Pseudo-excitation Method Research Articles

Wind-Induced Vibration Analysis of Overhead Working Truck

As to the complicated characteristics of overhead working truck under effects of random dynamic wind, the traditional method is difficult to reflect its dynamic response in real time, in the study; it proposes the random wind induced vibration response analysis method based on the finite element method and pseudo-excitation method. An it regards the vibration of the fluctuating wind load as coherent random vibration under stationary random excitation, and it uses Davenport wind velocity spectrum which does not change with height, the correlation of the wind excitation are considered. It takes the folding type arm overhead working truck as example, the random wind vibration analysis are performed, and it gets the acceleration response spectrum and root mean square the of aerial work platform. The analysis results show that the low-order frequency will cause great vibration of the work platform, and the vertical one third of the root-mean-square of acceleration is below international standards, it has no uncomforted effect on operation workers.

Nonlinear Response of Structures Subjected to Stochastic Excitations via Probability Density Evolution Method

Stochastic response analysis plays an increasingly important role in assessing the performance and reliability of engineering structures subjected to disastrous dynamic loads such as earthquakes and strong winds. In the past decade, a family of probability density evolution method (PDEM) has been developed where a completely decoupled generalized density evolution equation (GDEE) is proposed. The dimension of GDEE could be arbitrary and in most cases a reduced one-dimensional equation is adequate. This provides an efficient solution for stochastic response of complex engineering structures. In the present paper, PDEM is incorporated with the efficient representation of stochastic processes to implement stochastic dynamic response analysis of multi-degree-of-freedom (MDOF) systems subjected to stochastic excitations. Stochastic dynamic responses of linear and nonlinear base-excited systems are investigated by PDEM, the pseudo-excitation method and the Monte Carlo simulations. The Sobol' sequence is employed to generate representative white noise process, and a high-performance stochastic harmonic function representation with fewer random variables is employed to generate representative time histories of a stochastic process with specified power spectral density model. The involved seismic excitations are modeled by banded white noise, Kanai-Tajimi filtered stationary process, Clough-Penzien filtered stationary process and Clough-Penzien filtered process with non-stationary modulation, respectively. Numerical results reveal that PDEM is feasible for stochastic response analysis of MDOF nonlinear systems subjected to stochastic excitations with fair accuracy and efficiency.

Fatigue damage analysis of the deepwater riser from VIV using pseudo-excitation method

The fatigue damage of a long deepwater riser undergoing in-line and cross-flow vortex-induced vibration (VIV) in deepwater is numerically studied using pseudo-excitation method (PEM) in present paper. For evaluating the fluid–structure interaction problem of vortex-induced vibration of deepwater riser at high Reynolds number, the strip theory is employed in this paper, and the discrete vortex method (DVM) is used to calculate the VIV of each strip to obtain the load spectrum as the pseudo-excitation, while the finite volume method (FVM) is employed to evaluate the structure dynamics of a deepwater riser. The VIV is considered as a stationary random process. The response of riser to vortex induced excitation is calculated using pseudo-excitation method. The DVM model and pseudo-excitation method are both validated by comparing their numerical results with experiments. The fatigue damage of one deepwater riser is evaluated based on the Palmgren–Miner Rule.

Damage Identification Based on Power Spectral Density Sensitivity Analysis of Structural Responses

A new method is proposed to identify structural damages based on the power spectral density sensitivity analysis. The responses of the structure under stationary and random excitations are obtained using pseudo excitation method, and then the sensitivities of power spectral density with respect to the structural damage parameters are obtained similarly. Finite element model updating method is adopted to identify the structural damages. A numerical example of a shearing structure demonstrates the satisfactory results obtained from the present method.

Failure Probability Analysis of Interlayer Sliding Belts of Gravity Dams Under Seismic Load

In this paper, an improved model is presented for analysis of failure probability of the interlayer sliding belts under seismic loads. Firstly, using the theory of the Markov chain, the relation between failure probabilities of specified interlayer sliding belts and elements in this interlayer sliding belt is deduced. Then, the failure function is proposed according to the destructive characteristic of concrete, the pseudo excitation method is utilized in order to obtain the probability distribution of element stresses in specified interlayer sliding belts, and the improved response surface method based on weighted regression is used to calculate the failure probability of elements in specified interlayer sliding belts. Finally, an algorithm is established to calculate the failure probability of the specified interlayer sliding belts. In this paper, the mean value and variance of the tensile strength of elements are changed when interlayer sliding belt is developed. The numerical results show that the conditional failure probability in specified interlayer sliding belts at the head of the dam tends to decrease. However, the tendency of conditional failure probability in the other specified interlayer sliding belts is complicated. And the interlayer sliding belt at head of the concrete gravity dam is the most dangerous. In addition, the tendencies of the mean value and mean square deviation of stresses in different specified interlayer sliding belts are similar. The mean value of stress in different specified interlayer sliding belts tends to decrease but the tendency of mean square deviation changes from decrease to increase. The range of the mean value and the mean square deviation of stress in specified interlayer sliding belts at the heel of the dam is the greatest of all.

