Pseudo-excitation Method Research Articles

Research on the random seismic response analysis for multi- and large-span structures to multi-support excitations

The pseudo excitation method (PEM) has been improved into a more practical form, on which the analytic formulae of seismic response power spectral density (PSD) of simplified large-span structural models have been derived. The analytic formulae and numerical computing results of seismic response PSD have been derived to study the mechanism of multi-support excitation effects, such as the wave-passage effect and incoherence effect, for the seismic response of multiand large-span structures. By using a multi-span truss as an example, the influence of multi-support excitation effects on the seismic response of such structures is studied.

Random Vibration Analysis for Impellers of Centrifugal Compressors Through the Pseudo-Excitation Method

Impellers of centrifugal compressors are generally loaded by fluctuating aerodynamic pressure in operations. Excessive vibration of the impellers can be induced by unsteady airflows and lead to severe fatigue failures. Traditional transient stress analyses implemented in time domain generally require multiple load-step, very time-consuming computations using input of temporal pneumatic force previously obtained from Computational fluid dynamics (CFD) analyses. For quick evaluation of structural integrity of impellers, it is necessary to develop random vibration models and solution approaches defined in frequency domain. In this paper, the Pseudo-Excitation Method (PEM) is used to obtain power spectral density of three-dimensional, dynamic displacement and stress of impellers. A finite element model of an unshrouded impeller of a centrifugal compressor is generated based on the result of unsteady CFD analysis. Compared with the direct transient stress analyses in time domain, the pseudo-excitation method provides accurate and fast estimation of dynamic response of the impeller, making it an applicable and efficient method for analyzing random vibration of impellers.

Topology optimization of large-scale structures subjected to stationary random excitation: An efficient optimization procedure integrating pseudo excitation method and mode acceleration method

Structural topology optimization related to dynamic responses under stationary random force excitation is investigated in this paper. It is shown that the commonly used Complete Quadratic Combination method (CQC) in previous optimization work is not only computationally expensive but also results in non-convergent design pattern due to the low computing accuracy of random responses for large-scale problems. To circumvent these difficulties, an efficient and accurate optimization procedure integrating the Pseudo Excitation Method (PEM) and Mode Acceleration Method (MAM) is introduced into the dynamic topology optimization. In this framework, random responses are calculated using the PEM to ascertain a high efficiency over the CQC. More importantly, the accuracy of random responses is improved indirectly by solving the pseudo harmonic responses involved in the PEM with the help of the MAM. Numerical examples fully demonstrate the validity of the developed optimization procedure and its potential applications in practical designs.

Random vibration analysis of train-slab track-bridge coupling system under earthquakes

This study aimed to investigate the random vibration characteristic of train-slab track-bridge interaction system subjected to both track irregularities and earthquakes by use of pseudo-excitation method (PEM). Each vehicle subsystem was modeled by multibody dynamics. A three-dimensional rail-slab- girder-pier finite element model was created to simulate slab track and bridge subsystem. The equations of motion for the entire system were established based on the constraint condition of no jump between wheel and rail. The random load vectors of equations of motion were formulated by transforming track irregularities and seismic accelerations into a series of deterministic pseudo-excitations according to their respective power spectral density (PSD) functions by means of PEM. The time-dependent PSDs of random vibration responses of the system were obtained by step-by-step integration method, and the corresponding extreme values were estimated based on the first-passage failure criterion. As a case study, an ICE3 high-speed train passing a fifteen-span simply supported girder bridge simultaneously excited by track irregularities and earthquakes is presented. The evaluated extreme values and the PSD characteristic of the random vibration responses of bridge and train are analyzed, and the influences of train speed and track irregularities (without earthquakes) on the random vibration characteristic of bridge and train are discussed.

Numerical Analysis of Thermoacoustic Characteristics of Components inside a Complex Aircraft Related to the Coupling Effect of High Temperature and Random Vibration

Hypersonic aircraft always face bad flight environment related to the coupling effects of high temperature and random vibration. Numerical analysis of thermoacoustic characteristics of components inside such an aircraft is presented in this paper. An actual aircraft cabin composite structure including a heat resistant layer, an adiabatic layer and metal frameworks is modeled with the finite element mesh generation method. Transient heat conduction of the hypersonic flight aircraft is analyzed based on a block-iterative coupling method which can consider the atmosphere-aircraft interaction. Then the Von Karman turbulence spectrum is employed to define the random vibration environment of the present aircraft. The thermodynamic response of the system is solved by the pseudo-excitation method which can improve the computation efficiency greatly. Finally, thermoacoustic characteristic of the cavity inside the aircraft cabin is analyzed when the transient heat conduction and random vibration due to atmosphere turbulence are both included. A numerical method is proposed based on a structure-acoustic coupling method which can use acoustic equations to simulate the propagation of the acoustic wave in the flow. It can be found from the computed results that the change of the temperature influences both the thermodynamic characteristic of the aircraft cabin and thermoacoustic characteristic of the component inside the present aircraft significantly. So the coupling effects of high temperature and random vibration on thermoacoustic characteristic of a hypersonic flight aircraft cannot be neglected. The proposed numerical analysis method in this paper can be widely applied to numerical investigations of thermoacoustic systems inside hypersonic aircraft.

