Random Vibration Analysis Research Articles

Design and Analysis of a Deployment Mechanism with Clearance Compensation for High Stiffness Missile Wings

The deployment performance of the unfolded wing determines whether the winged missiles can fly normally after being launched, infecting the attack performance of the winged missiles. The paper proposes a new deployment mechanism with clearance eliminator. Based on the slider-crank principle, the proposed deployment mechanism achieves fast and low-impact deployment of the wings. The proposed clearance eliminator with shape memory alloy (SMA) effectively eliminates the clearance of the sliding pair and improves the support stiffness and stability of the deployed wing. The collision characteristics and the clearance elimination are studied for the deployment mechanism. The influence of the collision force on the motion state of the wing during the deployment is analyzed. The static stiffness of the wing under the clearance state and the deformation is analyzed. The dynamic stiffness under the catapult clearance elimination state is modeled based on the fractal geometry and contact stress theory. The relationship between the locking force and the support stiffness is revealed. The kinetic simulation is used to analyze the motion response during the action of the deployment mechanism. Modal analysis, harmonic response analysis, and random vibration analysis were conducted for the whole wings. A prototype was developed to verify the ejection performance of the wing according to the input load characteristics. The dynamic stiffness of the unfolded wings is tested by the fundamental frequency experiments to verify the performance of the clearance elimination assembly. The experimental results show that the designed deployment mechanism with clearance compensation achieves fast ejection and high stiffness retention of the missile wing.

Robust optimization of MTMD systems for the control of vibrations

Multiple Tuned Mass Dampers (MTMD) is one of the simplest and most reliable solution to control the vibrations of a structure, e.g. allowing to deal with a wide distribution of structural natural frequencies and usually showing inherent stability. Nevertheless, uncertainties in the behavior of structures under random dynamic input may induce implications on the MTMD effectiveness, e.g. detuning or amplifications. Typically, uncertainties in the input are exclusively considered, while uncertainties affect as much also the mechanical parameters.This paper proposes a robust optimum design of the MTMD, considering uncertainties both in the structural parameters and in the earthquake input. At this aim, a random vibration analysis of the response is adopted, and a direct linear perturbation method is applied on the uncertain parameters. Results show that a deterministic optimization is inappropriate for sensible systems as TMDs, while a robust optimization aims to better control the response with low computational efforts. Furthermore, the selection of the objective functions significantly affects the optimal design parameters, as the number of TMDs influences the robust designs.

Topology Optimization and Multiobjective Optimization for Drive Axle Housing of a Rear Axle Drive Truck.

As one of the important load-bearing components of a truck, the drive axle housing must meet the requirements of stiffness and strength. The traditional design method uses redundancy design to meet the performance requirements. The joint design between the three-dimensional mathematical model and finite element model is adopted, and the optimal design of the drive axle housing is realized based on topology optimization and multiobjective optimization. Firstly, the static analysis of the drive axle housing of a rear axle drive truck was carried out with four typical working conditions. It was concluded that the four working conditions all operate under the yield limit of the material, and it was found that the maximum equivalent stress of the four working conditions occurs at the step of the half-shaft casing. Among the four working conditions, the most critical one is the maximum vertical force working condition. Then, based on the maximum vertical force working condition, the fatigue life analysis is conducted, and the minimum fatigue life appears at the transition position of the half-shaft sleeve and the arc transition position of the main reducer chamber. The remaining parts can meet the design requirements. The overall safety factor of the drive axle housing is mainly between 1 and 5 when operating under this working condition. Then, through modal analysis, the first to sixth natural frequency and vibration modes of the drive axle housing are extracted. Based on the modal analysis, the dynamic characteristics of the drive axle housing are further studied by harmonic response analysis and random vibration analysis. Finally, two kinds of lightweight optimization schemes for the drive axle housing are given. Topology optimization reduces the mass of the drive axle housing by 17.4%, but the overall performance slightly decreases. Then, the five dimensional parameters of the drive axle housing are selected as design variables. The mass, maximum deformation, equivalent stress, service life, and the first-, second- and third-order natural frequencies are defined as objective functions. Through the optimal space-filling design method, the experimental designs are performed and the sample points are obtained. Based on the results of experiment design, the multiobjective genetic algorithm and response surface method are combined to optimize the objective functions. The analysis results show that the mass is reduced by 4.35%, the equivalent stress is reduced by 21.05%, the minimum life is increased by 72.28%, and the first-, second-, and third-order natural frequency are also increased to varying degrees. Two different optimization strategies are provided for the design of the drive axle housing.