A simplified computational method for random seismic responses of a jacket platform

A simplified method for modeling Jacket Offshore Platform was developed and numerical examples were presented to demonstrate the validity of the proposed method. In this method, a jacket platform was described as a cantilever beam subjected to an axial compressive load acting at the top-end centre of the jacket. The random seismic responses of the model were derived by using both the pseudo-excitation method and the classical Ritz method. The authors found and demonstrated in this paper that this proposed method may be used to calculate the random responses accurately and efficiently. In particular, the responses of a non-uniform beam, in the form of an auto-PSD function, cross-PSD or higher spectral moments could be solved directly without the need to determine the normal modes. The writers included an example in which the solution was obtained using the proposed method with a selected Ritz function. The results were compared with that obtained using the conventional finite element method (FEM). The findings of the study showed that the proposed method was effective, practical and useful in the seismic design of platforms.

Stochastic vibration of the vehicle–bridge system subject to non-uniform ground motions

A study of a train moving along a cable-stayed bridge is performed by considering both the stationary track irregularity and a non-stationary earthquake. A detailed bridge model with 3972 degrees of freedom is established while the train model consists of two locomotives and eight carriages. The equations of motion of the coupled system are obtained by using the displacement continuous condition at the contact, with track irregularities. The earthquake is assumed to occur once the train has entered the bridge. The pseudo-excitation method is used to find the random responses of the coupled system, and the results indicate that the effect of the earthquake is much greater than that of the track irregularities. The paper discusses the influence of the intensity of the earthquake, the wave propagation velocity, the speed of the train, and the dynamic interaction between the vehicles and the bridge.

Dynamic Reliability of Stochastic Truss Structures under Random Load

Aim at the dynamic reliability of stochastic truss structures under stationary random excitation. In consideration of the randomness of structural physical parameters and the geometric parameters and the random excitations were first transformed into sinusoidal ones in terms of the pseudo excitation method ( PEM) , that turned the joint-random problem into a single random problem for which only structural parameters remain random, and thus the analysis is greatly simplified. The mean value and the variance of the mean square value of the structural displacement and velocity were computed by using the theory of spectral analysis. And then the expressions of stochastic truss structural dynamic reliability were educed from the Poisson formula. Finally, the influence of the randomness of structural parameters on the structural dynamic reliability was analyzed by an example; the method of this paper was proved feasible and available comparing with the Monte Carlo method.

Numerical Simulation of Vertical Random Vibration of Train-Slab Track-Bridge Interaction System by PEM

The paper describes the numerical simulation of the vertical random vibration of train-slab track-bridge interaction system by means of finite element method and pseudoexcitation method. Each vehicle is modeled as four-wheelset mass-spring-damper system with two-layer suspension systems. The rail, slab, and bridge girder are modeled by three-layer elastic Bernoulli-Euler beams connected with each other by spring and damper elements. The equations of motion for the entire system are derived according to energy principle. By regarding rail irregularity as a series of multipoint, different-phase random excitations, the random load vectors of the equations of motion are obtained by pseudoexcitation method. Taking a nine-span simply supported beam bridge traveled by a train consisting of 8 vehicles as an example, the vertical random vibration responses of the system are investigated. Firstly, the suitable number of discrete frequencies of rail irregularity is obtained by numerical experimentations. Secondly, the reliability and efficiency of pseudoexcitation method are verified through comparison with Monte Carlo method. Thirdly, the random vibration characteristics of train-slab track-bridge interaction system are analyzed by pseudoexcitation method. Finally, applying the 3σrule for Gaussian stochastic process, the maximum responses of train-slab track-bridge interaction system with respect to various train speeds are studied.

Seismic Response of Base-Isolated High-Rise Buildings under Fully Nonstationary Excitation

Stochastic seismic responses of base-isolated high-rise buildings subjected to fully nonstationary earthquake ground motion are computed by combining the pseudoexcitation and the equivalent linearization methods, and the accuracy of results obtained by the pseudoexcitation method is verified by the Monte Carlo method. The superstructure of a base-isolated high-rise building is represented by a finite element model and a shear-type multi-degree of freedom model, respectively. The influence of the model type and the number of the modes of the superstructure participating in the computation of the dynamic responses of the isolated system has been investigated. The results of a 20-storey, 3D-frame with height to width ratio of 4 show that storey drifts and absolute accelerations of the superstructure for such a high-rise building will be substantially underestimated if the shear-type multi-degree of freedom model is employed or the higher modes of the superstructure are neglected; however, this has nearly no influence on the drift of the base slab.

