Random Dynamic Response Research Articles

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Random dynamic response analysis of an asphalt concrete core wall dam on deep overburden with double random factors

The spatial variability of material parameters and the randomness of ground motion are factors that influence the seismic response of a dam. To obtain more reliable seismic response results, it is crucial to study the influence of various uncertain factors on the response to earthquakes. In this paper, the K-L series expansion method and LH sampling technique are combined to characterize the spatial correlation of material parameters using a Gaussian autocorrelation function. This allows for the simulation of random fields of material parameters. By improved the Clough-Penzien power spectrum model and incorporating the concept of a random function, it becomes possible to generate nonstationary random ground motion that accurately reflects the site conditions. Taking an asphalt concrete core dam on deep overburden as an example, a random dynamic response analysis was conducted, considering various random factors. Statistical analysis and distribution testing were conducted on the horizontal acceleration and vertical permanent deformation responses. The process of the evolution of the probability density of the horizontal acceleration at the top of the dam was determined using the generalized probability density evolution method. This method helps to reveal the influence of various random factors on the response of the dam body. The research results show that among the spatial variability of material parameters and the randomness of ground motions, the randomness of ground motions is the main influencing factor of the random response results of the dam body. The mean response of two random factors is significantly larger than that of a single random factor. When considering dual random factors simultaneously, the complexity of the random factors increases, resulting in statistical properties that differ from those of single random factors. Therefore, to obtain more reliable random seismic response results, it is necessary to consider both the spatial variability of material parameters and the randomness of ground motions.

Multi-hazard stochastic response analysis and reliability evaluation of a 5 MW monopile offshore wind turbine based on extended platform FAST-S

This study investigates the random dynamic response of a 5 MW monopile offshore wind turbine (MOWT) subjected to wind, wave and earthquake loads. Based on the aero-hydro-servo-elastic code FAST, a multi-field coupled simulation module considering earthquake, FAST-S, is developed for the fully coupled multi-hazard analysis of OWTs. Compared to the original FAST code, a seismic analysis module (SeismoDyn) and a soil-structure interaction (SSI) module (SoilDyn) have been supplemented in FAST-S. SeismoDyn is developed by modifying the Kane’s kinetic equation in the FAST, and the SoilDyn is developed through Winkler foundation model in order to consider the nonlinear SSI. Moreover, FAST-S has been validated by other recognized codes. Based on FAST-S, a fully coupled numerical analysis model of the NREL 5 MW MOWT is established, the random responses and reliability evaluation of the offshore wind turbine under wind, wave and earthquake loads are analyzed by probability density evolution method. The results show that the aerodynamic and hydrodynamic actions increase the damping of the wind turbine system, which has a certain effect on inhibiting the tower’s vibration caused by the earthquake. Therefore, compared with the coupled wind-wave-earthquake case, the sole earthquake case may be more unfavorable, and should be paid more attention to in high risk earthquake regions. The results show that the probability density functions of offshore wind turbine response under strong earthquakes obviously deviates from the typical regular distribution models. Based on the theory of equivalent extreme value event, the dynamic reliability of the offshore wind turbine is calculated. Seismic actions maybe the major factor in the design of the support structure. Nevertheless, owing to the aerodynamic and hydrodynamic damping effects of wind and wave loadings, the structural responses under wind-wave-earthquake are more moderate than ones subjected to solely earthquake. The strong seismic loads would cause significant complex variations of time-dependent probability density function of the OWT response.

Analysis of random induced dynamic response of rural roads considering friction effect and nonlocal effect under the load of construction vehicles

Abstract The objective of this paper is to propose a novel computational model for solving the problem of accurately evaluating the randomly induced road vibration response of engineering vehicles traveling on rural roads. The computational model, first, focuses on the unique pavement characteristics of rural roads, constructs a tire grounding function model and innovatively introduces a dynamic friction factor, and successfully develops a coupled stochastic excitation system model for the interaction between the dynamic loads of 1/4 vehicle tires and the pavement of rural roads by applying the power spectral density function of the rural roads and combining it with the elastic roller model of the vehicle tires. Second, considering the nonlocal superposition effect of the soil skeleton of the roadbed, a coupled vibration response model of a 1/4 automobile rural road is successfully developed, and a validation method is given. Finally, the coupled vibration response characteristics of engineering vehicles and rural roads under random excitation at different speeds are analyzed. The analysis results show that the model proposed in this paper can well predict the degree and influence the range of rural road vibration caused by random excitation of construction vehicles traveling at any speed.

