Random Vibration Analysis Research Articles

Non-stationary non-Gaussian random vibration analysis of Duffing systems based on explicit time-domain method

Non-stationary non-Gaussian random vibration problems of structures are challenging and drawing increasing attention. In the present study, firstly, an explicit time-domain method (ETDM) is proposed to determine the higher-order response statistics of linear systems subjected to non-stationary non-Gaussian random excitations, in which the first four orders of cumulants of dynamic responses are directly formulated through the cumulant operation rule based on the explicit expressions of responses. Secondly, an equivalent linearization – explicit time-domain method (EL-ETDM) is further developed to solve the non-stationary non-Gaussian random vibration problems of Duffing systems, in which the equivalent linear system is derived discarding the assumption of Gaussian response, and the corresponding higher-order cumulant analyses of the linearized system are accomplished by the efficient ETDM. The present approach can account for non-Gaussian random excitations with arbitrary forms, and two specific applications to the Poisson white noise and the square form of Gaussian random process are investigated. Four numerical examples are presented to demonstrate the effectiveness of the proposed methods.

Evaluation of aircraft random vibration under roughness excitation during taxiing

The assessment of runway smoothness or roughness is intimately tied to the vibrational response of aircraft during taxiing. In this study, employing the pseudo excitation method (PEM) based on random vibration analysis, we unearthed the relationship between the random vibrations of five distinct aircraft types and runway irregularities. Initially, we established two three-dimensional (3D) models of aircraft taxiing vibration and derived the response output under roughness excitation. Subsequently, we employed MATLAB to analyze the power spectral characteristics of the vibrational response in different parts of the aircraft. Lastly, we examined the effects of taxiing speed, aircraft type, runway roughness, and lift on the aircraft's vibration. Our findings indicate that the distribution of vibration power spectral density (PSD) exhibits multiple peaks, correlating with the degrees of freedom of the aircraft. We further note that the frequency that aligns most closely with the response peak should be the focus of investigation. High-frequency excitation impacts the pilot and nose landing gear more significantly than the passenger and main landing gear. Absent the consideration of lift, increased taxiing speed amplifies the impact of roughness excitation on aircraft taxiing safety. Larger aircrafts are more sensitive to long-wave roughness. With lift in consideration, all aircraft types exhibit a speed sensitivity to vibration, which should be the primary concern in runway roughness evaluations.

Random vibration and reliability analysis of fluid-conveying pipe under white noise excitations

Due to the random excitation in the external environment, the fluid-conveying pipe would inevitably undergo random vibration. This paper investigates the random vibration and reliability of simply-supported fluid-conveying pipes under white noise excitations. Dynamic equations of the nonlinear pipe conveying fluid under white noise excitations are modeled by the generalized Hamilton principle. Then probability density functions (PDFs) of the amplitude and energy of the system are determined by using the modified stochastic averaging method. The PDFs of displacement and velocity of the system are also discussed. The accuracy of results is verified by the Monte Carlo method. In addition, the first-passage problem of the pipe system is investigated for the first time. In order to obtain the PDFs of reliability and first failure time of the system, the forward finite difference method is adopted to solve the backward Kolmogorov equation of the system. The effects of different parameters on the amplitude, energy, reliability, and first failure time are investigated. The results show that the amplitude of the system becomes large and the first-passage time is advanced with the increase of excitation intensity or fluid speed. The amplitude of the system is decreased and the first-passage time is delayed with the increase of the damping coefficient.

An electro-mechanical shell model for predicting stochastic vibration behavior of smart piezoelectric structure utilizing the Spectral-Tchebyche method

Random vibration analysis is an important indicator for conducting fatigue analysis as well as reliability analysis of engineering structures. At present, the vibration analysis for plate and shell structures is mostly limited to simple plate and shell structures, while the analysis of random vibration of smart piezoelectric structures is really scarce. In this paper, an electro-mechanical coupling model is proposed to examine the stochastic vibration characteristics of smart piezoelectric structures based on the Spectral-Tchebychev method (S-T), whose type of random excitation is pseudo-excitation method (PEM). By comparing the FEM, the literature and experiments, it is observed that S-T electromechanical coupling model proposed in this paper consumes much less computational time in predicting the stochastic response than the existing methods. Secondly, we focus on the effect of the piezoelectric layer on the stochastic vibration characteristics of the host structure. Then, artificial spring technique is also adopted to simulate the general boundary of the coupled electromechanical model for the random vibration analysis. The research work on the random vibration of piezoelectric smart structures in this paper can provide practical engineering experience for the design and equipment of smart structures.

