Overview of the New OMAH Technique for Scaling OMA Mode Shapes

Methods for scaling mode shapes determined by operational modal analysis(OMA)have been extensively investigated in the last years.A recent addition to the range of methods for scaling OMA mode shapes is the so-called OMAH technique,which is based on exciting the structure by harmonic forces applied by an actuator.By applying harmonic forces in at least one degree-of-freedom(DOF),and measuring the response in at least one response DOF,while using at least as many frequencies as the number of mode shapes to be scaled,the mode shape scaling(modal mass)of all modes of interest may be determined.In previous publications on the method the authors have proven that the technique is easy and robust to apply to both small scale and large scale structures.Also,it has been shown that the technique is capable of scaling highly coupled modes by using an extended multiple reference formulation.The present paper summarizes the theory of the OMAH method and gives recommendations of how to implement the method for best results.It is pointed out,as has been shown in previous papers,that the accuracy of the mode scaling is increased by using more than one response DOF,and by selecting DOFs with high mode shape coefficients.To determine the harmonic force and responses,it is recommended to use the three-parameter sine fit method.It is shown that by using this method,the measurement time can be kept short by using high sampling frequency and bandpass filtering whereas spectrum based methods require long measurement times.This means that even for structures with low natural frequencies,the extra measurement time for scaling the mode shapes can be kept relatively short.

Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes:A semi-analytical non-intrusive approach

In this study,the mechanical properties of the composite plate were considered Gaussian random fields and their effects on the buckling load and corresponding mode shapes were studied by developing a semi-analytical nonintrusive approach.The random fields were decomposed by the Karhunen−Loève method.The strains were defined based on the assumptions of the first-order and higher-order shear-deformation theories.Stochastic equations of motion were extracted using Euler-Lagrange equations.The probabilistic response space was obtained by employing the nonintrusive polynomial chaos method.Finally,the effect of spatially varying stochastic properties on the critical load of the plate and the irregularity of buckling mode shapes and their sequences were studied for the first time.Our findings showed that different shear deformation plate theories could significantly influence the reliability of thicker plates under compressive loading.It is suggested that a linear relationship exists between the mechanical properties’variation coefficient and critical loads’variation coefficient.Also,in modeling the plate properties as random fields,a significant stochastic irregularity is obtained in buckling mode shapes,which is crucial in practical applications.

Influence of Trailing-Edge Wear on the Vibrational Behavior of Wind Turbine Blades

To study the impact of the trailing-edge wear on the vibrational behavior of wind-turbine blades,unworn blades and trailing-edge worn blades have been assessed through relevant modal tests.According to these experiments,the natural frequencies of trailing-edge worn blades-1,-2,and-3 increase the most in the second to fourth order,thefifth order increases in the middle,and thefirst order increases the least.The damping ratio data indi-cate that,in general,thefirstfive-order damping ratios of trailing-edge worn blades-1 and trailing-edge worn blades-2 are reduced,and thefirstfive-order damping ratios of trailing-edge worn blades-3 are slightly improved.The mode shape diagram shows that the trailing-edge worn blades-1 and-2 have a large swing in the tip and the blade,whereas the second-and third-order vibration shapes of the trailing edge-worn blade-3 tend to be improved.Overall,all these results reveal that the blade’s mass and the wear area are the main fac-tors affecting the vibration characteristics of wind turbine blades.

Roll System and Stock's Multi-parameter Coupling Dynamic Modeling Based on the Shape Control of Steel Strip

The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.

Finite Element Model Updating for Structural Health Monitoring

This paper provides a model updating approach to detect,locate,and char-acterize damage in structural and mechanical systems by examining changes in mea-sured vibration responses.Research in vibration-based damage identification has been rapidly expanding over the last few decades.The basic idea behind this technology is that modal parameters(notably frequencies,mode shapes,and modal damping)are functions of the physical properties of the structure(mass,damping,and sifies).Therefore,changes in the physical properties will cause changes in the modal proper-ties which could be obtained by structural health monitoring(SHM).Updating is a process fraught with numerical difficulties.These arise from inaccuracy in the model and imprecision and lack of information in the measurements,mainly taken place in joints and critical points.The motivation for the development of this technology is.presented,methods are categorized according to various criteria such as the level of damage detection provided from vibration testing,natural frequency and mode shape readings are then obtained by using modal analysis techniques,which are used for updating structural parameters of the associated finite element model The experi-mental studies for the laboratory tested bridge model show that the proposed model.updating using ME scope technique can provide reasonable model updating results.

