Random Response Analysis Research Articles

Response and Reliability of Composite Post Insulators Under Random Earthquake

Abstract This article examines the stochastic response and seismic reliability of composite post-insulators under random seismic excitation. A random seismic motion model, tailored for power facility seismic research in China and compliant with the “Seismic Design Specification for Power Facilities” (GB50260-2013), is developed. This model accounts for both amplitude and frequency non-stationary. A nonlinear dynamic model for composite post insulators is then established, incorporating the nonlinearity at the multi-section insulator and flange connections. Numerical methods are employed for random seismic response analysis to address the non-stationary nature of seismic motion. The proposed model’s validity is confirmed by comparing it with the vibration table test results. Finally, the seismic reliability of composite post insulators, with root stress as the control criterion, is assessed using the probability density evolution method.

Detailed development and validation of a finite element model for studying the entire spinal vibration behavior within a seated human body

Studying the vibration behavior of the entire spine can guide the design of seat comfort and vibration safety. However, due to simplification of traditional biomechanical models, very few studies have analyzed in detail the vibration behavior characteristics of the entire spine inside a seated human body. Therefore, this study aimed to provide guidance and reference for spinal modeling and biomechanical research in ergonomics. A developed finite element model of three-dimensional seated human body was validated and adjusted based on anatomical data of human spine in detail. Static analysis, modal analysis and random response analysis (under vertical excitation between 0 and 20 Hz at 1 m/s2 r.m.s.) were conducted. The range of motion, modal frequencies and the tri-axial transmissibility of the developed models matched well with experimental results. In the vertical resonance mode, the entire spine contained both vertical deformation (60% of the total) and vertical displacement (40%), in addition, the cervical spine, especially the lumbar spine, also contained bending deformation which could alleviate the impact, but led to complex alternating stresses, increasing the risks of the spinal injuries under vertical whole-body vibration. From the bottom to the top of the spine, the frequency distribution of vertical transmissibility became steeper, the peak value increased, and the number of peaks decreased. This study provided new insights into the vibration behavior and frequency response of the entire spine inside a seated human body for improving seat comfort and vibration safety.

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.

Study on the biodynamic characteristics and internal vibration behaviors of a seated human body under biomechanical characteristics.

To provide reference and theoretical guidance for establishing human body dynamics models and studying biomechanical vibration behavior, this study aimed to develop and verify a computational model of a three-dimensional seated human body with detailed anatomical structure under complex biomechanical characteristics to investigate dynamic characteristics and internal vibration behaviors of the human body. Fifty modes of a seated human body were extracted by modal method. The intervertebral disc and head motions under uniaxial white noise excitation (between 0 and 20Hz at 1.0, 0.5 and 0.5m/s2 r.m.s. for vertical, fore-aft and lateral direction, respectively) were computed by random response analysis method. It was found that there were many modes of the seated human body in the low-frequency range, and the modes that had a great impact on seated human vibration were mainly distributed below 13Hz. The responses of different positions of the spine varied greatly under the fore-aft and lateral excitation, but the maximum stress was distributed in the lumbar under different excitations, which could explain why drivers were prone to lower back pain after prolonged driving. Moreover, there was a large vibration coupling between the vertical and fore-aft direction of an upright seated human body, while the vibration couplings between the lateral and other directions were very small. Overall, the study could provide new insights into not only the overall dynamic characteristics of the human body, but also the internal local motion and biomechanical characteristics under different excitations.

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.

Design and Failure Analysis of Motorbike Sub-frame Using Finite Element Analysis

<div>All two-wheeler industries validate their product’s fatigue life on proving track before heading for mass production. Proving test tracks are made to simulate the end-user environment in order to find out the possible fatigue failures during each development stage of vehicle design, which in turn helps the CAE analysts to verify the design before it goes to the end-user hands. In this article we present the design and failure analysis of sub-frame assembly of motorbike observed during the accelerated fatigue test on proving track. Sub-frame main rod was found broken exactly between two weld endings during fatigue test before reaching 6% of the target fatigue life. Possible causes of sub-frame failures have been identified/analyzed in detail using fish bone diagram. A finite element analysis (FEA) model of sub-frame assembly was developed and a random response analysis was carried out on initial design. Acceleration input loads measured from test track have been given at the sub-frame mounting points to calculate output responses. Output responses show a high magnitude of amplitude stresses on the sub-frame main rod exactly where track test failure occurred. Fishbone diagram analysis indicates that the improper design of the stay bracket, stress concentrations regions in the design, improper weld/tool fixture, and method of welding could be reasons for failure. FEA on the final design concept shows a reduction of amplitude stress to 49% and an increase of fatigue life to an infinite limit as compared to initial design.</div>

