force-moment-type neutraliser can be used to improve their overall performance. It is also shown that in the limit of many neutralisers in the array, the performance tends to that of a continuous neutraliser.     

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.     

Modal control of beam flexural vibration

An active control system was developed to control the flexural vibrations of a beam with a modal filtering with only one secondary actuator. Segmented piezoelectric actuators and sensors were used for driving and sensing the bending beam vibrations. The primary actuator was fed by a broadband random disturbance signal in order to excite the first five modes of the structure. However, only the second to fifth modes were controlled. The control algorithm was implemented on a DSP board and the input and output signals were filtered using high order low pass filters. These filters, implemented on the DSP board avoid the degrading effect on the control performances of the higher order modes and which are not controlled. The modal filtering was achieved by computing. To this end, it is based on a previous identification procedure. This latter models, in one step, the dynamics of the structure and also the transfer function of the electronic circuits of the controller. The identified filtered modes were then used to compute the gain matrix using a LQR technique (linear quadratic regulator). Simulations of the active control were carried out and practical implementation of the control algorithms was performed. Experimental and simulation results were then compared and discussed.     

Dynamic particle-surface tribocharging: The role of shape and contact mode

Triboelectric particle charging features in many industrial processes. Dynamic particle-surface contact is the key charging mechanism in many types of particle tribocharger. Models of dynamic charging have tended to assume that the particle is spherical, but experiments have shown that particle shape can strongly influence the charging behaviour. We review some experimental work, then present a simple two-dimensional model of the dynamic contact charging of an elliptical particle, of varying roundness ratio, with a flat surface. A rich variety of contact modes (sliding, rolling, tumbling) are captured, each producing distinctive charging behaviour.     

Vibration analysis of nanomechanical mass sensor using carbon nanotubes under axial tensile loads

Carbon nanotubes (CNTs) are nanomaterials with many potential applications due to their excellent mechanical and physical properties. In this paper, we proposed that CNTs with clamped boundary condition under axial tensile loads were considered as CNT-based resonators. Moreover, the resonant frequencies and frequency shifts of the CNTs with attached mass were investigated based on two theoretical methods, which are Euler–Bernoulli beam theory and Rayleigh’s energy method. Using the present methods, we analyzed and discussed the effects of the aspect ratio, the concentrated mass and the axial force on the resonant frequency of the CNTs. The results indicate that the length of CNTs could be easily changed and could provide higher sensitivity as nanomechanical mass sensor. Moreover, the resonant frequency shifts of the CNT resonator increase significantly with increasing tensile load acting on the CNTs.     

Improvement of the axial trapping effect using azimuthally polarised trapping beam

A dual optical tweezers system,which consists of a doughnut mode optical tweezer (DMOT) with the azimuthally polarised trapping beam and a solid mode optical tweezer (SMOT) with the Gauss trapping beam was constructed to compare the axial trapping effect of DMOT and SMOT.The long-distance axial trapping of ST68 microbubbles (MBs) achieved by DMOT was more stable than that of SMOT.Moreover the axial trapping force measured using the viscous drag method,was depended on the diameter of the particle,the laser power,and the numerical aperture (NA) of the objective lens.The measurement of the axial trapping force and the acquisition of CCD images of trapping effect confirmed that the DMOT showed excellent axial trapping ability than SMOT.A simple and effective method is developed to improve axial trapping effect using the azimuthally polarized beam as trapping beam.This is helpful for the long-distance manipulating of particles especially polarised biological objects in axial direction.     

Accurate identification of the frequency response functions for the rotor-bearing-foundation system using the modified pseudo mode shape method

In this paper, an identification technique in the dynamic analyses of rotor-bearing-foundation systems called the pseudo mode shape method (PMSM) was improved in order to enhance the accuracy of the identified dynamic characteristic matrices of its foundation models. Two procedures, namely, phase modification and numerical optimisation, were proposed in the algorithm of PMSM to effectively improve its accuracy. Generally, it is always necessary to build the whole foundation model in studying the dynamics of a rotor system through the finite element analysis method. This is either unfeasible or impractical when the foundation is too complicated. Instead, the PMSM uses the frequency response function (FRF) data of joint positions between the rotor and the foundation to establish the equivalent mass, damping, and stiffness matrices of the foundation without having to build the physical model. However, the accuracy of the obtained system's FRF is still unsatisfactory, especially at those higher modes. In order to demonstrate the effectiveness of the presented methods, a solid foundation was solved for its FRF by using both the original and modified PMSM, as well as the finite element (ANSYS) model for comparisons. The results showed that the accuracy of the obtained FRF was improved remarkably with the modified PMSM based on the results of the ANSYS. In addition, an induction motor resembling a rotor-bearing-foundation system, with its housing treated as the foundation, was taken as an example to verify the algorithm experimentally. The FRF curves at the bearing supports of the rotor (armature) were obtained through modal testing to estimate the above-mentioned equivalent matrices of the housing. The FRF of the housing, which was calculated from the equivalent matrices with the modified PMSM, showed satisfactory consistency with that from the modal testing.     