Extraction of real modes and physical matrices from modal testing

A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.

Shape Anisotropy and Resonance Mode Guided Reliable Interconnect Design for In-plane Magnetic Logic

Dipole coupled nanomagnets controlled by the static Zeeman field can form various magnetic logic interconnects.However, the corner wire interconnect is often unreliable and error-prone at room temperature. In this study, we address this problem by making it into a reliable type with trapezoid-shaped nanomagnets, the shape anisotropy of which helps to offer the robustness. The building method of the proposed corner wire interconnect is discussed,and both its static and dynamic magnetization properties are investigated. Static micromagnetic simulation demonstrates that it can work correctly and reliably. Dynamic response results are reached by imposing an ac microwave field on the proposed corner wire. It is found that strong ferromagnetic resonance absorption appears at a low frequency. With the help of a very small ac field with the peak resonance frequency, the required static Zeeman field to switch the corner wire is significantly decreased by ~21 m T. This novel interconnect would pave the way for the realization of reliable and low power nanomagnetic logic circuits.

Influence of Non-uniform Parameter of Bolt Joint on Complexity of Frequency Characteristics of Cylindrical Shell

Bolt connection is one of the main fixing methods of cylindrical shell structures.A typical bolted connection model is considered as a tuned system.However,in the actual working conditions,due to the manufacturing error,installation error and uneven materials of bolts,there are always random errors between different bolts.To investigate the influence of non-uniform parameters of bolt joint,including the stiffness and the distribution position,on frequency complexity characteristics of cylindrical shell through a statistical method is the main aim of this paper.The bolted joints considered here were simplified as a series of springs with random features.The vibration equation of the bolted joined cylindrical shell was derived based on Sanders’thin shell theory.The Monte Carlo simulation and statistical theory were applied to the statistical analysis of mode characteristics of the system.First,the frequency and mode shape of the tuned system were investigated and compared with FEM.Then,the effect of the random distribution and the random constraint stiffness of the bolts on the frequency and mode shape were studied.And the statistical analysis on the natural frequencies was evaluated for different mistuned levels.And some special cases were presented to help understand the effect of random mistuning.This research introduces random theory into the modeling of bolted joints and proposes a reference result to interpret the complexity of the modal characteristics of cylindrical shells with non-uniform parameters of bolt joints.

Modal analysis of prestressed draft pad of freight wagons using finite element method

The present work intends to investigate dynamic behaviour of draft gear using finite element method. The longitudinal force that the draft gear absorbs usually leads to the failure of its components, especially, the load bearing draft pads. Dynamic behaviour of an individual draft pad and a draft gear is determined and characterized with exciting frequen- cies and corresponding mode shapes. The effect of compressive prestress load on the dynamic behaviour of an individual draft pad is also determined as the draft pads in assembled state are under constant axial compressive force in the draft gear. The vibration characteristics of individual draft pad are compared with draft pads that are part of draft gear. The modal analysis gives us a basis for subjecting a draft pad to higher frequency loading for determining its fatigue behaviour.

Ambient Vibration Testings and Field Investigations of Two Historical Buildings in Europe

In this study,the methodology and results of ambient vibration-based investigations of the historical Tash Mosque in Kosovo and a 3-story historical building in Bulgaria are presented.The investi gations include full-scale in situ testing of both structures due to ambient vibrations induced by micro-seismic,wind,traffic,and other human activities.To this aim,Ranger seismometers and Kinemetric products were used.Measurements were performed in both horizontal directions in several points along the structures'height utilizing a high-speed data acquisition device.All recorded data have been analyzed and processed by the software developed at IZIIS,and then the processed data were used as input for modal analysis.The basic assumption is that the excitation can be considered as a stationary random process to have a relatively flat spectrum.The paper clearly describes the procedure used for investigations and presents the dynamic properties of the whole structures.The inv estigated structures are both historical buildings and defined as architectural heritage and the outcome of this study including the natural vibration frequencies and mode shapes)can be very benefi-cial for the verification stage of the analytical/numerical models for future retro-fiting/rehabilitation schemes.

