Random Vibration Research Articles

An efficient method for solving high-dimension stationary FPK equation of strongly nonlinear systems under additive and/or multiplicative white noise

Engineering structures may suffer from drastic nonlinear random vibrations in harsh environments. Random vibration has been extensively studied since 1960s, but is still an open problem for large-scale strongly nonlinear systems. In this paper, a random vibration analysis method based on the Neural Networks for large-scale strongly nonlinear systems under additive and/or multiplicative Gaussian white noise (GWN) excitations is proposed. In the proposed method, the high-dimensional steady-state Fokker–Planck-Kolmogorov (FPK) equation governing the state’s probability density function (PDF) is firstly reduced to low-dimensional FPK equation involving only the interested state variables, generally one or two dimensions. The equivalent drift coefficients (EDCs) and diffusion coefficients (EDFs) in the low-dimensional FPK equation are proven to be the conditional mean of the coefficients given the interested variables. Furthermore, it is shown that the conditional mean can be optimally estimated by regression. Subsequently, the EDCs and EDFs, as functions of the retained variables, are approximated by the semi-analytical Radial Basis Functions Neural Networks trained with samples generated by a few deterministic analyses. Finally, the Physics Informed Neural Network is employed to solve the reduced steady-state FPK equation, and the PDF of the system responses is obtained. Four typical examples under additive and/or multiplicative GWN excitations are used to examine the accuracy and efficiency of the proposed method by comparing its results with the exact solution (if available) or Monte Carlo simulations. The proposed method also exhibits greater accuracy than the globally-evolving-based generalized density evolution equation scheme, a similar method of its kind, especially for strongly nonlinear systems. Notably, even though steady-state systems are applied in this paper, there is no obstacle to extending the proposed framework to transient systems.

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

Determination of the characteristics of drill string vibrations during the drilling process

The object of research is vibration processes of a certain origin in the drill string with typical design deviations depending on the mode parameters of drilling. A drill string is an oscillating system with an infinite number of degrees of freedom of a multifactor system. An exhaustive study of oscillatory processes in the drill string is impossible neither analytically nor experimentally, due to the specifics of the hole deepening in various rocks, the design of the well, its shape, etc. Therefore, in practice, they try to solve the problems of the dynamics of the drill string for an idealized system and, while preserving the main oscillatory properties, solve some problems of the rod system. The work carried out was aimed at experimental studies of vibrations of the drill string during the drilling process. It is shown that the effectiveness of the use of hydrodynamic cavitation requires the development of methods and devices for intensifying the well drilling process. It is proven that the design of the cavitation generator organically fits into the existing well drilling equipment and allows for the intensification of technological processes with lower specific energy consumption. It is found that all oscillatory processes that occur in the drill string are random in nature and must be considered using the mathematical apparatus of the theory of random oscillations. The study of vibrations during well drilling shows that vibrations can be considered as random stationary processes, since transient modes have a sufficiently short duration for homogeneous rocks with fixed drilling modes. The analysis of the vibrations of the drill string elements based on random oscillations in a number of cases allows to increase the reliability of determining the vibration reliability of the drill string elements. It has been proven that the response of drill string elements to broadband random vibration can be defined as the combined effect of several narrowband random vibrations.

Design and mechanical properties of metal rubber secondary multidirectional vibration isolation system under random vibration

Design and mechanical properties of metal rubber secondary multidirectional vibration isolation system under random vibration

Nonstationary random vibration analysis of hysteretic systems with fractional derivatives by FFT-based frequency domain method

Nonstationary random vibration problems of nonlinear fractional systems are challenging and drawing increasing attention. This study presents an efficient numerical method for the random vibration analysis of large-scale nonlinear fractional systems subjected to fully nonstationary excitations. Firstly, the fast Fourier transform (FFT)-based frequency domain method originally proposed for the nonstationary random vibration analysis of linear integer-order systems is extended to linear fractional systems, in which the explicit expression of dynamic responses of fractional systems is derived based on the load superposition principle and Newmark method. Secondly, an equivalent linearization analysis framework is constructed to solve the nonstationary responses of hysteretic systems with fractional derivatives, in which the nonstationary response analyses of equivalent linear systems are accomplished by the FFT-based frequency domain method. The presented method can account for nonstationary excitations with arbitrary forms of evolutionary power spectrum, even of the non-separable one. Two numerical examples are used to confirm its superior performance in terms of accuracy and computational efficiency.