Influence of foot excitation and shin posture on the vibration behavior of the entire spine inside a seated human body

Due to ethical issues and simplification of traditional biomechanical models, experimental methods and traditional computer methods were difficult to quantify the effects of foot excitation and shin posture on vibration behavior of the entire spine inside a seated human body under vertical whole-body vibration. This study developed and verified different three-dimensional (3D) finite element (FE) models of seated human body with detailed anatomical structure under the biomechanical characteristics to predict vibration behavior of the entire spine inside a seated human body with different foot excitation (with and without vibration) and shin posture (vertical and tilt posture). Random response analysis was performed to study the transmissibility of the entire spine to seat under vertical white noise excitation between 0 and 20 Hz at 0.5 m/s2 r.m.s. The results showed that although the foot excitation could reduce the fore-aft transmissibility in the cervical spine (23% reduction), it could significantly increase that in the lumbar spine (52% increase), which resulted in complex alternating stresses at lumbar spine and made the lumbar spine more vulnerable to injury in long-term vibration environment. Moreover, the shin tilt posture made the maximum fore-aft transmissibility in the lumbar spine move to the upper lumbar spine. The study provided new insights into the influence of foot excitation and shin posture on the vibration behavior of the entire spine inside a seated human body. Foot excitation exposed the lumbar spine to complex alternating stresses and made it more vulnerable to injury in long-term whole body vibration.

Numerical analysis of random vibration fatigue for a typical airborne equipment

In this paper, the fuel pump impeller was selected as a typical airborne equipment for the investigation of random vibration fatigue. First, based on the platform of ANSYS WORKBENCH, the reasonable calculation of FSI for the impeller was carried out. Then, the stress was transferred to modal analysis, and the prestress-structure modal was extracted. Through random vibration response analysis, the stress of the impeller was obtained. The Palmgren and Miner rule and Dirlik fatigue calculation method was used to calculate fatigue life, and the result was consistent with practice. The work in this paper provided a method about how to obtain random vibration fatigue life with prestress-structure, which was critical references for aviation technologists.

Random Fatigue Analysis of Cryogenic Liquid Tanker Under Road Spectrum Load and a Simplified Algorithm

AbstractThe lightweight of liquefied natural gas (LNG) tanker can reduce transportation cost and improve transportation efficiency. However, in lightweight design, the random vibration analysis based on fluid–structure interaction (FSI) is difficult, which demands to be effectively solved by simplifying the finite element model and load. The vibration test and fluid–structure interaction modal numerical analysis of a tanker model were carried out, respectively, and the results are in good agreement. Taking the DC18 LNG tanker as an example, the random vibration response analysis was carried out based on the fluid–structure interaction modal numerical analysis, and the random fatigue damage coefficient of the support region of the inner container was obtained, which was used as the benchmark for the model and load simplification. The finite element model of the LNG tanker was simplified by applying the equivalent liquid mass to the walls of the inner container in the form of density. It is found that when the equivalent liquid mass ratio is 40%, the random vibration response characteristics of the DC18 LNG tanker are close to the actual structure. In the static calculation of the simplified model, the stress response of the container support area is close to the actual structural when the equivalent road spectrum load is 0.95 g vertical acceleration. In this case, the stress result and the overall damage coefficient equivalent to the actual structure can be obtained just by static calculation, which greatly simplifies the solution process.

Investigation of nonproportional damping characteristics of structure with energy dissipation system

AbstractThe spatial and traveling wave effects on a structure with an energy dissipation system can be conveniently considered using the random vibration method. In this study, the pseudo‐excitation method is introduced to perform random spatial seismic response analysis of such a structure considering different damper arrangements. The analysis results show the effects of nonproportional damping characteristics due to these arrangements, and the nonproportional damping characteristic index can estimate the strength of these characteristics. Moreover, the virtual excitation method can be used to determine the weak parts of the structure. The effect of the traveling wave on the energy dissipation system and damping structure is relatively low. The response results of the structure in the case of multipoint consistent excitation obtained by the complex vibration decomposition reaction spectrum method are compared. The method accounts for the effects of nonproportional damping and vibration velocity. Accurate time history results can be obtained by complex vibration decomposition time history analysis.