STOCHASTIC SEISMIC ANALYSIS OF A CFST ARCH BRIDGE UNDER SPATIALLY VARYING GROUND MOTIONS

This paper presents a comprehensive theoretical analysis of an actual concrete-filled steel tubular (CFST) arch bridge under tridirectional spatial motions using the pseudo-excitation method (PEM). Formulations for modelling tridirectional spatial motions at varying sites are derived. Then, stochastic seismic analysis of the CFST arch bridge is conducted, by considering the dimensionality, incoherence effect, wave-path effect of ground motions, and local site effects with different and irregular site conditions. It is concluded that 1) the site effect can significantly affect structural responses; 2) the softer site conditions can amplify the larger structural responses; 3) the varying and irregular site conditions can induce significant variations of structural responses; 4) effect of dimensionality of earthquake motions and inclusion of the vertical ground motions should be considered in the seismic analysis to avoid erroneous response predictions.

다중지점 지진하중에 대한 아치구조물의 지진응답 분석

Spatial structures have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and seismic response for seismic design of spatial structure. Keel arch structure is used as an example structure because it has primary characteristics of spatial structures. In case of spatial structures with different ground condition and time lag, multiple support excitation may be subjected to supports of a keel arch structure. In this study, the response of the keel arch structure under multiple support excitation and with time lag 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. It is known that the seismic responses of spatial structure under multiple support excitation are different from those of spatial structure under simple excitation. And the seismic response of spatial structure with time lag are different from those of spatial structure without time lag. Therefore, it has to be necessary to analyze the seismic response of spatial structure under multiple support excitation and time lag because the spatial structure supports may be different and very long span. 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.

Application of the pseudo-excitation method to assessment of walking variability on footbridge vibration

The pseudo-excitation method is applied to determine the non-stationary vibration response of footbridges to variable pedestrian excitation. Excitation forces are described by their spectral densities, the models of which are taken from the literature. In addition a simple spectral model is proposed to encompass both intra- and inter-pedestrian variability. Comparison is made to Monte Carlo simulations of random pedestrian events and a means of estimating extreme statistics of random walking is given. The method is shown to be accurate and efficient. Consequently, this work should find value in explaining differences between observed and modelled responses.

Typhoon-induced non-stationary buffeting response of long-span bridges in complex terrain

This paper presents a framework for predicting typhoon-induced non-stationary buffeting response of long-span cable-supported bridges located in a complex terrain. First, a non-stationary typhoon wind model is proposed based on observations from measured typhoon wind data. The wind model includes mainly time-varying mean wind speed, mean wind speed profile and evolutionary power spectral density (EPSD) function. Typhoon-induced wind loading on a bridge deck is then represented by time-varying mean wind forces, non-stationary buffeting forces associated with time-dependent aerodynamic coefficients and self-excited forces characterized by time-dependent aerodynamic derivatives. A nonlinear static analysis is performed to determine time-varying mean wind response, whereas the pseudo excitation method is employed to compute the EPSD-expressed non-stationary buffeting response of a long-span cable-supported bridge. The proposed framework is finally applied to predict non-stationary buffeting responses of a long-span cable-stayed bridge located in a complex terrain during a strong typhoon as a case study. The case study demonstrates how to apply the proposed framework and the results show that the proposed framework is feasible and necessary.

Frequency domain response of a parametrically excited riser under random wave forces

Floating Production, Drilling, Storage and Offloading units represent a new technology with a promising future in the offshore oil industry. An important role is played by risers, which are installed between the subsea wellhead and the Tension Leg Deck located in the middle of the moon-pool in the hull. The inevitable heave motion of the floating hull causes a time-varying axial tension in the riser. This time dependent tension may have an undesirable influence on the lateral deflection response of the riser, with random wave forces in the frequency domain. To investigate this effect, a riser is modeled as a Bernoulli–Euler beam. The axial tension is expressed as a static part, along with a harmonic dynamic part. By linearizing the wave drag force, the riser's lateral deflection is obtained through a partial differential equation containing a time-dependent coefficient. Applying the Galerkin method, the equation is reduced to an ordinary differential equation that can be solved using the pseudo-excitation method in the frequency domain. Moreover, the Floquet–Liapunov theorem is used to estimate the stability of the vibration system in the space of parametric excitation. Finally, stability charts are obtained for some numerical examples, the correctness of the proposed method is verified by comparing with Monte-Carlo simulation and the influence of the parametric excitation on the frequency domain responses of the riser is discussed.