Thermomechanical Collaborative Design and Experimental Verification of a Sandwich Structure with a Polyimide Foam Core

This paper introduces the technology and performance of a new sandwich structure consisting of carbon fiber composite face sheets, a polyimide foam core, and an aluminum honeycomb panel with both heat insulation and load-bearing functions. The heat-resistant performance of the sandwich structure was evaluated. The vacuum thermal conductivity of the sandwich structure in the vertical direction ranges from 0.54 to 0.92 (W/[m⋅K]) with increasing temperature from −170 to 135°C. A multilayer finite element model of carbon fiber cloth, polyimide foam, and aluminum honeycomb was established. Finally, a comprehensive evaluation of the mechanical and thermal insulation performance of the sandwich structure was conducted through random vibration testing and thermal vacuum testing. The results showed that the sandwich structure had good stiffness and thermal insulation performance, successfully verifying the effectiveness of the collaborative design.

Spatially variable seismic underground motions in layered porous seabed medium induced plane wave

In ocean engineering anti-seismic filed, the marine environment is usually regarded as the coupling field of seawater-layered porous seabed-elastic bedrock. This paper presents a theoretical method to study the spatially variable seismic underground motions in stratified seabed system. Based on the potential flow theory, Biot's porous model and random vibration theory, the transfer function and coherence function model of the underground seismic motions in the marine coupling field are derived. On the basis of the above theoretical derivation, the program of the spatial variability seismic underground motions of the coupling field is simulated and developed, and its accuracy and effectiveness are verified. Moreover, the effects of soil stiffness and overlying seawater level on the seismic response are also analyzed. Numerical results show that spatially variable seismic underground motions are significantly different from those on the ocean bottom. The simulation of spatially variable seismic underground motions for layered seabed field is significant for both theoretical study and ocean engineering application.

Structural Analysis of AlAinSat-1 CubeSat

This paper presents the process of conducting the structural analysis of AlAinSat-1 CubeSat through a numerical solution using Siemens NX. AlAinSat-1 is a 3U remote-sensing CubeSat carrying two earth observation payloads. The CubeSat is scheduled for launch on SpaceX Falcon 9 rocket. To ensure the success of the mission and its ability to withstand the launch environment, several scenarios should be analyzed. For AlAinSat-1 model the finite element analysis (FEA) method is used, and four types of structural analyses are considered: modal, quasi-static, buckling, and random vibration analyses. The workflow cycle includes idealizing, meshing, assembling, applying connections and boundary conditions, and eventually running the simulation utilizing the Siemens Nastran solver. The simulation results of all analysis types indicate that the model can safely withstand the loads exerted during launch. Also, the numerical results of the Command and Data Handling Subsystem (CDHS) module of AlAinSat-1 are experimentally validated through a vibration test conducted using an LV8 shaker system. The module successfully passed the test based on the test success criteria provided by the launcher.

PSD estimation and modal parameter identification for random vibrations with blade tip timing measurement

Abstract Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.

A Novel Semi-Active Control Approach for Flexible Structures: Vibration Control through Boundary Conditioning Using Magnetorheological Elastomers

This research study explores an alternative method of vibration control of flexible beam type structures via boundary conditioning using magnetorheological elastomer at the support location. The Rayleigh–Ritz method has been used to formulate dynamic equations of motions of the beam with MRE support and to extract its natural frequencies and mode shapes. The MRE-based adaptive continuous beam is then converted into an equivalent single-degree-of-freedom system for the purpose of control implementation, assuming that the system’s response is dominated by its fundamental mode. Two different types of control strategies are formulated including proportional–integral–derivative control and on–off control. The performance of controllers is evaluated for three different loading conditions including shock, harmonic, and random vibration excitations.