An Efficient Algorithm for Multi-dimensional and Multi-point Random Seismic Response Analysis of Spatial Grid Structure based on Computer

An Efficient Algorithm for Multi-dimensional and Multi-point Random Seismic Response Analysis of Spatial Grid Structure based on Computer

A symplectic homotopy perturbation method for random structural dynamics response analysis based on Birkhoffian systems

With the enhancement of the engineering structure complexity, numerical computation plays a prominent role in structural dynamics analysis. In theory, general mechanical systems can be transformed into Birkhoffian forms, whose matching symplectic numerical algorithms perform well in accuracy and stability. Besides, the influence of uncertainty cannot be ignored in practical engineering, but the research on uncertainty symplectic algorithms of Birkhoffian systems is still weak. This paper proposes a symplectic homotopy perturbation method (SHPM) for general Birkhoffian equations with random uncertainties. Different from the traditional perturbation method, the proposed method does not depend on small parameters. Based on the homotopy perturbation method, embedded parameters are introduced to establish the matrix and parameter perturbation equations of random Birkhoffian equations, respectively. Then the formulas for calculating the mean value and standard deviation of the response are derived with probability theory. Combined with Birkhoffian symplectic preserving algorithms, a symplectic homotopy perturbation method for the numerical solution of random Birkhoffian equations is proposed. Finally, numerical examples are given to verify the applicability and effectiveness of the proposed method and its superiority compared with the traditional non-symplectic method.

Random response analysis of hydraulic pipeline systems under fluid fluctuation and base motion

Aero hydraulic pipeline systems are subjected to internal fluid fluctuations and random base motions during operation, resulting in time-varying system parameters and nonstationary random responses. To analyse this situation, a nonstationary random response analysis method and a fatigue damage assessment formula for periodic time-varying systems under stationary random excitations are proposed. The nonstationary random response is described by a time-varying power spectral density function, which is strictly characterised by a set of pseudo responses of a periodic time-varying system under a series of harmonic excitations. A frequency-domain iterative solution format for the pseudo responses is constructed and combined with the fast Fourier transform to obtain the time-varying power spectral density function. A fatigue damage assessment formula is derived by discretising the time-varying power spectral density function of the pipeline stress in both the time and frequency domains. The proposed method only requires a few iterations at specific frequency points to calculate each pseudo response in a wide-band random airframe motion environment, showing high computational efficiency. A practical application concerning a section of the wingtip hydraulic pipeline is presented to demonstrate the correctness and efficiency of this method. The variations of pipeline responses and fatigue damage rates under fluid fluctuations and random base motions are also discussed.

Random response analysis of nonlinear structures with inerter system

Most researches on inerter focused on the mechanism or deterministic vibration analysis, and some studies lied in the random vibration of linear structures. However, many structures exhibit the nonlinear characteristics under a large excitation, and the effects of inerter system on additional properties and probabilistic distribution of random response of nonlinear structure under random excitation have rarely been considered at present. Based on the enhancement effect of inerter system on nonlinear structure, the influence of various components of inerter system on the response suppression of nonlinear structure is investigated from the probability level, and a developed response analysis method suitable for inerter system is proposed in this paper. The stochastic differential equation of nonlinear structure with inerter is established in this work, in which both the nonlinear structure without hysteresis and the hysteretic structure are considered. The probability density function of structural response is obtained by the exponential polynomial closure (EPC) method combined with the state-space-split technique. In terms of nonstationary random excitation, a scheme of equivalent stationary excitation is proposed to split the state space vector. Meanwhile, the EPC method is developed through the reduction of undetermined coefficients in the probabilistic solution, which significantly improves the efficiency. Numerical results show that the response suppression effectiveness of inerter system is robust to nonlinear structures, and the inerter system mainly provides additional damping for the primary structure, thereby achieving the vibration mitigation. However, an excessively rigid inertia system may lead to a negative additional stiffness for the primary structure and inhibit the vibration mitigation.

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.