Random Vibration Analysis of a Vehicle–Bridge Interaction System Subjected to Traveling Seismic Ground Motions Using Pseudo-excitation Method

Random Vibration Analysis of a Vehicle–Bridge Interaction System Subjected to Traveling Seismic Ground Motions Using Pseudo-excitation Method

An harmonic equivalent excitation method for random vibration response

Many loads on engineering structures had obvious randomness, such as earthquakes, wind, sea waves, uneven pavement, etc. The calculation and analysis of random vibration were complicated and inefficient, which has perplexed the development of engineering technology for a long time. To solve the above problems, this paper proposed a harmonic equivalent excitation method for structural random vibration analysis. The excitation force of multi-frequency action in continuous time interval was converted into harmonic excitation force with the same effect as superposition excitation in each discrete time interval by a harmonic equivalent method. The frequency and amplitude of harmonic excitation force in discrete-time intervals were calculated, which were then taken as the deterministic load input of the structure. The response of the structure was calculated by the conventional structural dynamic analysis method. Finally, the harmonic equivalent excitation method was used to analyze random pavement excitation and its application in the control of time-delay vibration reduction. The results show that the harmonic equivalent excitation method simplifies the calculation form of random vibration analysis without reducing the accuracy, and provides an effective method for analyzing random vibration in the engineering field.

Direct convolution integration method for random vibration analysis of structures subjected to nonuniformly modulated nonstationary excitations

A comprehensive direct convolution integration method is presented in this study for the random vibration analysis of linear structures subjected to multiple nonuniformly modulated nonstationary excitations. The structural unit impulse responses with respect to each independent excitation are first identified and stored by a few time-history analyses. Then the structural response statistics are calculated by the direct convolution integration of unit impulse responses and excitation statistics. Further, two fast Fourier transform algorithms are presented to speed up the convolution integration. Because the convolution expressions are explicit, the presented method can be used to only calculate the responses at some specific degrees of freedom of interest in engineering. Furthermore, it can only calculate the responses at a small number of sparse moments in consideration of the time slow-varying property of nonstationary processes. Finally, the random vibration analysis of a frame structure excited by the fully coherent and incoherent nonstationary excitations is utilized to demonstrate its high accuracy and efficiency. Some suggestions of application are given.

Random simulation method of track irregularities and its application in vehicle-track dynamic analysis

ABSTRACT Track irregularity holds strong randomicity, evolvability, and large data sets during the long-term operation of a rail line, possessing a significant influence on the dynamic performance of vehicle-track systems. In this work, methods for simulating track random irregularities are developed by combining the track irregularity probability model (TIPM) and the number theory method and by the Karhunen-Loève expansion (KLE). Furthermore, the vehicle-track interaction model considering the interaction between the vehicle, track, and wheel-rail interaction is constructed at a 3-D space, where the multi-rigid-body dynamics, finite method, and wheel-rail contacts are applied to construct matrix-coupled vehicle-track interaction equations. Finally, a unified random vibration analysis framework for the vehicle-track system is presented. From perspectives of the amplitude, power spectral density, and probabilistic distribution, the accuracy and efficiency of TIPM and KLE models in simulating track random irregularities and revealing system dynamics performance are compared and analysed in detail.

Stochastic dynamic analysis of nonlinear MDOF systems under combined Gaussian and Poisson noise excitation based on DPIM

Random vibration analysis of structures subjected to combined Gaussian and Poisson white noise excitation is a challenging issue. In this paper, a novel direct probability integral method (DPIM) is suggested to address stochastic responses and dynamic reliability of nonlinear multi-degree-of-freedom (MDOF) systems under combined excitation. Firstly, probability density integral equation (PDIE) of MDOF system under combined excitation is derived based on the principle of probability conservation. Then, DPIM is proposed to achieve the probability density function of stochastic response by solving deterministic motion equation of MDOF system and PDIE in sequence. To solve PDIE, two techniques, i.e., partition of input probability space and smoothing of Dirac delta function, are introduced. From the perspective of probability conservation, furthermore, the equivalent relationship between the PDIE and the corresponding probability density differential equation of a Markov system under combined Gaussian and Poisson noise is established. Since Dirac delta function is analytically integrated as Heaviside function, the first-passage dynamic reliability of MDOF system under combined excitation is readily evaluated by introducing the extreme value mapping of stochastic response. Finally, two nonlinear MDOF systems, including multiple-span bridge under combined vehicle load and non-stationary seismic excitation, are solved. Results demonstrate that the proposed DPIM is effective for random vibration and dynamic reliability analyses of MDOF structures excited by combined Gaussian and Poisson noise, and considering the randomness of vehicle load and seismic excitation simultaneously in the bridge design benefits the safe operation of bridge.