Seismic Response of Ultra High-Pier Railway Bridge under Spatially Varying Site Conditions of Earthquake Excitations

An ultra high-rise pier railway bridge in Guizhou province, China, is selected as an engineering example to study the effect of spatially varying site conditions on the seismic performance of mountainous ultra high-rise pier railway bridges. A seismic performance analysis and a numerical simulation of the bridge are conducted while subjecting the bridge to spatially varying site conditions using the pseudo excitation method. The influence of the distribution of different spatially varying combinations of firm, medium, and soft site conditions on the stochastic seismic response of this type of bridge is then considered for seismic analysis under multi-directional earthquake excitations. Results show that (1) combinations of different site conditions have varying influences on the seismic response of the ultra high-rise pier railway bridge, and in particular, the influence of local site conditions has the greatest structural response on the highest pier; (2) it is of considerable importance to avoid the most unfavorable condition of soft soil beneath the highest pier, and to avoid hard soil conditions beneath other piers; and (3) to ensure that structural responses are not underestimated, it is necessary to consider the spatially varying site conditions when conducting a seismic analysis of ultra high-rise pier railway bridge structures that are likely to be subjected to earthquake action.

Creep influence on structural dynamic reliability

Creep brings forth considerable influences on both static and dynamic behaviours of concrete structures. This paper intends to deepen the investigation on the creep influence on structural dynamic performance, evaluating their relationship from the view of reliability. The influencing mechanism of concrete creep on structural dynamic behaviour is first stated. Integration of the structural creep analysis by the Model B3 and the age-adjusted effective modulus method with the stochastic seismic analysis by the pseudo-excitation method is then proposed. Based on the creep-influenced structural static and stochastic seismic behaviours, formulations for the dynamic reliability with the consideration of creep effect are derived using the first-passage failure criterion and Poisson crossing assumption. A systematic numerical simulation is conducted on a long-span concrete filled steel tube arch bridge, considering (1) the creep influence on concrete mechanical properties and structural configuration and internal forces; (2) the dimensionality, wave passage effect and incoherence effect of random ground motions; and (3) the uncertainties existing in the structure and creep behaviour. Critical conclusions are drawn and it is recommended to consider the long-term effect of dead loads in seismic design to ensure structural seismic safety.

Random seismic response analysis of jacket structure with Timoshenko's beam theory

Today many complex three-dimensional (3D) models, typically finite element method (FEM) models, have been used in the analysis of jacket platforms. However, these comprehensive models are not readily adopted in engineering practice, especially during the preliminary design stage. The main reasons are the large computing resources required and the lack of detailed information for setting up the FEM model. In this paper, a simplified response analysis method is proposed to make preliminary estimate of the random seismic responses on jacket platforms. Based on Timoshenko's beam theory, the equation of bending motion was proposed and solved by using the classical Ritz method combined with the pseudo-excitation method. A computer code for computing random seismic responses was also developed and verified. A six-legged jacket platform was used as an example, whereby three types of Ritz functions were used to illustrate the validity of the model. The results of this study were compared with those obtained from a well-established complex 3D FEM model. The findings of the comparison showed that the accuracy of the simplified model was better than 95%. It was concluded that the proposed simplified method was effective, useful and practical in seismic design of platforms.

Random vibration analysis of train–bridge under track irregularities and traveling seismic waves using train–slab track–bridge interaction model

The frequent use of bridges in high-speed railway lines greatly increases the probability that trains are running on bridges when earthquakes occur. This paper investigates the random vibrations of a high-speed train traversing a slab track on a continuous girder bridge subjected to track irregularities and traveling seismic waves by the pseudo-excitation method (PEM). To derive the equations of motion of the train–slab track–bridge interaction system, the multibody dynamics and finite element method models are used for the train and the track and bridge, respectively. By assuming track irregularities to be fully coherent random excitations with time lags between different wheels and seismic accelerations to be uniformly modulated, non-stationary random excitations with time lags between different foundations, the random load vectors of the equations of motion are transformed into a series of deterministic pseudo-excitations based on PEM and the wheel–rail contact relationship. A computer code is developed to obtain the time-dependent random responses of the entire system. As a case study, the random vibration characteristics of an ICE-3 high-speed train traversing a seven-span continuous girder bridge simultaneously excited by track irregularities and traveling seismic waves are analyzed. The influence of train speed and seismic wave propagation velocity on the random vibration characteristics of the bridge and train are discussed.