Assessment of train running safety on railway bridges based on velocity-related indices under random near-fault ground motions

Random analysis has emerged as the dominant approach for analyzing train-bridge coupled (TBC) systems, replacing deterministic analysis. This shift is driven by considerations of system economy and randomness. However, the seismic train running safety assessment with multiple non-Gaussian distribution parameters faces the double dilemma of low computational efficiency and inaccuracy for TBC systems. In this study, an approach is applied by the combination of the new point estimate method and moment expansion approximation (NPEM-MEA) to address this problem. Furthermore, the application of this approach is illustrated by the random dynamic responses of a three-dimensional TBC system subjected to random near-fault ground motions. Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method, and comparative analysis confirms the accuracy and efficiency of the method. Additionally, the influences of random near-fault ground motions are discussed based on the random dynamic responses and train running safety indices in the TBC system. The simulation results underscore the necessity of simultaneously considering the randomness of multiple parameters in seismic train running safety assessment. This methodology holds potential for safety assessments involving non-Gaussian random processes in complex systems of a similar nature.

Dynamic Amplification Factors of an Arch Bridge Under Random Traffic Flows

Among large-span bridges, arch bridges have relatively high stiffness, which may lead to large dynamic amplification factors (DAFs). The DAFs suggested by current codes mostly originate from common simply supported beam bridges. Previous DAF studies on dynamic vehicle–bridge solutions for arch bridges have mainly focused on one or two side-by-side vehicles. However, complex traffic flows with randomness rather than one or two vehicles act on bridges. DAFs that consider the effects of random traffic flows have not previously been reported. In this study, a random traffic–bridge vibration solution was established to explore the DAFs of arch bridge components. The randomness of the traffic parameters and road roughness was explored. The randomness of the external excitation, including traffic flow and road roughness, resulted in random dynamic responses and DAFs of the arch bridge components. Normal distributions could be used to fit the DAF distributions of each arch bridge component under random vehicle spacing, weight, speed, and road roughness. Under random traffic parameters, the coefficients of variation of the DAFs exceeded the 5% accepted level. The shortest suspenders were more sensitive to the randomness of the traffic flow parameters. Both the mean and coefficient of variation of the DAFs increased with worsening of the road conditions. The influence of the randomness of the road roughness on the DAFs of arch bridges must be considered, particularly for the shortest suspender. The 95% upper confidence limits of the DAFs for all components may be greater than the suggested values in the code.

First Passage Dynamic Reliability Analysis of Non-Stationary and Non-Gaussian Buffeting Random Dynamic Responses of Long-Span Suspension Bridge

In the complex mountain wind environment, especially in the strong wind, fluctuating wind speed is a non-stationary and non-Gaussian random process. With the increase of suspension bridges’ span, they are more sensitive to wind-induced vibration response. In this paper, a non-stationary and non-Gaussian buffeting reliability analysis method for long-span bridges is presented. Firstly, the non-stationary wind speed is simulated by the modulation function based on the stationary wind speed model. Secondly, the load is obtained by simulated wind speed, the obtained loads are loaded on the finite element model by ANSYS and the whole bridge time-domain analysis is performed, the time history of displacement response is obtained. Thirdly, based on the first excursion failure criterion of random vibration, the samples of the non-stationary and non-Gaussian displacement time history are transformed into a standard Gaussian process through a modified Fleishman approximation method, and then the non-stationary Poisson distribution method is used for structural reliability analysis. Finally, a mountainous long-span suspension bridge is used as the engineering background, and the proposed reliability analysis method is applied to analyze the reliability of the bridge. The influence of different wind attack angles and modulation functions on the dynamic reliability of the bridge is further studied. The results indicate that the displacement response obtained by the transformation of non-stationary and non-Gaussian random process is less reliable than that obtained by traditional analysis method. Its dynamic reliability is maximum at 1[Formula: see text] wind attack angle, the reliability of negative wind attack angle is lower than that of positive wind attack angle, and decreases with the increase of wind attack angle. The reliability obtained by using different modulation functions is lower than that of traditional method. If the traditional analysis method is still used for reliability analysis, it will produce unsafe consequences and reduce the engineering safety reserve.

