Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function （FRF）. The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

Effects of surface finish and treatment on the fatigue behaviour of vibrating cylinder block using frequency response approach

This paper presents the effects of surface finish and treatment on the high cycle fatigue behaviour of vibrating cylinder block of a new two-stroke free piston engine at complex variable amplitude loading conditions using frequency response approach. Finite element modelling and frequency response analysis was conducted using finite element analysis software Package MSC.PATRAN/MSC.NASTRAN and fatigue life prediction was carded out using MSC.FATIGUE software. Based on the finite element results, different frequency response approach was applied to predict the cylinder block fatigue life. Results for different load histories and material combinations are also discussed. Results indicated great effects for all surface finish and treatment. It is concluded that polished and cast surface finish conditions give the highest and lowest cylinder block lives, respectively; and that Nitrided treatment leads to longest cylinder block life. The results were used to draw contour plots of fatigue life and damage in the worst or most damaging case.

Frequency response range of terahertz pulse coherent detection based on THz-induced time-resolved luminescence quenching

It has been proposed previously that the coherent detection of a terahertz（THz） pulse can be achieved based on the time-resolved luminescence quenching. In this paper, we investigate the frequency response range of this novel detection technology by simulating the motion of carriers in gallium arsenide（GaAs） by the ensemble Monte Carlo method. At room temperature, for a direct-current（DC） voltage of 20 kV/cm applied to the semiconductor（GaAs） and sampling time o140 fs, the luminescence quenching phenomena induced by terahertz pulses with different center frequencies are studied The results show that the quenching efficiency is independent of the THz frequency when the frequency is in a range o0.1 THz–4 THz. However, when the frequency exceeds 4 THz, the efficiency decreases with the increase of frequency Therefore, the frequency response range is 0.1 THz–4 THz. Moreover, when the sampling time is changed to 100 fs the frequency response range is extended to be approximately 0.1 THz–5.6 THz. This study of the frequency-dependen characteristics of the luminescence response to the THz pulse can provide a theoretical basis for the exploration of THz detection technology.

Wavelet-Based Response Computation for Base-Isolated Structure under Seismic Excitation

This paper presents a wavelet-based approach for estimating the response of the base-isolated structure under seismic ground motions. The seismic ground motion record is expressed as the multi-scale wavelet coefficients which presents the time frequency characteristics of the seismic excitation. The wavelet domain governing differential equation between the wavelet coefficients of the excitation and response is derived. Numerical study on a one-storey base isolated structure is performed. The result shows that the wavelet based response computation method is of high precision.

Seismic response analysis of continuous rigid frame bridge considering canyon topography effects under incident SV waves

To evaluate the importance of the canyon topography effects on large structures, based on a rigid frame bridge across a 137-m-deep and 600-m-wide canyon, the seismic response of the canyon site is analyzed using a two-dimensional finite element model under different seismic SV waves with the assumptions of vertical incidence and oblique incidence to obtain the ground motions, which are used as the excitation input on the pier foundations of the bridge with improved large mass method. The results indicate that canyon topography has significant influences on the ground motions in terms of inci- dent angle. The peak ground acceleration values vary greatly from the bottom of the canyon to the upper comers. Under ver- tical incident SV waves, at the upper comers of canyon the peak ground accelerations greatly increase; whereas the peak ground accelerations diminish at the bottom comers of canyon. Under oblique incident SV waves, the shaking of the canyon slope perpendicular to the incidence direction is much more severe than that of the opposite side of canyon. And the ground surface has been characterized by larger deformations in the case of oblique incident waves. It is also concluded that the low piers and frame of the continuous rigid frame bridge ape more sensitive to the multi-support seismic excitations than the flexible high piers. The canyon topography as well as the oblique incidence of the waves brings the continuous rigid frame bridge severe responses, which should be taken into account in bridge design.

Seismic Response of Submerged Floating Tunnel Tether

A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.

Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

For the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations,a longitudinal integral response deformation method classified as a practical approach is proposed in this paper.The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well.When applying the proposed method,the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads.Then,the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation.Afterwards,the critical longitudinal seismic responses of the tunnel are obtained.The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing,determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-of-plane and in-plane waves.The results show that the proposed method has a clear concept with high accuracy and simple progress.Meanwhile,this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure.Therefore,the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.

A simplified multisupport response spectrum method

A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.

Excited response of granular ores in vibrating field

The dynamical theory was utilized to probe into the law of the excited response of granular ores generated by the exciting action of exciter and the influence of wave propagation in vibrating field. The exciter with double axes was presented as an example, and the principle of exciter and its mathematical expression of the excitation force were given. The granular ores have viscidity and damping speciality, on the basis of which the motion equation of excited response of ores was established and the approximate expression of mode displacement by harmonic excitation and the steady effect solution of coordinate response were deduced. Utilizing the step by step integration method, the recursion relation matrix of displacement, velocity and acceleration of the excited response of ores were obtained, and the computational flow chart and a computational example were given. The results show that the excited response can change the dynamical character and the flowing characteristic of granular ores.

