Random Vibration Analysis Research Articles

Spectral element method for random vibration analysis of the vehicle-track coupling system

In this paper, we propose a new random vibration analysis model for the vertical vehicle-track coupling system, which combines the symplectic method and the spectral element method (SEM) to enhance calculation efficiency and accuracy. The model assumed that the vehicle is composed of a multi-rigid body with 10 DOFs, and its motion equation is derived using the traditional frequency analysis method. Tracks are considered periodic structures, and the part between sleeper support points is considered a substructure. The motion equation of the periodic track-substructure is established by spectral element method (SEM), and the propagation of vibration wave between the substructures is calculated by the symplectic method. The frequency responses of the vehicle-track coupling system are calculated by using the German low-interference irregularity spectrum and short-wave irregularity spectrum as excitation. Then, the rationality of this method is verified by comparing it with the results from the traditional symplectic method and simulations using Universal Mechanism software. The comparison shows that this method surpasses the traditional symplectic method in high-frequency accuracy while maintaining high computational efficiency. Although the finite element method also has the capability for high-frequency analysis, this method can calculate the high-frequency vibration of an infinitely long track using just one element, making it more suitable for the efficient analysis of vehicle-track coupling systems. Finally, the model is applied to analyze the distribution characteristics of the vibration response of the coupled system in the frequency domain.

Random thermal-vibration mechanisms of sandwich ventral fin-type plate-shell systems with porous functionally graded core

The stochastic thermal-vibration mechanisms within a sandwich ventral fin-type plate-shell system, featuring a porous functionally graded (FG) core, are exhaustively analyzed under various random loading conditions employing an innovative node-based, meshless computational approach. The studied structure is decoupled into several plates and open cylindrical panel according to the geometric characteristics, and the mechanical relationships at the structural boundaries or connection interfaces are equivalently simulated by using penalty parameters. Following the general Hamilton's principle, the meshless approach combined with the first-order shear deformation theory (FSDT) incorporating thermal effects is employed to derive the vibration equations of the sandwich ventral fin-type plate-shell systems. Also, the pseudo excitation method (PEM) is introduced to calculate stationary and nonstationary random responses. In order to verify the accuracy of the meshless algorithm in this study, the convergence and correctness are studied comprehensively. And then, the effects of some parameters such as temperature variation, porosity parameters, power-law index and random excitations on the thermal vibration characteristics of the sandwich ventral fin-type plate-shell systems with porous FG core are presented. The results show that the power-law index and temperature can increase the frequency parameter of the structure. The smooth power spectral density (PSD) excitation only affects the amplitude of the response curve, and does not affect the frequency corresponding to the peak. In the analysis of non-stationary random vibration, the influence of modulation parameters on response is very significant.

Random vibration analysis of functionally graded sandwich plates with different skin layers subjected to double explosive load: mathematical model with numerical solution proposition

Random vibration analysis of functionally graded sandwich plates with different skin layers subjected to double explosive load: mathematical model with numerical solution proposition

Dynamic Characteristics of Composite Sandwich Panel with Triangular Chiral (Tri-Chi) Honeycomb under Random Vibration.

A full triangular chiral (Tri-Chi) honeycomb, combining a honeycomb structure with triangular chiral configuration, notably impacts the Poisson's ratio (PR) and stiffness. To assess the random vibration properties of a composite sandwich panel with a Tri-Chi honeycomb core (CSP-TCH), a two-dimensional equivalent Reissner-Mindlin model (2D-ERM) was created using the variational asymptotic method. The precision of the 2D-ERM in free and random vibration analysis was confirmed through numerical simulations employing 3D finite element analysis, encompassing PSD curves and RMS responses. Furthermore, the effects of selecting the model class were quantified through dynamic numerical examples. Modal analysis revealed that the relative error of the first eight natural frequencies predicted by the 2D-ERM consistently remained below 7%, with the modal cloud demonstrating high reliability. The PSD curves and their RMS values closely aligned with 3D finite element results under various boundary conditions, with a maximum error below 5%. Key factors influencing the vibration characteristics included the ligament-rib angle of the core layer and layup modes of the composite facesheets, while the rib-to-ligament thickness ratio and the aspect ratio exert minimal influence. The impact of the ligament-rib angle on the vibration properties primarily stems from the significant shift in the core layer's Poisson's ratio, transitioning from negative to positive. These findings offer a rapid and precise approach for optimizing the vibration design of CSP-TCH.