Analysis of random wind-induced response of isolation structure with viscoelastic damper and TMD

The analysis method of wind vibration response of the seismically isolated structure with viscoelastic damper and tuned mass damper(TMD) under Davenport wind load was studied systematically. Firstly, using the general integral models of viscoelastic dampers to establish the exact dynamic integral-differential response equations in original structural space for isolated structure with general linear viscoelastic damper and TMD. Then, adopting the transfer function method to obtain the exact non-orthogonal modal superposition solution in original structural space for the displacement response standard deviation and the equivalent wind force transient response in the time domain of the isolated structure with viscoelastic damper and TMD under wind loading. These exact solutions can accurately discover the vibration properties of viscoelastic dissipative structures. That is, the dissipative structural modes are not orthogonal, the dynamic equations cannot be decoupled with the structural modes, while transient structural response can be accurately represented as an individual superposition of modal responses. The analysis of the calculation example showed that the isolated structure with viscoelastic damper and TMD can more effectively reduce the actual values of wind-induced displacement response standard deviation, equivalent wind vibration force and design value of equivalent wind. Since the results obtained in this paper are exact solutions, it can provide a theoretical basis for the design of the structures with viscoelastic damper and TMD, the optimization of damper and TMD parameters.

Biomechanical analysis of lumbar nonfusion dynamic stabilization using a pedicle screw-based dynamic stabilizer or an interspinous process spacer.

This study aimed to investigate and compare the effects of two widely used nonfusion posterior dynamic stabilization (NPDS) devices, pedicle screw-based dynamic stabilizer (PSDS) and interspinous process spacer (IPS), on biomechanics of the implanted lumbar spine under static and vibration loadings. The finite element model of healthy human lumbosacral segment was modified to incorporate NPDS device insertion at L4-L5 segment. Bioflex and DIAM were used as PSDS-based and IPS-based NPDS devices, respectively. As a comparison, lumbar interbody fusion with rigid stabilization was also simulated at L4-L5. For static loading, segmental range of motion (ROM) of the models under moments of four physiological motions was computed using hybrid testing protocol. For vibration loading, resonant modes and dynamic stress of the models under vertical excitation were extracted through random response analysis. The results showed that compared with the rigid fusion model, ROM of the nonfusion models was higher at L4-L5 level but lower at adjacent levels (L1- L2, L2-L3, L3-L4, L5-S1). Compared with the Bioflex model, the DIAM model produced higher ROM at L4-L5 level but lower ROM at adjacent levels, especially under lateral bending and axial rotation; resonant frequency of the DIAM model was slightly lower; dynamic response of nucleus stress at L4-L5 level was slightly higher for the DIAM model, and the dynamic stress at adjacent levels was no obvious difference between the nonfusion models. This study reveals biomechanical differences between the Bioflex and DIAM systems, which may provide references for selecting surgical approaches in clinical practice.

Sensitivity Analysis of Random Frequency Responses of Hybrid Multi-functionally Graded Sandwich Shells

Sensitivity Analysis of Random Frequency Responses of Hybrid Multi-functionally Graded Sandwich Shells

Vibration response analysis and hoop layout optimization of spatial pipeline under random excitation

PurposeIn many cases, the external pipelines of aero-engine are subjected to random excitation. The purpose of this paper is to reduce the vibration response of the pipeline system effectively by adjusting the hoop layout.Design/methodology/approachIn this paper, a spatial pipeline supported by multi-hoops is taken as the object, the methods of solution of the vibration response of the pipeline system by using pseudo excitation and hoop layouts optimization with amplitude reduction of vibration response as the goal are presented. First, the finite element model of the spatial pipeline system is presented. Then, an optimization model spatial pipeline is established. Finally, a case study is carried out to prove the rationality of the random vibration response analysis of the pipeline system. Furthermore, the proposed optimization model and genetic algorithm are applied to optimize the hoop layout.FindingsThe results show that the maximum response variance after optimization is reduced by 32.8%, which proves the rationality of the developed hoop layout optimization method.Originality/valueThe pseudo excitation method is used to solve the vibration response of aero-engine pipeline system, and the optimization of the hoop layout for aero-engine spatial pipelines under random excitation to reduce random vibration response is studied systematically.

Dynamic analysis and structural simulation of aluminum composite material based automobile chassis

The vibration in automobiles is an important issue to be noted in which the road excitation forces on the automobiles create the vibration and noise due to random vibration that affects the comfort of the passengers; hence this paper aims to investigate aluminium based polymer composite structure analysis in which the effect of random vibration can be check by using the steady-state, modal and random response analysis using the power spectral densities (PSD) and the resonance frequency in which the recommendations can be made using the optimization of the structure of the displacement for the safe application of the loads with the lightweight structure. The resonant frequency of the structure is determined as the 57 Hz.