Random dynamic responses of solar array under thermal-structural coupling based on the isogeometric analysis

Random dynamic responses of solar array under thermal-structural coupling based on the isogeometric analysis

A high-performance calculation scheme for stochastic dynamic problems

The goal of stochastic dynamic problems is to efficiently and accurately calculate statistical moments and random dynamic responses. Thus, a high-performance calculation scheme is proposed to achieve the goal. First, to enhance the accuracy of the statistical moments, we proposed an adaptive weights quasi-Monte Carlo (AWQMC) method. Compared to the integration weights of the traditional quasi-Monte Carlo method, the adaptive weights can better reflect the discrepancy of the sample points to obtain more accurate statistical moments. Additionally, the adaptive weights only depend on the sample set, which can be applied to other stochastic problems. Second, the reduced-order model technology is introduced to improve the calculation efficiency of random dynamic responses. Combining of the Galerkin method, a novel reduced-order model based on deterministic reduced bases is proposed for random dynamic system. Then, an efficient dynamic equation solver is constructed based on the deterministic reduced bases and the Newmark method. Finally, according to the three numerical examples, the high-performance calculation scheme combined the AWQMC method and the efficient dynamic equation solver can significantly improve the accuracy and efficiency of statistical moments for stochastic dynamic problems.

Permanent displacement reliability analysis of soil slopes subjected to mainshock-aftershock sequences

It is of great significance for disaster prevention to study the influence of mainshock-aftershock sequences on reliability of the soil slope. Considering the uncertainty of the mainshock-aftershock sequences, a new analysis method is proposed for the random dynamic response analysis and permanent displacements reliability evaluation of soil slopes under the action of mainshock-aftershock sequences. Firstly, a simulation method of random seismic sequence based on Copula function considering the correlation between mainshock and aftershock is introduced in this paper. Then, the permanent displacement of soil layered slope under 86 randomly generated mainshock-aftershock sequences and single mainshocks is calculated based on Newmark method. And the influence of aftershocks on the permanent displacement of slope is analyzed through the mean value. Besides, the influence of peak ground acceleration (PGA) on the permanent displacement and sliding surface of slope is also discussed. Finally, based on the probability density evolution method (PDEM), the influence of aftershocks on the permanent displacement reliability of slope is explained from the perspective of probability for the first time. The results show that the randomly generated mainshock-aftershock sequence can meet the needs of random dynamic analysis and probability analysis of soil slope by comparing with the target value. Based on the random dynamic calculation results, compared with single mainshocks, the soil slope has larger permanent displacement under the mainshock-aftershock sequences. However, there are obvious uncertainties in the permanent displacement and the position of the most dangerous sliding surface according to the different soil layer distributions and ground motions. It is very necessary to study the influence of mainshock-aftershock sequence on slope reliability from the perspective of probability. When the threshold is 1 m, the reliability of the slope will be reduced by 2 %∼15 % by aftershocks.

Random vibration and structural reliability of composite hyperbolic–parabolic membrane structures under wind load

The paper presents the random vibration and structural reliability of composite hyperbolic–parabolic membrane structures under wind load. First, the non-linear random vibration equation of the hyperbolic–parabolic membrane structures is established by the moment-free theory of thin shells, von Karman’s large deflection theory, and the potential flow theory. The results of random dynamic responses are obtained with the Fokker Planck Kolmogorov equation method (FPK) solving the equation. Then, the structural performance function of composite membrane structures is established based on the Displacement First Passage Failure Criteria (DFPFC) and the results of random dynamic responses. Furthermore, the reliability index (RI) of the performance function is calculated by the JC method. Finally, the theoretical model proposed is validated by experimental investigation utilizing the Monte Carlo sampling method (MCS). Additionally, the influence of wind speed, pretension force, and rise–span ratio on hyperbolic–parabolic membrane structure reliability is analyzed. The paper can provide important references for the design and analysis of membrane structures.

Stochastic vibration suppression of composite laminated plates based on negative capacitance piezoelectric shunt damping

This paper studies the stochastic vibration suppression of the composite laminated plates by using the negative capacitance piezoelectric shunt damping. The energy method and Hamilton’s principle are employed to formulate the dynamic model of the composite laminated plate with negative capacitance piezoelectric shunt damping circuit. The random dynamic response of the coupled system subjected to nonstationary stochastic excitations is further obtained based on the modified Ritz method and pseudo excitation method (PEM). The accuracy of the proposed method is validated by comparing the obtained random results with those from the published literature and satisfactory agreements can be observed between them. Furthermore, the vibration suppression performance of the proposed piezoelectric shunt damping with series negative capacitor or parallel negative capacitor is discussed, respectively. Finally, the effects of key parameters of the piezoelectric shunt damping on the vibration suppression performance are discussed in detail.