Random Vibration and Noise Analysis of Vehicle Seat Using Numerical Method

The development of vehicle seat used is a challenging task for the automotive industry. In this research the safeness of automotive seats by structural analysis and a random vibration analysis were studied. Hence, the main objective of this study is to determine the suitable vehicle seat configuration based on Noise, Vibration, and Harshness (NVH) performance. In order to achieve this objective, CFD software which is ANSYS was used to analyse frequency and deformation using different force distributed and different material on seat vehicle structure which the force applied from 250 N until 1000 N. The material used is aluminium alloy, magnesium alloy and structural steel to analyse the strength of seat structure. At the end of the study, the effect of different types of material vehicle seat structure was studied. The results confirm that by changing the seat structure material, the rattle noise and in general BSR noise can be improved or controlled accordingly. Consequently, for the seat system which has an identifiable structural dynamic, the BSR noise can be managed and controlled in early design phase by using the seat CAE model.

Random vibration analysis of nonlinear structure with viscoelastic nonlinear energy sink

Most engineering structures serve in complex and harsh dynamic environments and suffer from nonlinear vibrations generated by random excitations such as strong winds and waves, which need to be mitigated. To this end, a novel viscoelastic nonlinear energy sink (VNES) device is proposed for the vibration control of structures, whereby the random vibration of a nonlinear oscillator with a VNES device is analyzed in this paper. Specifically, the mathematical model of the structure-VNES is formulated. An approximate technique for the treatment of viscoelastic damping element modeled by the fractional derivative is developed, whereby an equivalent nonlinear system without fractional derivative is derived. The averaged Itô equations associated with the amplitude envelopes are then obtained by resorting to the stochastic averaging method. The closed-form solution of the stationary response is solved from the Fokker–Planck–Kolmogorov (FPK) equation and verified by the Monte Carlo simulation (MCS) data simultaneously. The effects of system parameters and noise intensity on the stationary response are sequentially examined. By comparing the VNES system to the case without attachment and one equipped with the commonly used tuned mass damper (TMD) device, the performance and robustness of the VNES are highlighted. The conclusions of this work may contribute to the efficacy of the application of the VNES in practice.

Random vibration analysis of composite laminated conical–cylindrical cabin structures of air vehicles considering thermal load

This study proposes a novel semi-analytical random dynamic model using the meshless method to precisely predict and quickly analyze the frequency-domain random response properties of composite laminated conical–cylindrical cabin structures (CL-CCCSs) of air vehicles under stationary random loads. In addition, thermal load is considered in the analysis. The first-order shear deformation theory (FSDT) is used to develop a random dynamic theoretical model for CL-CCCSs based on the spectro-geometric method (SGM) and pseudo-excitation method (PEM). Variable stiffness springs are employed to handle diverse boundary cases and compatibility conditions in the current model. Also, the displacement admissible functions for laminated conical shell and cylindrical shell are uniformly depicted with SGM, which depends on sine and cosine functions. After that, the PEM is employed to transform stationary random loads into pseudo harmonic loads. Subsequently, the energy variation principle is used to derive theoretical discrete random dynamic equations for vibration model of CL-CCCSs considering the thermal effect. The results of numerical vibration analyses are compared to confirm the reliability of the established model. Finally, the effect of certain parameters, such as the lamination scheme, layer number, and temperature, on the random vibration response of a CL-CCCS is thoroughly explained.