Random Vibration Analysis of Train Moving over Slab Track on Bridge under Track Irregularities and Earthquakes by Pseudoexcitation Method

This paper investigates the random vibration and the dynamic reliability of operation stability of train moving over slab track on bridge under track irregularities and earthquakes by the pseudoexcitation method (PEM). Each vehicle is modeled by multibody dynamics. The track and bridge is simulated by a rail-slab-girder-pier interaction finite element model. The coupling equations of motion are established based on the wheel-rail interaction relationship. The random excitations of the track irregularities and seismic accelerations are transformed into a series of deterministic pseudoexcitations by PEM. The time-dependent power spectral densities (PSDs) of the random vibration of the system are obtained by step-by-step integration method, and the corresponding dynamic reliability is estimated based on the first-passage failure criterion. A case study is then presented in which a high-speed train moves over a slab track resting on a simply supported girder bridge. The PSD characteristics of the random vibration of the bridge and train are analyzed, the influence of the wheel-rail-bridge interaction models on the random vibration of the bridge and train is discussed, and furthermore the influence of train speed, earthquake intensity, and pier height on the dynamic reliability of train operation stability is studied.

The dynamic characteristics of the damage probability of a gravity dam

A first-order approximate probabilistic analytical method to investigate the damage of concrete gravity dams, based on the pseudo-excitation method (PEM), is proposed. This method constructs stochastic stiffness under stochastic stimulus using second-order perturbation. It involves the following steps. First, the PEM and the Mazar damage models are utilised to analyse the way to calculate the expected value and variance of the damage of a dam excited by a random earthquake load and a static load in the initial condition. Next, the evolutive process of the probability distribution of the tensile damage of a dam is analysed in the damage condition based on perturbation theory. Finally, a numerical example is given to verify and analyse the convergence and stability of this model. The calculated results show that the expected values of the probability distribution of the stochastic structure under a stochastic stimulus are steady under a second-order perturbation. The results indicate that, compared to PEM, the salient features of the method proposed provide a probabilistic analysis for the nonlinear response of a concrete gravity dam.

다중지점 지진하중을 받는 돔 구조물의 지진응답 제어

Spatial structures as like dome structure have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and effectively control of seismic response of spatial structure subjected to multi-supported excitation. In this study, star dome structure that is subjected to multi-supported excitation was used as an example spatial structure. The response of the star dome structure under multiple support excitation are analyzed by means of the pseudo excitation method. Pseudo excitation method shows that the structural response is divided into two parts, ground displacement and structural dynamic response due to ground motion excitation. And the application of passive tuned mass damper(TMD) to seismic response control of star dome structures has been investigated. From this numerical analysis, it is shown that the seismic response of spatial structure under multiple support seismic excitation are different from those of spatial structure under unique excitation. And it is reasonable to install TMD to the dominant points of each mode. And it is found that the passive TMD could effectively reduce the seismic responses of dome structure subjected to multi-supported 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.

A simplified method for the analysis of the stochastic response in discrete coordinates

Nowadays, the problem of the computational cost vs. the accuracy of the results is an important field of research in engineering, particularly for the analysis of the response of a stochastic system. By using a set of discrete coordinates, this response can become computationally challenging, especially when using a modal representation. Many dynamic load cases, significant for engineering applications, have random and convective properties such as wall pressure fluctuations due to the turbulent boundary layer (TBL). In this work, a new method for the evaluation of the dynamic response of a linear system excited by a TBL like load is proposed: it is named as frequency modulated pseudo-equivalent deterministic excitation (PEDEM) and it is based on the pseudo-excitation method (PEM). The latter is an exact representation since it uses the modal decomposition of the cross-spectral density matrix of the load. Unfortunately, the extraction of the eigensolutions of the load matrix is required at each frequency step and thus can become computationally unacceptable when a large number of eigensolutions is required. PEDEM tries to overcome this computational bottleneck by introducing some approximations, which are based on the analysis of the eigensolutions of the dynamic load matrix vs. frequency. Three different approximations are proposed and thus modulated for the three frequency ranges wherein the dynamic matrix of the considered random and convective load has different characteristics. A criterion to identify the above-mentioned frequency ranges is also proposed by introducing a dimensionless representation of the frequency. The results show that the proposed approximations combine a good accuracy in representing the stochastic system response with a 40 per cent of reduction of the computational costs if compared to a full stochastic response. The method is successfully applied to a simple 1D configuration, a chain of oscillators, which still presents the main features of a generic system. The extension to 2D systems is also analysed considering a preliminary test case with a flexural plate.