Investigation of dynamic characteristics and fatigue life prediction of Pb free solder material under random vibration

Electronic packages are employed in diverse industries, including automotive, aerospace, and defense. However, their susceptibility to failure arises from exposure to uncontrolled operating conditions, particularly vibrations.Therefore, an investigation has been conducted to explore the effect of vibration in fatigue life of SAC305 lead free solder material employed in Printed Circuit Board (PCB) assembly with ball grid array (BGA) 144 electronic package. Finite Element Analysis (FEA) of a printed circuit board with BGA 144 electronic package was conducted to find their dynamic characterisics like natural frequencies and their mode shapes. Experiments were conducted to validate the numerically developed model, where first, second and third modes shapes from FEA and experimental results were compared. In addition, random vibration analysis was performed using numerical simulation where individual solder balls were analysed for stress distribution and experimentswere conducted on specially fabricated PCBs using electro dynamic shaker for validation. Analysis shows that the failure was prominent at the solder balls located at the corner of the package. Further, Minor’s rule was used to estimate the fatigue life of the Pb free solder material in BGA 144 package.

On the random vibration-based progressive fatigue damage detection and classification for thermoplastic coupons under population and operational uncertainty

The problem of vibration-based progressive fatigue damage detection and Fatigue State (FS) determination for thermoplastic coupons is experimentally addressed under significant population and experimental uncertainty. The study involves 13 coupons subjected to tension–tension fatigue testing with interruptions at 10,000-cycle intervals. Utilizing non-parametric random vibration analysis and a robust, uncertainty-tolerant methodology, the research employs Multiple Model Representations of uncertain dynamics through parametric ARMA(AutoRegressive-Moving Average)-type random vibration response modeling. Results, validated by ultrasonic C-Scan testing, reveal (a) the significance of uncertainties, (b) a resonant structural frequency indicating fatigue accumulation, (c) remarkable detection performance, achieving 100 % accuracy even at 10,000 cycles, and (d) FS determination with over 80 % accuracy across all coupons. This study offers promising avenues for automated fatigue damage detection and FS determination in thermoplastic structures, eliminating the need to interrupt their operational cycles.

A novel model for vehicle/turnout nonlinear random vibration analysis based on full probability irregularity spectrum

A novel model for vehicle/turnout nonlinear random vibration analysis based on full probability irregularity spectrum

Ritz Solutions of Stationary Random Vibrations for GPL-Reinforced FG Rectangular Plate

This paper aims to establish a comprehensive model for evaluating the response characteristics of functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates under stationary random acceleration excitation. Utilizing the first-order shear deformation theory (FSDT) and Halpin–Tsai assumptions, a dynamic model for the rectangular plate is derived, followed by obtaining the variational solution using the Rayleigh–Ritz method. To describe displacement components associated with dynamic equations and boundary conditions, a spectral geometry method (SGM) is employed. Additionally, a pseudo-excitation method (PEM) is utilized for the analysis of stationary random vibration. The proposed calculation method is validated through convergence analysis and comparative evaluation with existing literature and finite element models. Furthermore, the study investigates the influence of various factors, such as boundary conditions, the number and size of functionally graded rectangular plate layers, GPL distribution types, and material parameters, on the stationary random response attributes of FG rectangular plates. This research contributes to a deeper understanding of the dynamic response of functionally graded materials in structural configurations and offers a valuable analytical approach for researchers in this field.

Random Vibration Analysis of Double Deck Rocking Self-Centering Pier Under Seismic Excitation

This paper investigates nonlinear random vibration of double deck rocking self-centering pier structure subjected to seismic excitation. First of all, a novel type of double deck rocking self-centering pier that offers better resilience is designed. The stochastic dynamical model of the system is then established, in which the seismic excitation is viewed as Kanai–Tajimi filtered white noise and the self-centering restoring force is characterized by classical flag-shaped hysteretic model. Subsequently, the self-centering restoring force is decomposed into equivalent quasi-linear elastic and damping forces by adopting the harmonic balance (HB) scheme. Following this, the stochastic averaging (SA) technique is implemented to derive the averaged Itô equation. The steady-state response probability density with respect to the amplitudes is solved from the averaged Fokker–Planck–Kolmogorov (FPK) equation. Finally, the effects of system parameters on the stochastic response of the double deck rocking self-centering pier structure are performed, and validated by the Monte Carlo simulation (MCS). In addition, with the help of the Laplace transform, the transition function as well as conditional power spectral density are achieved, which are combined with the steady-state probability density to obtain the power spectral density response. This research will contribute to the optimal seismic design of double-deck rocking self-centering piers.