Free and random vibration analyses of hourglass lattice sandwich panel using an equivalent model based on variational asymptotic method

The hourglass lattice sandwich panel (hourglass LSP) represents a novel type of lightweight and high-strength structure, showcasing new random vibration characteristics related to its distinct geometric configuration. In this paper, a two-dimensional equivalent plate model (2D-EPM) is constructed based on the equivalent stiffness obtained by the variational asymptotic homogenization of the unit cell. The accuracy of 2D-EPM in analyzing the random vibration characteristics (power spectral density (PSD) and root mean square (RMS) responses, as well as effective mass fraction) is validated by the three-dimensional direct numerical simulation and experiments, and its computational efficiency is greatly improved due to the reduced degree of freedoms. On this basis, the effects of structural parameters on the free and random vibration characteristics are systematically analyzed by using the novelty of unit-cell tailorability. The investigation revealed direct correlations between the displacement PSD and RMS with the aspect ratio and lattice rod radius, whereas the inclination angle and face-to-core thickness ratio exhibited inverse correlations. Furthermore, similarities in the low-frequency behaviors of hourglass, pyramid and auxetic LSPs were evident. Specifically, the displacement–RMS curve of the auxetic LSP was comparatively lower, and the hourglass LSP exhibited a similar response, with the second-lowest RMS curve implying correspondingly strong deformation resistance.

Refined nonlinear fractional derivative model of vehicle-track coupling dynamics

The coupled vehicle-track system (CVTS) dynamics have been extensively investigated for decades. However, the calculation accuracy of prevailing vehicle-track coupling models needs to be improved in the high frequency range due to the inappropriate model simplification and neglect of material nonlinearity. In this study, we propose a refined numerical model of the CVTS that considers the nonlinear properties of the railpads and primary suspension using the fraction derivative Zener model. Furthermore, we more realistically simulate the wheelset, rail and railpad configuration with the elastic axle, solid finite element and surface-support models, respectively, and improve the computation efficiency by employing the mode superposition method. The results demonstrate that the refined CVTS model is more accurate than the classical model in simulating vehicle-track coupling dynamics above 2 kHz. In particular, there are significant differences in the dynamic response of the elastic wheelset model compared to the rigid model over a broad frequency range, with an 11% difference in the bogie acceleration response at the first dominant frequency. When the railpads are modeled using the surface-support model, the rail acceleration differences exceed 41% near 1 kHz and 44% near 2650 Hz, compared to the point-support model. Additionally, the rail response at various locations across the rail cross section can be calculated using the finite element method in this refined model. Overall. the proposed CVTS model provides high accuracy and efficiency for random vibration analysis, especially in the high frequency domain.

A comparison study on the derivation of in-structure FRS during seismic events for application of ITER upper port 18

The design of in-structure components in Port Plug (PP) requires the accurate reaction of the seismic events on the particular points of interest to properly define the vibration behavior of PPs. The most common way to represent the seismic event used is by Floor Response Spectral (FRS). To define the seismic FRS at the particular locations of the ITER diagnostics components, IO has been developed a suitable methodology by a “direct spectra-to-spectra method”. The developed methodology in the frequency domain, has four main steps: first, conversion of the response spectral into artificial equivalent Power Spectral Density (PSD); second, performing random vibration analysis using the artificial equivalent PSD; third, extraction of the output PSD at specific points; fourth, inverse conversion of the generated PSD into response spectra. This methodology to find seismic FRS at the particular points of in-structure in Upper Port 18 (UP18) is presented in this work. A comparison result for different Upper Port Plug (UPP) models is also discussed.

A consistent approach to characterize random vibrations of nanobeams

While there is a numerous amount of research on the random vibrations of classical structures in the literature, merely some limited attempts exist to formulate the random vibrations of nano-sized structures. This study deals with the random vibration of elastic beams at the ultra-small scale. The mixture unified gradient theory of elasticity is invoked to appropriately take into consideration the size-effect. Within the introduced augmented elasticity framework, the nanoscopic effects associated with the strain gradient theory and the stress gradient theory are consistently integrated into the classical elasticity theory. The corresponding boundary-value problem of dynamic equilibrium is, accordingly, established. The exact closed-form solution of the space-time correlation function and the mean-square of the transverse displacements of the mixture unified gradient elastic beam with simply supported ends is obtained for the space-time white noise excitation. The spatial variation of the mean-square value of the transverse displacements of the elastic nanobeam in terms of gradient length-scale parameters is graphically illustrated and thoroughly discussed. A consistent approach to characterize random vibrations of elastic nanobeams within the context of the mixture unified gradient elasticity theory is presented providing important insight into the random vibration analysis of nanostructures.