Test and numerical investigations on static and dynamic characteristics of extra-wide concrete self-anchored suspension bridge under vehicle loads

The present work is aimed at studying the mechanic properties of the extra-wide concrete self-anchored suspension bridge under static and dynamic vehicle loads. Based on the field test using 12 heavy trucks and finite element simulations, the static deformations of different components, stress increments and distributions of the girder, as well as the vibration characteristics and damping ratio of the Hunan Road Bridge were analyzed, which is the widest self-anchored suspension bridge in China at present. The dynamic responses were calculated using the Newmark-β integration method assisted by the simulation models of bridge and vehicles, the influences on the dynamic impact coefficient(DIC) brought by the vehicle parameters, girder width, eccentricity travel and deck flatness were also researched. The spatial effect of the girder is obvious due to the extra width, which performs as the stress increments distribute unevenly along the transverse direction, and the girder deflections and stress increments of the upper plate change as a "V" and "M" shape respectively under the symmetrical vehicle loads affected by the shear lag effect, cross slope and local effect of the wheels, the maximum of stress increments are located in the junctions with the inner webs. The obvious girder torsional deformation and the apparent unevenness of the hanger forces between the two cable planes under the eccentric vehicle loads, together with the mode shapes such as the girder transverse bending and torsion which appear relatively earlier, all reflect the weakened torsional rigidity of the extra-wide girder. The transverse displacements of towers are more obvious than the longitudinal ones. As for the influences on the DIC, the static effect of the heavier vehicles plays a major role when pass through with a higher speed and the changes of vehicle suspension stiffness generate greater impacts than the suspension damp. The values of DIC in the vehicle-running side during the eccentric travel, affected by the restricts from the static effects of the eccentric moving trucks, are significantly smaller than the vehicle-free side, the increase in the road roughness is the most sensitive one among the above influential factors. The results could provide references for the design, static and dynamic response analysis of the similar extra-wide suspension bridges.

Effects of Joint on Dynamics of Space Deployable Structure

Joints are necessary components in large space deployable truss structures which have significant effects on dynamic behavior of these joint dominated structures.Previous researches usually analyzed effects of one or fewer joint characters on dynamics of jointed structures.Effects of joint stiffness,damping,location,number,clearance and contact stiffness on dynamics of jointed structures are systematically analyzed.Cantilever beam model containing linear joints is developed based on finite element method,influence of joint on natural frequencies and mode shapes of the jointed system are analyzed.Analytical results show that frequencies of jointed system decrease dramatically when peak mode shapes occur at joint locations,and there are cusp shapes present in mode shapes.System frequencies increase with joint damping increasing,there are different joint damping to achieve maximum system damping for different joint stiffness.Joint nonlinear force-displacement is described by describing function method,one-DOF model containing nonlinear joints is established to analyze joints freeplay and hysteresis nonlinearities.Analysis results show that nonlinear effects of freeplay and hysteresis make dynamic responses switch from one resonance frequency to another frequency when amplitude exceed demarcation values.Joint contact stiffness determine degree of system nonlinearity,while exciting force level,clearance and slipping force affect amplitude of dynamic response.Dynamic responses of joint dominated deployable truss structure under different sinusoidal exciting force levels are tested.The test results show obvious nonlinear behaviors contributed by joints,dynamic response shifts to lower frequency and higher amplitude as exciting force increasing.The test results are further compared with analytical results,and joint nonlinearity tested is coincident with hysteresis nonlinearity.Analysis method of joint effects on dynamic characteristics of jointed system is proposed,which can be used in optimal design of joint parameters to achieve optimum dynamic performance of jointed system.

Vibration of composite beams with two overlapping delaminations

Delaminations in composite laminates may de-velop from small cracks due to fabrication and impact load-ing,or from places of high stress concentration.The locationsof the delaminations are not determinate.In this research,ananalytical solution for the free vibration of a composite beamwith two overlapping delaminations is presented.The dela-minated beam is analyzed as seven interconnected beamsusing the delaminations as their boundaries.The continuityand equilibrium conditions are satisfied between the adjoin-ing regions of the beams.Classical beam theory is applied toeach of the beams.Complex vibration behaviors emerge fordifferent sizes and locations of the delaminations.Compar-ison with analytical results reported in the literature verifiesthe validity of the present solution.

Dynamic analysis of beam-cable coupled systems using Chebyshev spectral element method

The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.