Optomechanical system design under road vibration conditions

Optomechanical systems used in vehicles or moving platforms are exposed to vibration loads from road effects. This study investigated the dynamic behavior of an optomechanical system exposed to random vibrations. Random vibration analysis and laboratory tests of the system were performed with the MIL-STD-810 test method standard. The relative displacements of two lenses in the optomechanical system were obtained under vibration loads by using the finite element (FE) method. The displacements were examined by tests. The obtained relative displacements of the lenses were used as input to the optical analysis and the laser spot position was obtained. The obtained spot positions were evaluated comparatively with the tests. The optical analysis results were consistent with the tests. Using the verified FE and optical models, structural modifications were made in the basic design. Five different design changes were examined. The natural frequencies and the mass of the entire system and the relative displacements of the lenses were obtained for comparative evaluation. Finally, the optimum design minimally affected by vibration loads was achieved.

Random Vibration Analysis of a Coupled Aircraft/Runway Modeled System for Runway Evaluation

Runway roughness is one of the most critical performance factors for runway evaluation, which directly impacts airport operation safety and pavement preservation cost. Properly evaluated runway roughness could optimize the decision-making process for runway preservation and therefore reduce the life cycle cost of the runway pavement asset. In this paper, the excitation effect of runway roughness is analyzed using a coupled aircraft/runway system. The coupled system is composed of a two degrees-of-freedom (2-DOF) aircraft model and a typical asphalt runway structure model established under runway roughness random excitation in this work. The dynamic differential equations for the coupled system are derived based on D’Alembert’s principle. The system’s vibration responses are determined via the pseudo excitation method and three response laws, i.e., the center of gravity acceleration (CGA), the dynamic load coefficient (DLC) of the landing gear, and the runway structural displacement, which are investigated under different modes. The results show that the first-order mode of the runway structure, vertical deformation, is the most significant of the four modes. Moreover, uneven excitation has a significant effect on the distribution of the aircraft’s vibration response. Compared with a single aircraft system, the developed coupled aircraft/runway system has different dynamic responses, and the degree of difference depends on the taxiing speed. The coupled effect on the CGA increases significantly with an increase in speed, with up to a 7.3% percentage difference. The coupled effect on the DLC first increases and then decreases as the aircraft speed increases, reaching a maximum of about 6% percentage difference at 120 km/h.

Auxiliary harmonic excitation generalized method for random vibration analysis of linear structures under non-stationary Gaussian excitation

Frequency-domain methods are the most fundamental and effective methods for non-stationary random vibration analysis. However, the existing frequency-domain methods often involve truncation for degree of mode or decomposition of the power spectrum in multi-correlation conditions, which may have impact on the computational accuracy and efficiency of the methods. To avoid the truncation for degree of mode and the decomposition of the power spectrum, an accurate and efficient auxiliary harmonic excitation generalized method is proposed for random vibration analysis of linear structures under non-stationary Gaussian excitation. First, several existing frequency-domain analysis methods are investigated and discussed. Second, the generalized impulse response function, the generalized frequency response function, and the evolutionary generalized frequency response function are proposed. Meanwhile, the physical meaning of the evolutionary frequency response function is re-investigation, in which the response for the evolutionary harmonic excitation and the evolutionary frequency response function proves equivalent. Subsequently, according to the physical meaning, a novel and easy-to-implement algorithm of the response PSD is proposed. The response for the evolutionary auxiliary harmonic excitation can be quickly evaluated based on the time-domain explicit formulation method. Finally, two examples are investigated to verify the accuracy and efficiency of the proposed method.