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.

A VAM-based equivalent model for random vibration of composite sandwich plate with arrowhead-on cores

The composite sandwich plate with an arrowhead-on core (arrowhead-on CSP) is a new type of composite structure that has the advantages of a low weight, high specific strength, high specific stiffness, and negative Poisson’s ratio. In this study, the equivalent plate properties were obtained using the variational asymptotic method (VAM) to asymptotically analyze the energy functional stored in the unit cell. On this basis, a two-dimensional virtual equivalent model was constructed for random vibration analysis using the pseudo excitation method. To verify the accuracy and effectiveness of the equivalent model, the dynamic behaviors (free and random vibrations) of arrowhead-on CSPs under different conditions were analyzed. The power spectral density (PSD), the root mean square (RMS) values of the lateral displacement, velocity, and acceleration responses under a base acceleration excitation, and the modal effective mass fraction under vibrations were also investigated. Finally, the effects of the layup configuration of the composite facesheets and the geometric parameters of the arrowhead-on core on the dynamic characteristics of the equivalent plate were studied. The study revealed that the equivalent model was very efficient and accurate in free and random vibration analysis, which provided a reference for the dynamic characteristic optimization of arrowhead-on CSPs.

Stochastic Optimization of Dissipation Structures Based on Lyapunov Differential Equations and the Full Stress Design Method

This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as the optimization objective, the position of the damper as the optimization object, and the random vibration analysis method as the calculation method to optimize seismic frame structures with viscous dampers. A precise integral solution is derived for the Lyapunov equation based on the general expression of the Lyapunov differential equation for the damping system under the excitation of a nonstationary stochastic process using two types of modulation functions: g(t)=1 and g(t)=t. Finally, the optimal damping arrangement is achieved using this method with a six-layer non-eccentric planar frame. In addition, the optimization results of this study are verified with those in the literature using time-history analysis, which verifies the feasibility and effectiveness of the proposed method. This study provides a method for the optimal configuration of dampers for seismic response of structures, which is beneficial for engineering applications and the protection of seismic structures.

A Volterra-PEM approach for random vibration spectrum analysis of nonlinear systems

In this paper, the Volterra series and the pseudo-excitation method (PEM) are combined to establish a frequency domain method for the power spectral density (PSD) analysis of random vibration of nonlinear systems. The explicit expression of the multi-dimensional power spectral density (MPSD) of the random vibration response is derived analytically. Furthermore, a fast calculation strategy from MPSD to physical PSD is given. The PSD characteristics analysis of the random vibration response of nonlinear systems is effectively achieved. First, within the framework of Volterra series theory, an improved PEM is established for MPSD analysis of nonlinear systems. As a generalized PEM for nonlinear random vibration analysis, the Volterra-PEM is used to analyse the response MPSD, which also has a very concise expression. Second, in the case of computation difficulties with multi-dimensional integration from MPSD to PSD, the computational efficiency is improved by converting the multi-dimensional integral into a matrix operation. Finally, as numerical examples, the Volterra-PEM is used to estimate the response PSD for stationary random vibration of a nonlinear spring-damped oscillator and a non-ideal boundary beam with geometrical nonlinearity. Compared with Monte Carlo simulation, the results show that by constructing generalized pseudo-excitation and matrix operation methods, Volterra-PEM can be used for input PSD with arbitrary energy distribution, not only restricted to broadband white noise excitation, and accurately predict the secondary resonance phenomenon of the random vibration response of nonlinear systems in the frequency domain.

Stochastic simulation of velocity pulses of near-fault ground motions based on multivariate copula modeling