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.

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.

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.

Pseudo-equivalent model for sandwich panels with egg-shaped honeycomb-grid core

The novel sandwich panel with egg-shaped honeycomb-grid core (SP-EHC), formed by chamfering the grid walls, can achieve a balance between lightweight and high-strength, as well as promote effective ventilation and drainage due to the semi-closed honeycomb design. To determine the panel’s equivalent stiffness properties, an asymptotic analysis of the energy functional stored within the periodic unit cell is conducted. On this base, a 2D pseudo-equivalent model (2D-PEM) in the form of the Reissner–Mindlin model was formulated. The pseudo-excitation method was employed to analyze the self-power spectral density function and root mean square response of the 2D-PEM under random vibration. The accuracy and effectiveness of the model were validated through comparisons of the three-point bending experimental results of the 3D-printed specimen, exhibiting relative errors of 2.95%. In addition, free and random vibration analyses were conducted on the hybrid SP-EHC to further validate the model. Furthermore, the influence of material and structural parameters on specific stiffness, natural frequencies and first velocity RMS was systematically investigated. The findings reveal that enhancing the grid wall’s chamfering ratio is beneficial in achieving the desired objectives of lightweight and high-strength. In addition, compared to sandwich panels with orthogonal and pyramid grid cores, this improvement positively impacts the vibration characteristics of the sandwich panel. These findings offer valuable insights for the future design and optimization of such sandwich panels.

Random Vibration Characteristics and Vibration Suppression of an Aero-engine Inlet Rake Fabricated by Laser Powder Bed Fusion

The inlet rake is generally installed in aero-engine during rig and flight test for flow field pressure and temperature measuring. There are usually complex flow channels and pipelines inside the rake to extract air flow to the sensor. The laser powder bed fusion(L-PBF) technique was applied in rake fabrication recently due to its progressive layer stacking molding procedure. However, the difference of thermoforming method between L-PBF and the traditional casting process leads to the mechanical property disparities of the material. In this work, the determinants of random vibration response of the inlet rake manufactured by L-PBF with GH4169 powder were studied individually. The stiffness and yield property of the material were investigated by the specimen tensile test, which indicates higher elasticity modulus and yield stress comparing to the ones by castling or forging process. The damping ratio of the inlet rake was obtained through stress attenuation characteristics experiment and analysis under stepwise excitation. The stress distribution and resonance margin of the inlet rake under the aero-engine random vibration spectrum were simulated by finite element modal and random vibration analysis. The results showed that the damping ratio of the L-PBF inlet rake is much smaller than engineering recommendations, and the resonance margin is insufficient. Thus, the stress level of the inlet rake was very high, especially in the blade root section, quite close to the yield limit of the material. To solve this problem, the vibration suppression methods of the inlet rake were studied from the perspective of structural design optimization and damping ratio increasing. Through the rational design of the resonance margin and addition of vibration damping structure, the vibration stress of inlet rake was significantly suppressed. As the result, the rake was installed in the inlet during the aero-engine rig test for flow field pressure and temperature measurement successfully.

Analysis of Vibration in Hybrid Composite Leaf Spring

Vibration-related failures more frequently occur than material failures, analysis is crucial to the design of composite leaf springs. It must also have an outstanding fatigue life and be lightweight. To minimize vertical vibrations, hits, and bumps caused by irregular roads and to ensure a comfortable ride, springs are essential suspension components in automobiles. Hence, the material with the highest strength and lowest longitudinal elastic modulus is ideal for use in leaf springs. In the automotive business nowadays, composite materials primarily replace metal elements. Consequently, it is important to use a hybrid composite leaf spring that evenly distributes graphite, carbon, and glass fibers throughout the resin matrix and has a lower spring rate. Hybrid composite materials offer many advantages over conventional composite materials because they use glass and carbon fibers instead of them. These advantages include maximum strength, minimum longitudinal modulus of elasticity, reduced weight as well as vibration, better packaging, enhanced durability, cost savings, fatigue life, and strain energy capacity. The first use of modal analysis is to determine Eigen-vectors, or mode shapes, and Eigen-values, or natural frequencies. Moreover, random vibration analysis is used to distinguish between smooth and rough vibrations, and harmonic analysis is used to determine the response’s amplitude.