Nonstationary random vibration analysis of fractionally-damped systems by numerical explicit time-domain method

Random vibration analysis of fractionally-damped systems has received considerable attentions over the past two decades. In this paper, an efficient explicit time-domain approach is developed to determine the response statistics of multi-degrees-of-freedom linear systems endowed with fractional derivative terms subjected to nonstationary random excitations. The explicit time-domain expression of the state vector is constructed for the fractionally-damped system, and on this basis, the statistical moments of responses are directly formulated with the moment operation rule or efficiently calculated with the Monte-Carlo simulation. Dimension-reduced statistical analysis can be easily conducted just focusing on certain responses of interest with the use of the explicit expressions of dynamic responses. The present approach can account for nonstationary random excitations with arbitrary evolutionary power spectrum forms, even of the non-separable kind. A 20-degrees-of-freedom shear-type fractionally-damped system subjected to fully nonstationary random excitation is analysed to illustrate the accuracy and efficiency of the proposed method.

FEM verification of accelerated vibration test method based on Grms - T curve

Accelerated random vibration test is now the important dynamic performance and safety evaluation technique for transport packaging system during transportation. The current widely used time scale of accelerated random vibration test in engineering test and some standards is “Inverse power law,” which is based on Basquin (power function) fatigue damage model and [Formula: see text] curve, but is not completely suitable for transport packaging system. In author’s previous research, the general theory of accelerated random vibration test based on acceleration PSD and [Formula: see text] curve was developed which is applied for any fatigue damage model besides Basquin type. The study in this paper is the further and extensive research of previous research. The definite expression between response von Mises equivalent stress ([Formula: see text]) of the products and tri-axial acceleration Root-Mean-Square (RMS) was developed, based on which [Formula: see text] curve was transformed to [Formula: see text] curve to describe the product damage. Time scale of accelerated random vibration was obtained. The proposed method was verified by finite element analysis. In addition, the effects of excitation spectrum shape and system damping on the response vibration of products were discussed. This study is valuable in engineering for safety assessment and random vibration analysis of transport packaging system.

Random analysis of coupled vehicle–bridge systems with local nonlinearities based on explicit time-domain method

Based on the explicit time-domain method, an efficient analysis algorithm is developed for the random vibration analysis of the coupled vehicle–bridge system with local nonlinear components. In this work, the coupled vehicle–bridge system is divided into two subsystems, including the linear bridge subsystem and the nonlinear vehicle subsystem. Firstly, using the equivalent linearization technique, the equivalent linearized subsystem is constructed for the vehicle subsystem with the hysteretic suspension spring at a given time instant. Then, the explicit expressions of the responses of the linearized vehicle subsystem and the linear bridge subsystem are constructed corresponding to contact forces, respectively. Further, the explicit expression of the contact forces is derived in consideration of the compatibility condition. Lastly, the dimension-reduction vibration analysis for the equivalent linearized coupled vehicle–bridge system can be carried out based on the explicit time-domain method. The numerical example about a coupled vehicle–bridge system under the random irregular excitation is investigated, and the results indicate that the proposed approach is of feasibility.

Modal Analysis of Passive Engine Mount Assembly using Finite Element Analysis

Engine mounts play a vital role in reduction of noise and vibration. For an internal combustion engine, there exist two basic dynamic disturbances: a) the firing pulse due to the combustion of fuel in the cylinder and b) the inertia force and torque caused by the rotating and reciprocating parts. The firing pulses will cause a torque to act on the engine block about an axis parallel to the crank. The inertial forces are both parallel to the piston axis and perpendicular to the crank and piston axes. This dissertation describes the finite element approach for modal and static structural analysis of the engine mount used on an inline four-cylinder petrol engine. A 3D model of the mount was created with the help of Solid-Edge V19 software and the same was analysed for natural frequencies and total deformation using Ansys Workbench software. Further, torsional stiffness of the mount was obtained using finite element analysis and validated using experimental testing. Viscoelastic behaviour of rubber has also been discussed with the help of a Generalized Maxwell model (GMM). GMM was chosen after reviewing all the commonly used models. Later, an in-depth analysis of transmissibility was carried out using finite element analysis approach and a 6-DOF Mathematical model approach. Random vibration analysis was carried out and the resulting RMS accelerations were compared with the ISO-2631 standard.