Probabilistic evaluation approach for nonlinear vehicle–bridge dynamic performances

Railroad vehicle and bridge coupled lateral vibration problems are traditionally solved through detailed nonlinear models in time domain using limited samples to represent rail irregularity. Ideally, a random vibration and reliability based approach should be implemented because of the random nature of the excitation process. In this study, vehicle–bridge coupled dynamic equation was derived using the principle of virtual work utilizing a linearized wheel–rail contact equation. This simplification enables the calculation of the system random lateral responses through the pseudo-excitation method. By applying rail irregularity as random excitations to the system, this study utilized an explicit linearization method to avoid iterative solution at each time step of the integration. The results from the linearized method were validated through comparison with results obtained from Monte-Carlo simulations. By applying the linearized approach to probabilistic assessment of the vehicle–bridge system reliability, it was shown that system probability of exceedance of admissible limits increases with train speed and reduces with increased bridge self-weight. It is concluded that the proposed approach provides a viable efficient alternative to investigate the random dynamic characteristics of vehicle–bridge system especially in the lateral direction, which is dominated by the random rail irregularities.

Structural damage identification based on power spectral density sensitivity analysis of dynamic responses

A new method is proposed to identify locations and severities of structural damages based on the power spectral density sensitivity analysis. Firstly, the structural responses and power spectral density under stationary and random excitations are calculated using pseudo excitation method. Then, the sensitivities of power spectral density with respect to the structural damage parameters are obtained. Finally, the finite element model updating method is adopted to identify the structural damages from the calculated and the simulated measured power spectral density. Two numerical examples demonstrate the satisfactory identification results obtained from the present method.

Stochastic hydroelastic analysis of a very large floating structure using pseudo-excitation method

This paper is concerned with the linear hydroelastic response of a pontoon-type very large floating structure (VLFS) in short-crested irregular waves. The linear potential theory is employed for the analysis of VLFS in frequency domain. To decouple the fluid–structure interaction, the higher-order boundary element method (HOBEM) combined with the finite element method (FEM) is adopted. VLFS is modeled as a Mindlin plate, and the mode superposition method is used to reduce the dimension of dynamic equations. The pseudo-excitation method (PEM) is adopted to analyze the stationary stochastic response of the floating structure. The efficiency of this new calculation scheme with the application of PEM is investigated in comparison with the conventional method for stochastic response by analyzing the computational complexity theoretically. Finally, the new calculation scheme is validated by comparing with the experimental data as well as the existing numerical results calculated in the conventional way. In addition, the efficiency of the present numerical approach is also testified which indicates that the proposed numerical scheme is time-saving.

A highly efficient and accurate stochastic seismic analysis approach for structures under tridirectional nonstationary multiple excitations

This paper proposes an improved high precision direct integration method (I-HPDIM) and an absolute-response-oriented scheme of pseudo-excitation method (PEM) for nonstationary stochastic seismic analysis of large structures under tridirectional nonuniformly modulated spatial ground motions. The proposed approaches resolve the bottle-neck problem of conventional HPDIM and significantly improve computational efficiency of both PEM and HPDIM, making the proposed nonstationary stochastic analysis scheme more attractive for engineering purposes. Hence, it has been implemented in general finite element platforms, having powerful and versatile modelling and analysis capabilities, for stochastic seismic analysis of large and complex structures under tridirectional nonstationary spatial seismic motions.

Random Response of Rotor System on the Filtered Gaussian White Noise Earthquake Ground Acceleration

With the pseudo-excitation method, the random response of a cantilever double-disc rotor system under the filtered Gaussian white noise earthquake ground accelerated random excitations, is analyzed by computer numerical simulation. The results show that the random response is relatively strong during an earthquake of the horizontal direction while the cantilever disk vibration is the strongest. The inherent frequency of the site soil has a great effect on the random response in the horizontal direction, while the system frequency characteristics have a great effect on the random response in the vertical direction. The rotor imbalance random excitation intensity does not change the peak frequency of the response spectrum. However, the system random vibration response is large when the excitation intensity is in a high level state. It has a great impact on the low and high frequency of non-cantilever disc, the low frequency of the cantilever disc, the high-frequency of non-cantilever bearing vertical vibration and the high-frequency of cantilever bearing the intensity around the high-frequency random response.

Parameter Influences of Light Floating Slab on Its Vertical Vibration Excited by Track Irregularity

According to the structure characteristics of railway viaduct with light floating slabs, a frequency domain dynamic model of the vehicle-light floating slab track-viaduct bridge vertical coupling system is established. The Green functions are used to quickly calculate the receptance response of the system, and then the pseudo excitation method is used to further analyze the parameter influences of the floating slab on the vertical vibration excited by the track irregularity. The parameters of the floating slab have obvious effects on its vertical vibration, so as we strive to reduce the vibration and noise radiation of the railway by changing the parameters of the floating slab, the disadvantages to the vibration and noise control of the floating slab have to be taken into consideration.