Due to the featured high-amplitude, long-period pulses in velocity or displacement time–history, the near-fault ground motion may have a stronger destructive effect on engineering structures. Therefore, studying velocity pulses modeling of near-fault ground motions has been an important topic in the earthquake engineering community. However, the variability and probabilistic correlation of pulse model parameters have not received enough attention. To this end, an elegant method for stochastic simulation of velocity pulses of near-fault ground motions is proposed based on the classical Gabor wavelet modeling and probabilistic correlation analysis of associated model parameters by multivariate copula modeling. Especially, an efficient scheme of iteratively determining the optimal copulas pertinent to edges of a complex vine structure is developed, and two parameters relevant to the near-fault ground motion records, i.e., the rupture distance and the strongest pulse orientation, are introduced which provides a physical basis for addressing the dependence structure among variables. For illustrative purposes, the ground accelerograms recorded by near-fault instruments in the 1999 Chi-Chi earthquake are used. It is shown that the multivariate copula modeling enables the efficient representation of probabilistic correlation between model parameters which is consistent with their physical mechanism. The time histories and spectral characteristics of velocity pulses of near-fault ground motions and their stochastic fluctuations with respect to the rupture distance are well simulated. While the empirical linear regression model does not meet the requirements of random vibration analysis and thus cannot guide the safety design of seismic structures.

Random vibration analysis of an uncertain vehicle-track coupled system based on a polynomial dimensional decomposition

ABSTRACT In this paper, the uncertainty propagation of an uncertain vehicle-track coupled system (VTCS) subjected to track irregularity is quantified using a polynomial-dimensional decomposition (PDD). Firstly, the conditional power spectral density (PSD) of response related to uncertain parameters is derived using the pseudo-excitation method. Secondly, the PDD surrogate model that can describe the probabilistic characters of the uncertainty propagation is established by conducting the dimensional decomposition to the conditional PSD with component functions and performing the Fourier expansion to the component functions. Finally, the dimensional reduction integration and Gauss integration are introduced to overcome the difficulty of high-dimensional integration when calculating the expansion coefficients. In numerical example, the proposed method is applied to the uncertainty quantification of vertical vibration response of an uncertain VTCS, the accuracy and efficiency of the proposed method are verified by comparing the results of the PDD method with that of Monte-Carlo simulation.

An FEA Investigation of the Vibration Response of the BEATS Detector Stage

The Synchrotron-light for Experimental Science and Application in the Middle East (SESAME) facility is in the process of designing, procuring, and installing a new beamline for tomography (BEATS). The BEATS experimental hutch, hosting sample and detectors, will be located 43 m away from the undulator in the synchrotron ring. Noise in the form of vibration originating from different sources transferred to the detector stage can be a source of poor image quality thus it is important that the detector stage is analysed for its vibration transmission properties. In this study, the result of a three-dimensional random vibration analysis using Finite Element Analysis (FEA) for the detector stage is presented which leads to an estimate of the severity of the vibrations. The random vibration source is that of the ground which was measured exactly where the detector stage will be mounted. The random vibration analysis is conducted in two stages; the modal frequencies of the structure are calculated, thereafter, the random vibration analysis is conducted and the response power spectrum density (PSD) of the structure is calculated along with the root mean square (RMS) displacement values. Since the beamline BEATS is under installation, an existing structure installed at beamline ID28 of the European Synchrotron Radiation Facility (ESRF) was used to validate the model. The model used on the ID28 structure deviated from the experimental results on modal analysis by 2% - 4% on random vibration analysis. This suggested that the model is valid. The analysis as applied to the BEATS detector stage design predicts that the RMS displacement values are less than the pixel size of the detector which is 1 μm. Thus, the structure is sufficiently engineered to moderate the floor vibrations.

An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures

Porous material structures have been widely used in civil engineering, mechanical engineering, aerospace engineering and other fields due to their high specific strength and specific stiffness. The stochastic response analysis of porous material structures under random excitations deserves more attention. The multiscale differential governing equations of porous material structures are derived based on the multiscale asymptotic homogenization method (AHM), and the macroscale and microscale explicit time-domain expressions of structural responses are further established. On this basis, the statistical moments of dynamic responses of porous material structures under non-stationary random excitations can be achieved with the explicit time-domain method (ETDM). The purposed method combines the advantages of AHM for high-efficient explicit formulation of macroscale and microscale dynamic responses of porous material structures and the advantages of ETDM for fast analysis of non-stationary random vibration problems. A numerical example is presented to validate the computational accuracy and efficiency of the present approach for non-stationary random vibration analysis of porous material structures.

Acoustic-induced random vibration analysis for spacecraft using wavenumber expression of joint acceptance

Acoustic-induced random vibration analysis for spacecraft using wavenumber expression of joint acceptance