Detecting ice on plate-like structures via flow-induced random vibration: a dispersion curve shift identification approach

Detecting ice on plate-like structures via flow-induced random vibration: a dispersion curve shift identification approach

Research on modal combination coefficients considering the spectral characteristics of strong ground motion

To address the limitations of traditional complete quadratic combination (CQC) modal combination coefficients in calculating ground motions with narrow bandwidth and long periods, a revised methodology is proposed. The new CQC modal combination coefficients are formulated by considering the spectral characteristics of strong ground motion, taking the modified Kanai-Tajimi spectrum model as a prerequisite, and applying random vibration theory. Simultaneously, a random phase simple harmonic process model for a single harmonic component is established, and corresponding combination coefficients are provided. The necessity and rationality of considering the spectral characteristics of strong ground motion are demonstrated from three perspectives: differences in power spectral models, variations in combination coefficients, and the inherent combination mechanism. As an illustrative example, the layer shear model is analyzed and compared with the results of the structure's modal combination taking different combination coefficients. This comparison is conducted under the influence of long-period simple harmonic waves, four natural seismic waves in the basin, and the 50 natural ground motions suggested by ATC-63, respectively. The results indicate that the modal combination coefficients developed by considering the spectral characteristics of strong ground motions are more reasonable and can serve as a viable replacement for traditional CQC combination rules. This is especially advantageous when dealing with ground motion inputs characterized by narrow bandwidth and long periods, providing significant benefits in such scenarios.

Method of non-stationary random vibration reliability of hydro-turbine generator unit

Method of non-stationary random vibration reliability of hydro-turbine generator unit

Load-equivalent model and loosening life prediction method of bolts under transverse loading

To establish a method for predicting the loosening life of bolts under random transverse vibration, this study first obtains the transverse displacement–loosening life (D–NL) curves of bolts under three loosening states (90 %, 80 %, and 70 % of the residual preload) through bolt-loosening tests under different transverse displacement loads. Based on the mechanical analysis model of bolt loosening with strict physical definitions, load-equivalent models of the bolt external load, screw load, and screw-tooth root stress are established by considering the transverse displacement load as the input excitation and the screw-tooth root stress as the output response; these achieve the transfer and conversion of the bolt external load and screw root stress with the screw load as the bridge. Subsequently, two types of finite element models of bolted connections are established and verification tests are performed. The equivalent relationships between the bolt external load, screw load, and screw-tooth root stress are simulated and tested, and the accuracies of the bolt-load equivalent models are verified. Finally, based on the bolt-load equivalent models, the D–NL curves for evaluating loosening using the directional macroscopic displacement load are converted to stress–loosening life (S–NL) curves to evaluate loosening using the undirected local stress. A calculation flow of the bolt-loosening life under random transverse vibrations is established, and a method of predicting bolt-loosening life based on the bolt-load equivalent relationship is developed. These findings provide a useful reference for optimizing bolted connection designs and preventing bolt loosening.

Exploring the relationship between the International Roughness Index (IRI) and the ISO 8608 roughness coefficient (Gd (n 0))

ABSTRACT Globally, diverse agencies employ varied metrics to gauge road roughness, complicating the exchange of information for pavement maintenance. This study addresses this challenge by establishing a theoretical connection between the International Roughness Index (IRI) and the ISO 8608 Power Spectral Density (PSD)-based roughness coefficient, namely Gd (n 0). Based on random vibration theory, this paper first deduces a closed-form explicit solution for IRI related to Gd (n 0), solidifying a theoretical link. Next, the variability and convergence of the proposed solution are examined through Monte Carlo simulations using a quarter-car vehicle model with the Golden Car parameters. Then, we compare computed results from this study with those existing solutions from past studies, verifying that the proposed solution captures the curve trend well and agrees with the average value of existing solutions based on field measurement data. Finally, this paper proposes the IRI values corresponding to various ISO road class thresholds and a new Gd (n 0) scale for ride quality assessment of highways.