FORMULATION AND EVALUATION OF AN ANALYTICAL STUDY FOR CYLINDRICAL HELICAL SPRINGS

The free vibration analysis of cylindrical helical springs is carried out by means of an analytical study. In the governing equations of the motion of the springs, all displacement functions are defined at the centroid axis and also the effects of the rotational inertia, axial and shear deformations are included in the proposed model. Explicit analytical expressions which give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies. Numerical examples are provided for fixed-fixed boundary conditions. The free vibrational pa- rameters are chosen as the number of coils （n = 4- 14）, the helix pitch angle （a = 5 - 30°） and as the ratio of the diameters of the cylinder and the wire （D/d = 4 - 18） in a wide range. Validation of the proposed model has been achieved through comparison with a finite element model using two-node standard beam elements and the results available in published literature, which in these cases indicates a very good correlation.

Cost Optimized Non-Contacting Experimental Modal Analysis Using a Smartphone

The vibrations behavior analysis is an essential step in the mechanical design process.Several methods such as analytical modelling,numerical analysis and experimental measurements can be used for this purpose.However,the numerical or analytical models should be validated through experimental measurements,usually expensive.This paper introduces an inexpensive smartphone as an accurate,non-intrusive vibrations’behavior measurement device.An experimental measurement procedure based on the video processing method is presented.This procedure allows the measurement of the natural frequencies and the mode shapes of a vibrating structure,simply by using a smartphone built-in camera.The experimental results are compared to those obtained using an accurate analytical model,where the natural frequencies error is less than 2.7%and the modal assurance criterion is higher than 0.89.In order to highlight the obtained results,a comparison has been done using a high quality and high frame per second(fps)camera-based measurement of material properties.Since the highest recovered natural frequency and its associated mode shape depend on the frame per second rate of the recorded video,this procedure has great potential in low frequencies problems such as for big structures like buildings and bridges.This validated technique re-introduces the personal smartphone as an accurate inexpensive non-contacting vibration measurement tool.

Dynamic Performance Analysis of the Coupling Shaft System in a Carpet Tufting Machine Utilizing the Transfer Matrix Method

The dynamic performance of the coupling shaft system in a carpet tufting machine is the most critical factor affecting the carpet tufting machine's efficiency,and the product quality of the tufted carpet. To determine how to avoid resonance produced by the coupling shaft system's vibration during the weaving process,the dynamic performance of a coupling shaft system in a carpet tufting machine was analyzed. Focusing on a DHGN801D-400 carpet tufting machine,a dynamic model of coupling shaft system was established by utilizing transfer matrix methodology. On the basis of this model,the natural frequencies and mode shapes of the coupling shaft system were obtained through simulations. The correctness of the theoretical model and the dynamic performance of the coupling shaft system were validated by experiments. The first order natural frequency of the coupling shaft system was close to 600 r / min. A conclusion can thus be drawn that operating the carpet tufting machine near this speed should be avoided as much as possible.

ODS & Modal Testing Using a Transmissibility Chain

In this paper, we show how Operating Deflection Shapes (ODS’s) andmode shapes can be obtained experimentally from measurements thatare made using only two sensors and two short wires to connect them to amulti-channel acquisition system. This new test procedure is depicted inFigure 1. Not only is the equipment required to do a test much more costeffective, but this method can be used to test any sized test article, especiallylarge ones.

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.

Vibration Serviceability of Large-Span Steel–Concrete Composite Beam with Precast Hollow Core Slabs Under Walking Impact

A large-span steel–concrete composite beam with precast hollow core slabs(CBHCSs)is a relatively new floor structure that can be applied to various long-span structures.However,human-induced vibrations may present serviceability issues in such structures.To alleviate vibrations,both the walking forces excited by humans and the associated floor responses must be elucidated.In this study,150 load–time histories of walking,excited by 25 test participants,are obtained using a force measuring plate.The dynamic loading factors and phase angles in the Fourier series functions for one-step walking are determined.Subsequently,walking tests are performed on seven CBHCS specimens to capture the essential dynamic properties of mode shapes,natural frequencies,damping ratios,and acceleration time histories.The CBHCS floor system generally exhibits a high frequency(>10 Hz)and low damping(damping ratio<2%).Sensitivity studies using the finite element method are conducted to investigate the vibration performance of the CBHCS floor system,where the floor thickness,steel beam type,contact time,and human weight are considered.Finally,analytical expressions derived for the fundamental frequency and peak acceleration agree well with the experimental results and are hence proposed for practical use.