Wood species identification using improved active shape model

In this paper, we propose a robust wood species identification scheme by using color wood surface images. First, a novel wood image acquirement system is devised, and the wood color image is converted into a V₁V₂I color-base image. Second, the corresponding grey histograms for V₁ and V₂ are established. Third, an improved active shape model is used to fulfill the curve deformation of the histogram curve of the standard specimen. This active shape model will then converge to the histogram curve of the test specimen. Finally, wood recognition is performed by comparing the initial and final active shape models with the histogram curve of the test specimen. We have experimentally proved that this scheme improves the mean recognition accuracy to approximately 90% for 5 wood species and that it can also be applied to the Gaussian noisy images. Moreover, the recognition accuracy can be further improved by combining this scheme with the texture feature recognition.     

Coupled axial and flexural vibration of 1-D members

The method of characteristics is used to model vibrations of one-dimensional members in the presence of coupling between axial and flexural waves. Only small deflections are considered and so the couple F_xδ_y is large only when the axial force F_x is large. Alternative numerical schemes are presented for the integration of terms describing coupling and a suitable explicit scheme is identified. The analysis is used to illustrate the influence of axial loads on frequencies and amplitudes of lateral oscillations of cantilever structures. Strong parametric behaviour is reproduced for a single-storey shear structure, including unstable resonance at double the linear natural frequency.     

Reflection hologram using one beam of light for holographic interferometry

A method for analysing the displacement field of a hologram from only one beam of light is proposed, and a method for stress and strain analysis is then derived. It possesses the advantages of being simple and precise and is capable of measuring structural strain. It is especially suitable for showing the stress distribution of concentrated stress regions. The validity of this method is proved by two typical kinds of experiment, the results of which coincide with the elasticity theory. The method has been applied to the measurement of gear stresses, including static stress and dynamic stress. The results are in agreement with values obtained by the finite element method.     

The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam

The non-linear vibration of a clamped-clamped beam at large displacement amplitudes is examined in this work. Complementary theoretical and experimental studies have been carried out to examine the amplitude dependence of the fundamental mode shape and its derivatives and the spatially-dependent harmonic distortion of the transverse displacement which occurs at large deflections.     

Dynamic lower mode control of a light beam wave front in a nonlinear medium

Dynamic control by focusing and tilting the wave front of a beam is analyzed allowing for the finite time to establish the response of the nonlinear medium for both a continuous and a discrete control algorithm. It is shown that the maximum response speed of the adaptive system is determined by the time to establish the response, the duration of the pulse, and the control constant. For the discrete control algorithm that uses an inertial mirror, a periodic operating regime is suggested to eliminate the divergence in the process of obtaining the optimum parameters.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 63–69, April, 1987.     

Vibration analysis of a non-linear beam subjected to moving loads by using the galerkin method

This paper presents the analysis of dynamic deflections of a beam, including the effects of geometric non-linearity, subjected to moving vehicle loads. The beam is assumed to be elastic and simply supported with immovable ends and the vehicles are assumed to be single degree of freedom spring-mass-damper. With the vehicles moving on the beam from one end to the other, the dynamic reflections of the beam and vehicles are computed by using the Galerkin method. Thus the dynamic deflections are assumed to be a set of time functions multiplied by approximate functions, respectively, and the time functions are numerically computed by solving the non-linear differential equations by the Newmark-β method.     

Propagation of flexural wave in periodic beam on elastic foundations

The propagation properties of flexural wave in the periodic beam on elastic foundations are studied theoretically. The wavenumbers and traveling wave characteristics in the beam on elastic foundations are analyzed. Basing on the equations of motion, the complex band structures and frequency response function are calculated by the transfer matrix method. And the Bragg and locally resonant gaps properties and the effects are researched. A gap with low frequency and wide range can exist in a beam on elastic foundations.