Reliability modeling of pre-stressed composite structures subject to interlayer slip failure under multi-axial random impact and vibration loads

A time-dependent reliability model for pre-stressed metal/polymer/metal composite structures subject to interlayer slip failure is developed in this study, allowing for predicting the probability of failure of the whole structure under multi-axial random multi-peak impact loads and transport vibration. A multi-Gaussian envelope model with uniform modulations is proposed to model random multi-peak impact loads, and the inverse sampling method is employed to model random transport vibration. An interlayer slip physics model is developed based on the contact surface friction mechanism under multi-axial vibration load and the stress-relaxation constitutive model. By implementing the interlayer slip physics model in the finite element method framework via the user-material routine, the geometry effect of the structure can be dealt with, and the reliabilities at an arbitrary location of the structure can be obtained. The proposed method is demonstrated using engineering examples. The results show that the proposed reliability assessment method provides a viable and systematical procedure of computing the time-dependent reliability of composite structures as a whole under multi-axial impact loads and vibrations.

Random Vibration Fatigue Life Prediction of Nano-Silver Solder Joint

Nano-silver is a very potential electronic interconnection material. It’s excellent physical and chemical properties, high thermal conductivity and good electrical conductivity make it very suitable for high power electronic devices. In practical engineering, 20% of the failure of electronic products is caused by vibration load, so it is necessary to study the vibration reliability of interconnected materials. In this paper, the modal and random vibration finite element analysis of nano-silver solder joints were analyzed with workbench software. Predicting random vibration fatigue life of nano-silver solder joint by Coffin-Manson high cycle fatigue empirical formula, Miner’s linear cumulative damage theory and Steinberg model. The random vibration fatigue life of the nanosilver solder joint is 8342 h. It is found that the vibration reliability of nano-silver is inferior to Sn3.0Ag0.5Cu and Sn63Pb37 and the diameter of solder joints and PCB thickness are proportional to the vibration fatigue life, and the PCB thickness has a greater effect on the vibration life than the solder joint diameter. Solder joint height and pad thickness are inversely proportional to vibration fatigue life, and pad thickness has little effect on vibration fatigue life.

Research on vibration test method of electric actuator

Abstract The stable, safe, and reliable operation of electric actuator valve systems is of great significance in industrial production. This paper proposes a vibration test method for electric actuators, employing the test to meet the test severity level as the first priority, with random frequency vibration within 10 Hz to 1000 Hz. The vibration acceleration is loaded with a Gaussian distribution, which can be used to simulate the irregular vibration of electric actuators in the actual working conditions of the working environment. The test is divided into up and down vibration (z-axis), left and right vibration (x-axis), and front and rear vibration (y-axis) in three directions independently to verify the electric actuator from the mechanical structure and the circuit structure in order to meet the reliability requirements of the actual production.

Vibration analysis of an open cylindrical thin shell under random excitation

This paper introduces an analytical approach to the random vibration of a cylindrical thin shell structure with an opening angle of 180°. The approach involves employing the exact analytical solution for the natural vibration of a thin shell structure with an opening, grounded in a continuum model, and a pseudo-excitation method to derive the exact analytical solution of the random response power spectral density for the open cylindrical thin shell structure. Simultaneously, a comparison is made between the results obtained through the analytical method and those obtained by using the finite element program, confirming the effectiveness of the analytical model constructed in this study. Finally, an analysis is conducted on the impact of thickness on the characteristics of the vibration response of the open cylindrical thin shell.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.