Lateral Response of Buried Pipeline through Three-Soil Site to Random Ground Motion

Using the pseudo-excitation method, a simple model was built to study the seismic response of buried pipeline laid through three-soil site for vertical incidence of seismic waves. Seismic ground motions are considered as stationary stochastic processes, and the cross-PSD function was established based on auto-PSD model, coherence model, and site response model. The results show that the peak bending stress depends on the properties of adjacent soils and the width of middle-soil, and appears in the pipeline near the soil interfaces.

PEDEM: a new method for the analysis of the stochastic response

The analysis of the response of a stochastic system, through a discrete coordinate representation, can become computationally challenging, even by using a full modal representation; in fact, many dynamic load cases have stochastic behaviour as the wall pressure fluctuations due to the turbulent boundary layer. In the present work, a new method is presented and discussed and it is named frequency modulated pseudo equivalent deterministic excitation (PEDEM). PEDEM is based on the pseudo excitation method (PEM), but it tries to overcome the computational neck-bottles of this latter by introducing some approximations which are based on the analysis of the eigensolutions of the dynamic load matrix versus frequency. The solution approach uses three different approximations for the load matrix with reference to three frequency ranges, named low, mid and high; these approximations derive from the eigenanalysis of the load matrix. A criterion to identify the three frequency ranges is proposed, too and it is expressed in terms of a reduced dimensionless frequency. PEDEM is thus applied to a plate response; this test case that contains the most relevant parameters of a structural problem. The results herein discussed show that the correlation area can play a fundamental role in discriminating the quality of the approximation. A good level of accuracy and representation of the stochastic system together with a significant reduction of the computational costs are obtained if compared to a full stochastic response (FSR) or PEM solution.

Local site effects on a high-pier railway bridge under tridirectional spatial excitations: Nonstationary stochastic analysis

This paper presents a theoretical nonstationary stochastic analysis scheme using pseudo-excitation method (PEM) for seismic analysis of long-span structures under tridirectional spatially varying ground motions, based on which the local site effects on structural seismic response are studied for a high-pier railway bridge. An absolute-response-oriented scheme of PEM in nonstationary stochastic analysis of structure under tridirectional spatial seismic motions, in conjunction with the derived mathematical scheme in modeling tridirectional nonstationary spatially correlated ground motions, is proposed to resolve the drawbacks of conventional indirect approach. To apply the proposed theoretical approach readily in stochastic seismic analysis of complex and significant structures, this scheme is implemented and verified in a general finite element platform, and is then applied to a high-pier railway bridge under spatially varying ground motions considering the local site effect and the effect of ground motion nonstationarity. Conclusions are drawn and can be applied in the actual seismic design and analysis of high-pier railway bridges under tridirectional nonstationary multiple excitations.

Riding comfort optimization of railway trains based on pseudo-excitation method and symplectic method

This research is intended to develop a FEM-based riding comfort optimization approach to the railway trains considering the coupling effect of vehicle–track system. To obtain its accurate dynamic response, the car body is modeled with finite elements, while the bogie frames and wheel-sets are idealized as rigid bodies. The differential equations of motion of the dynamic vehicle–track system are derived considering wheel–track interaction, in which the pseudo-excitation method and the symplectic mathematical method are effectively applied to simplify the calculation. Then, the min–max optimization approach is utilized to improve the train riding comfort with related parameters of the suspension structure adopted as design variables, in which 54 design points on the car floor are chosen as estimation locations. The K–S function is applied to fit the objective function to make it smooth, differentiable and have superior integrity. Analytical sensitivities of the K–S function are then derived to solve the optimization problem. Finally, the effectiveness of the proposed approach is demonstrated through numerical examples and some useful discussions are made.

Crack Identification of Cantilever Plates Based on a Kriging Surrogate Model

This work presents an effective method to identify the tip locations of an internal crack in cantilever plates based on a Kriging surrogate model. Samples of varying crack parameters (tip locations) and their corresponding root mean square (RMS) of random responses are used to construct the initial Kriging surrogate model. Moreover, the pseudo excitation method (PEM) is employed to speed up the spectral analysis. For identifying crack parameters based on the constructed Kriging model, a robust stochastic particle swarm optimization (SPSO) algorithm is adopted for enhancing the global searching ability. To improve the accuracy of the surrogate model without using extensive samples, a small number of samples are first used. Then an optimal point-adding process is carried out to reduce computational cost. Numerical studies of a cantilever plate with an internal crack are performed. The effectiveness and efficiency of this method are demonstrated by the identified results. The effect of initial sampling size on the precision of the identified results is also investigated.