Probabilistic Seismic Response Prediction of Three-Dimensional Structures Based on Bayesian Convolutional Neural Network

Seismic response prediction is a challenging problem and is significant in every stage during a structure’s life cycle. Deep neural network has proven to be an efficient tool in the response prediction of structures. However, a conventional neural network with deterministic parameters is unable to predict the random dynamic response of structures. In this paper, a deep Bayesian convolutional neural network is proposed to predict seismic response. The Bayes-backpropagation algorithm is applied to train the proposed Bayesian deep learning model. A numerical example of a three-dimensional building structure is utilized to validate the performance of the proposed model. The result shows that both acceleration and displacement responses can be predicted with a high level of accuracy by using the proposed method. The main statistical indices of prediction results agree closely with the results from finite element analysis. Furthermore, the influence of random parameters and the robustness of the proposed model are discussed.

Seismic time-history response and system reliability analysis of slopes considering uncertainty of multi-parameters and earthquake excitations

In practical geotechnical engineering of slopes, it is well-known that the uncertainty of soil properties and ground motions need to be considered for the safety of the project. The effect of uncertain parameters and stochastic ground motions on seismic responses as well as dynamic failure probabilities of slopes are analyzed and discussed in this study. A recently proposed generalized probability density evolution method (GPDEM) is formulated to investigate the system reliability of complex slopes with consideration to uncertainty in multiple slope parameters and in ground motions. Firstly, the fundamental theory of dynamic stability, GPDEM, dynamic system reliability, generation of random samples and stochastic ground motion model are described. Then, the efficiency and accuracy of proposed GPDEM are verified and a novel evaluating index is presented. Four complex slopes, each with multi-parameter uncertainties, are examined in separate study cases. Each study case uses GPDEM to study the random dynamic responses as well as probability responses of slopes while considering deterministic ground motion. The efficiency and accuracy of GPDEM used in complex slopes are validated by comparing with the Monte Carlo method (MCM). In addition, a novel evaluating index called the average large failure probability Pff, is proposed to describe the failure probability of the slopes, and can take the probability time histories intoaccount. Finally, the seismic system reliability of complex slopes is evaluated using the time-history method, and randomness in earthquakes, parameters and their coupling are investigated. The stochastic dynamic responses and probability responses of deterministic parameters subjected to stochastic earthquake excitations, and random parameters subjected to stochastic earthquake excitations are also discussed and are compared based on study case 3. The results demonstrate the high accuracy and validity of the GPDEM. Furthermore, the probability of failure and the degree of safety for the slopes can be directly estimated through probability analysis. In addition, the results also indicate that randomness in ground motions have a much larger influence than randomness in slope parameters, but randomness in slope parameters cannot be completely neglected.

Random vibration of composite saddle membrane structure under the impact loading

Large-span composite membrane structure is light in weight and small in stiffness, which may produce violent random vibration under the random impact, such as wind, rain, hail and windborne debris. In order to accurately understand the random vibration response of membrane structure, the dynamics of composite saddle membrane structure under the stochastic impact load is studied in this paper. The governing equation of random vibration is established based on the von Karman large deflection theory of thin shell and the shallow membrane assumption. The orthotropy, damping and geometrical nonlinearity are considered for the composite membrane. The stochastic pulse of the impact load is imposed based on the statistical data of impact velocity difference. The perturbation method is used to solve the stochastic vibration equation, and the statistical moments of the displacement are derived from the Galerkin method, which is then validated against the numerical simulations. The comparison shows that the analytical solution can well predict the random dynamic response of saddle membrane structure under the impact load. Finally, it is discovered by the parametric studies that the average displacement reduces with the increase of membrane pretension and arch span ratio, and grows with the increase of impact velocity difference.