A Bayesian deep learning approach for random vibration analysis of bridges subjected to vehicle dynamic interaction

Vehicle actions represent the main operational loading for various types of bridges. It is essential to conduct random vibration analysis due to the unavoidable uncertainties arising from both the vehicle and bridge structure. This paper proposes a novel approach for the vehicle-induced random vibration analysis of bridges integrating Bayesian deep learning. The dynamic equation of the stochastic vehicle-bridge interaction system in state space form is deduced, based on which an ensemble of deep neural network is proposed to construct the surrogate model consisting of two designed functional modules, i.e., convolutional layers for excitation input feature extraction and long short-term memory (LSTM) layers for bridge response time series prediction. According to the deduced state space equation, the conventional LSTM cell is modified by introducing randomness to a portion of cell parameters. Probability distributions of the selected network parameters are then estimated by Bayesian inference, enabling the surrogate model to convey the uncertainties of the vehicle-bridge interaction system and rapidly estimate random vibration responses of the bridge. The proposed approach is applied on a railway bridge under high-speed train loading to demonstrate its efficacy. A deep Bayesian neural network is tailored and developed using the present methodology for the studied train-bridge coupling dynamic system. Time-domain statistics and frequency-domain responses of the bridge are acquired through the Bayesian deep learning model and compared with the results from a validated vehicle-bridge interaction model. Robustness of the Bayesian deep learning approach is further examined by investigating the influence of training dataset size, vehicle speed, and model input noise.

Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation.

The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.

Study on Method of Structure Model Construction for Statistical Energy Analysis using FEM

This paper presents a structure model construction for statistical energy analysis (SEA) using FEM. Identifying SEA parameter regardless of the excitation method is demanded effectively. The proposed method is based on a combination of SEA and vibration response by base excitation like forced displacement vibration analysis, random vibration analysis, and large mass method. These methods are effective on an analytical cost performance compared with the conventional force excitation method that is called rain-on-the-roof-excitation. In this study, the proposal method is validated through the two types of model, (i) simple flat plate consisting of one subsystem, and (ii) an L plate consisting of two subsystems. As a result, the method is shown to work quantitatively well to the coupling loss factors.

이론적 열유동 및 랜덤 진동 해석을 적용한 EPS 보냉용기의 포장설계

Although it has recently been regulated for use as an eco-friendly policy in Korea, the use of EPS (Expanded Polystyrene) cooling boxes, which are used as cold chain delivery insulation boxes for fresh agricultural and livestock products, is also increasing rapidly as e-commerce logistics such as delivery have increased rapidly due to COVID-19. Studies were conducted to optimize the EPS cooling container through internal air heat flow of CFD (Computational Fluid Dynamics) analysis and FEM (Finite Element Method) random vibration analysis using domestic PSD (Power Spectral Density) profile of the EPS cooling box to which the refrigerant is applied in this study. In the analysis of the internal air heat flow by the refrigerant in the EPS cooling box, the application of vertical protrusions inside was excellent in volume heat flow and internal air temperature distribution. In addition, as a result of random vibration analysis, the internal vertical protrusion gives the rigid effect of the cooling box, so that displacement and stress generation due to vibration during transport are smaller than that of a general cooling container without protrusion. By utilizing the resonance point (frequency) of the EPS cooling box derived by the Model analysis of ANSYS Software, it can be applied to the insulation and cushion packaging design of the EPS product line, which is widely used as insulation and cushion materials.

Spectral decomposition-based explicit integration method for fully non-stationary seismic responses of large-scale structures

This paper presents a spectral decomposition-based explicit integration method for random vibration analysis of large-scale linear structures subjected to fully non-stationary seismic excitations. In this method, the seismic excitation process is decomposed using the spectral representation method, leading to a discrete representation of the excitation process in terms of an orthogonal random vector. Next, an explicit expression for the state response vector of structures with respect to the orthogonal random vector is derived by direct discretization and integration of the structural state equation, in which the time-dependent coefficient matrix can be obtained in a recursive manner. Since the state response vector contains only the displacement and velocity responses of structures, the finite-difference formulas are further used to obtain the explicit expression for the structural acceleration responses. These explicit expressions can be used not only to directly calculate the correlation matrix and evolutionary power spectral density of stochastic responses of structures, but also to efficiently evaluate the response samples required in the Monte Carlo simulation. For demonstration purposes, the proposed method is applied to the random vibration analysis of a coupled building system and a large-scale space-frame structure excited by two kinds of fully non-stationary seismic inputs; other existing methods are employed to illustrate the high accuracy and efficiency of the proposed method.