Dynamic response of electromagnetic launcher's rail subjected to harmonic magnetic pressure

In order to extend the rail life and improve the firing accuracy,the electromagnetic launcher's rail can be modeled as a beam on elastic foundation with simply supported beam with moving load.Euler beam theory is applied to build the mechanical model and the analytical solution of the equation subjected to harmonic magnetic pressure is derived in details,which has successfully avoided the errors caused by using the uniform pressure to approximately replace the variable force.Numerical analysis of the dynamic response on rail by using the MATLAB software shows that the peak values of maximal deflection and vibration velocity increase gradually as the exciting frequency increases.Taking the same speed of load into account,the dynamic response of rail is obviously smaller than that under constant force.Therefore the reliable theory basis is provided for the design and control of rail to promote the practical application of electromagnetic launcher.

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

Study of Vertical Seismic Response of Concrete Self-Anchored Suspension Bridges

Based on the variational prineiple of incomplete generalized potential energy with large deflection, the vertical nonlinear vibrational differential equation of self-anchored suspension bridge is presented by taking the effect of coupling of flexural and axial action into consideration. The linear vertical equation is obtained by omitting the nonlinear term, and the pseudo excitation method(PEM). Taking the self-anchored concrete suspension bridge over Lanqi Songhua river for an example, the expected peak responses of main beam, towers and cables are calculated. And the seismic spatial effects on vertical seismic response of self-anchored suspension bridges are discussed.

An Application of Direct Ritz Method for Random Seismic Responses of Jacket Platforms

In this paper, the jacket platform is simulated by a non-uniform cantilever beam subjected to axial force. Based on the Hamilton theory, the equation of bending motion is developed and solved by the classical Ritz method combined with the pseudo-excitation method for random responses with non-classical damping. Usually, random responses of this continuous structure are obtained by orthogonality of modes, and some normal modes of the structure are needed, causing inconvenience for the analysis of the non-uniform beam whose normal modes are not easy to be obtained. However, if the pseudo-excitation method is extended to calculate random responses by combining it with the classical Ritz method, the responses of a non-uniform beam, such as auto-PSD function, cross-PSD and higher spectral moments, can be solved directly avoiding the calculation of normal modes. The numerical results show that the present method is effective and useful in aseismic design of platforms.

Reliability Based Optimization of Composite Laminates for Frequency Constraint

The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of the structure is evaluated by the combination of response surface method （RSM） and finite element method. An optimization algorithm is developed based on the mechanism of laminate frequency characteristics, to optimize the laminate in terms of the ply amount and orientation angles. Numerical examples of composite laminates and cylindrical shell illustrate the advantages of the present optimization algorithm on the efficiency and applicability respects. The optimal solutions of RBO are obviously different from the deterministic optimization results, and the necessity of considering material property uncertainties in the composite structural frequency constraint optimization is revealed.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton＇s principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed- parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multi- layered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION AND CROSS POWER SPECTRUM UNDER UNKNOWN EXCITATION

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. This paper gives a theoretical formulation for the cross-correlation functions and cross-power spectra between the outputs under the assumption of white-noise excitation. It widens the field of modal analysis under ambient excitation because many classical methods by impulse response functions or frequency response functions can be used easily for modal analysis under unknown excitation. The Polyreference Complex Exponential method and Eigensystem Realization Algorithm using cross-correlation functions in time domain and Orthogonal Polynomial method using cross-power spectra in frequency domain are applied to a steel frame to extract modal parameters under operational conditions. The modal properties of the steel frame from these three methods are compared with those from frequency response functions analysis. The results show that the modal analysis method using cross-correlation functions or cross-power spectra presented in this paper can extract modal parameters efficiently under unknown excitation.

Analysis on Pseudo Excitation of Random Vibration for Structure of Time Flight Counter

Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method（PEM）is an effective method for calculation of random vibration.Due to complicated and coupling random vibration in rocket or shuttle launching,the new staging white noise mathematical model is deduced according to the practical launch environment.This deduced model is applied for PEM to calculate the specific structure of Time of Flight Counter（ToFC）.The responses of power spectral density and the relevant dynamic characteristic parameters of ToFC are obtained in terms of the flight acceptance test level.Considering stiffness of fixture structure,the random vibration experiments are conducted in three directions to compare with the revised PEM.The experimental results show the structure can bear the random vibration caused by launch without any damage and key dynamical parameters of ToFC are obtained.The revised PEM is similar with random vibration experiment in dynamical parameters and responses are proved by comparative results.The maximum error is within 9%.The reasons of errors are analyzed to improve reliability of calculation.This research provides an effective method for solutions of computing dynamical characteristic parameters of complicated structure in the process of rocket or shuttle launching.

Karhunen-loéve expansion for random earthquake excitations

This paper develops a trigonometric-basis-fimction based Karhunen-Loeve （KL） expansion for simulating random earthquake excitations with known covariance functions. The methods for determining the number of the KL terms and defining the involved random variables are described in detail. The simplified form of the KL expansion is given, whereby the relationship between the KL expansion and the spectral representation method is investigated and revealed. The KL expansion is of high efficiency for simulating long-term earthquake excitations in the sense that it needs a minimum number of random variables, as compared with the spectral representation method. Numerical examples demonstrate the convergence and accuracy of the KL expansion for simulating two commonly-used random earthquake excitation models and estimating linear and nonlinear random responses to the random excitations.