Random Dynamic Response Characteristics of Pipeline Subjected to Blasting Cylindrical SH Waves

It is essential to investigate the influence of blasting vibrations on pipelines, and the dynamic response is the crux in the safety issues. At present, the blasting seismic wave is usually regarded as a plane wave. However, there is little research about the dynamic response characteristics of underground structures subjected to nonplane waves. The analytical solution to dynamic stress concentration factor (DSCF) of pipelines subjected to cylindrical SH wave was derived. Besides, the randomness of the shear modulus of soil was considered, and the statistical analysis of DSCF was carried out by the Monte Carlo simulation method. Results show that the variability of the shear modulus of soil has a significant influence on the probability distribution of DSCF. The larger the variation coefficient of the shear modulus is, the more obvious the skewness of DSCF is. The influence of low‐frequency wave on pipeline increases with the reducing normalized distance r∗, while the influence of high‐frequency wave reduces and the variation amplitude of DSCF increases. Compared with the DSCF of pipe subjected to a plane wave, a lower dominant frequency or larger normalized distance for the cylindrical SH wave will generate a more similar statistical characteristic of DSCF.

Effects of Random Variations of Partially Saturated Soils Properties on Site Amplification of Seismic Ground Motions

Based on the principle of random vibration and the Tajimi-Kanai spectrum model, a seismic model with a given magnitude and epicenter distance is used to simulate the seismic motion. For the random variation of soil properties such as shear modulus, mass density, damping ratio and saturation of partially saturated soils, it is assumed that the input seismic wave is SH wave. The random dynamic response analysis of the site is conducted by using the linear wave propagation method and the Rosenblueth method, and the digital features of the amplified power spectral density function, the acceleration power spectrum density, the mean value and the standard deviation are obtained respectively. In a numerical example, a clay ground is considered. For the random variation of soil properties and the different of incident angles, the digital features of the amplified power spectral density function, the acceleration power spectral density, the mean value and the standard deviation are analyzed. The results show that the random variation of quasi saturated soils properties and the different of incident angles have great influence on the site amplification effect.

Nonlinear random seismic analysis of 3D high-speed railway track-bridge system based on OpenSEES

A new nonlinear track-bridge random model was established based on OpenSEES, of which the random seismic responses is systematically studied by using probability density evolution method (PDEM). First, a three-dimensional detail nonlinear random dynamic model of the track-bridge coupled system in high-speed railway is established considering the earthquake as the random excitation. The dynamic model is composed with the rail, CRTS II slab ballastless track, the simple supported bridges, bearing, pier and the pile foundation, from which the random dynamic equation of the random model is formulated. In order to evaluate the seismic performance of track structures from a random perspective, the random seismic responses of high-speed railway bridge under random seismic excitations are investigated and analyzed by using the PDEM. Eventually, the Newmark β integration method and the double edge difference method of TVD format are adopted to obtain the random responses involving the probability functions, which can be translated to get the mean value and the standard deviation of responses. Thus, the abundant probability information of seismic responses of the high-speed railway bridge under random seismic excitations can be obtained. The PDF and CDF of the sliding layer are obtained; thus, the failure probability and reliability of different damage grades of sliding layer are obtained. Discussions and significant conclusions on the random dynamic responses are presented.

The dynamic analysis of stochastic thin-walled structures under thermal–structural–acoustic coupling

Random dynamic analysis of the thin-walled structure subjected to coupling loads from three fields is addressed in the frame of the finite element method. Based on the proposed dynamic finite element equation of the deterministic structure under thermal–structural–acoustic coupling, when the randomness of structural physical parameters, temperature load and fatigue test data is fully considered, the dynamic responses of random structure subjected to coupling loads from three fields are dealt with by random factor method. The numerical characteristic values of the random temperature field and that of random dynamic responses are then derived through the moment method of random variables. Subsequently, the dynamic reliability of the stochastic structure under three-field coupling is evaluated using residual strength model, dynamic stress-intensity interference theory and the cumulative damage equal principle. Finally, the results from the methodology proposed are compared with that from Monte-carlo method for a case of numerical example, along with an inspection of the impacts of random variables on dynamic analysis results.

Train-bridge system dynamics analysis with uncertain parameters based on new point estimate method

In the analysis of train-bridge coupled vibration system, randomness of parameters of high-speed railway bridge cannot be ignored. The new point estimate method (NPEM) is a kind of accurate and efficient method to calculate the random response and reliability. In this paper, NPEM is applied to analyze the random dynamic responses of 3D train-bridge coupled system with random parameters, including parameters of bridge materials, environment factor and prestressing parameters. Newmark-β approach is applied as the integration algorithm, and the Monte Carlo method is used to validate the feasibility of the NPEM. The results show that NPEM can be combined with random system accurately and efficiently. Furthermore, the influences of different random parameters distributions are discussed.