Computational homogenization for dynamic characterization of a square cellular honeycomb vibration energy harvester

The prevailing literature on homogenization of cellular structures mainly focuses on computing their effective properties, but only a few studies demonstrate their subsequent use in practical applications. Moreover, the emphasis is largely on static analysis, and dynamic studies are limited to free vibration analysis with no specific applications. Therefore, this research aims to address these gaps by assessing the effectiveness of finite element based homogenization approach in characterizing cellular vibration energy harvester. In particular, the study considers a square cellular structure in cantilever mode and demonstrates the dynamic characterization using the homogenization approach. The results from free, forced, and random vibration analysis show close conformance between cellular and homogenized models with a maximum error of less than 10%. Further, the homogenized model was used to characterize the electro-mechanical response of the square cellular vibration energy harvester, and the predicted voltages for the cellular and homogenized models were 11 V and 13.8 V, respectively, validating the accuracy of homogenized model. Also, the computational time is reduced by 50–75% when using the homogenized model, thereby providing a computationally efficient alternative to experimental and full-scale time intensive finite element simulations.

Response spectrum-based analysis of airborne radar random vibration and multi-point control improvement

During the flight of a UAV (unmanned aerial vehicle), the LiDAR device undergoes random vibrations due to the changing flight attitude and wind speed conditions of the UAV. It is important to control the frequency and amplitude of the vibrations within a reasonable range by means of a damping structure. As the vibrations caused by various factors during flight are random and non-linear, this paper innovates the analysis principle and damping control means for the random vibrations of airborne optoelectronic devices. The response spectrum analysis theory is used to establish the shock response spectrum, and an optimised and improved recursive digital filtering method is used to fit the frequencies of random vibration to the synthetic shock response. Considering the uncertainty of the vibration excitation signal, a virtual excitation method is used for the first time to simulate the random vibration to which the radar may be subjected in the air, and to simplify the calculation steps. The shock plate structure is designed using a multi-point control method to innovate a passive response to the random excitation. Finally, a modal analysis of the synthesised impact response was carried out. It is verified that the first six modal frequencies are controlled within 220 Hz, realising the frequency reduction. The amplitude of the three x, y, and z directions is controlled to within 0.5 mm, thus achieving vibration damping.

The higher-order analysis of response for linear structure under non-Gaussian stochastic excitations with known statistical moments and power spectral density

The frequency-domain analysis method is a fundamental component of the random vibration analysis, in which the corresponding moment spectrum of excitations are the prerequisite. Nevertheless, the determination of the higher-order moment spectra for non-Gaussian stochastic excitations continues to pose a significant challenge in the existing research works. This paper introduces an accurate and efficient computational approach for determining higher-order moment spectra of non-Gaussian stochastic excitations with known statistical moments and power spectral density (PSD). Firstly, following the idea of the simulation method of non-Gaussian stochastic processes, the transformation model between the stationary non-Gaussian stochastic process and underlying Gaussian stochastic process is determined based on the known statistical moments, the PSD of the underlying Gaussian stochastic process is determined using the transformation model. Secondly, the approximate higher-order moment spectra models of stationary non-Gaussian stochastic processes are presented by the PSD of the underlying Gaussian process. Subsequently, the higher-order moment spectra models of non-Gaussian excitations are utilized to compute the higher-order moment spectra of response for the linear structure via the auxiliary harmonic excitation generalized method. Finally, three numerical examples are examined to assess the efficiency and accuracy of the proposed approximate models for the higher-order moment spectra of non-Gaussian stochastic processes.

Dynamic modeling and reliability analysis of satellite antenna deployment mechanism based on parameter uncertainty

AbstractThis study delves into the factors that affect the reliability of satellite antenna deployment mechanisms. It employs the Kolmogorov–Smirnov (K‐S) test to quantify uncertainty characteristics, leading to the acquisition of pertinent stochastic parameters. Subsequently, three‐dimensional models and finite element models of the satellite antenna deployment mechanism are established using SOLIDWORKS and ANSYS software. Modal distribution, harmonic response analysis, random vibration analysis, and deployment process simulation are conducted. Parameterized modeling of the deployment mechanism's dynamics simulation process is performed, taking into consideration parameter uncertainty. Finally, a Kriging surrogate model is utilized to formulate an approximate expression between the factors influencing the reliability of the antenna deployment mechanism and its dynamic response. Based on the general stress‐strength interference theory, a reliability analysis model is constructed. Combined with active learning algorithms, this approach achieves efficient and precise calculations of the reliability of the satellite antenna deployment mechanism.