Random Vibration Analysis Research Articles

A Study on the Flight Vibration Environmental Specification of Unmanned Flying Vehicle using Random Vibration Test and Analysis Methods

In this study, analysis of dynamic characteristics and flight vibration was performed to unmanned aerial vehicles. The analysis model was supplemented by performing a dynamic characteristic test and a random vibration test using manufactured dummy aerial vehicle. For the dynamic characteristic test, a bungee cable was used to implement the free end boundary condition. Prior to the flight vibration test using a multiple electric shaker, a random vibration test was performed to predict the excitation force during the actual flight vibration test. It was judged that the actual test could be predicted more accurately by supplementing the analysis model from the test results. In addition, it was possible to determine the feasibility of the test by predicting the excitation force of the flight vibration test.

Structural optimization and fatigue life analysis of landing gear upper lock

The upper lock is a key component of the landing gear system, and its fatigue life affects its service life and reliability. In this paper, the modal analysis, random vibration analysis, and fatigue life calculation are carried out for the upper lock. According to the analysis results, the upper lock structure is optimized, and the optimization scheme is proposed. The natural frequency, stress, and fatigue life are analyzed, and the scheme meets the design requirements. Finally, the optimized structure is verified to be reasonable and feasible through experiments.

Design and analysis of energy efficient wind turbine blades

Inspired by humpback whale flippers, this study presents the effect of leading-edge tubercles on the wind turbine blade. Force models for lift and drag are developed on the blade which have an important role in the wind turbine performance. The study compares the CFD simulation of fluid flow over blade with leading edge tubercles and the conventional blade. Present work also covers strength and random vibration analysis for both the blades. Furthermore, different tubercle blades have been compared for lift and drag coefficients by varying tubercle amplitude. Structural analysis shows tubercled blade is suitable from structural and strength point view. In tubercled blade overall lift to drag-coefficient ratio increased up to 8.5, whereas in conventional this ratio is about 1.7 which is found to be very low. This ratio clearly indicates that in the presence of tubercles on the blade, performance improving even in lower wind speed areas. Overall tubercled blade found to be more suitable for modern wind turbines.

Nonstationary random vibration analysis of structures with uncertain parameters based on a polynomial dimensional decomposition

AbstractBased on polynomial dimensional decomposition (PDD), a novel method for analysing nonstationary random vibration of structures with uncertain parameters is proposed in this paper. The uncertain structural parameters are assumed to be independent random variables, with certain types of probability distributions; thus, the nonstationary random vibration responses of the structures become stochastic functions of these uncertain parameters. A dimensional decomposition and Fourier expansion were applied to calculate the statistical characteristics of the nonstationary random vibration responses of the structures. To calculate the conditional power spectral density (CPSD) and conditional standard deviation (CSD) of the nonstationary random vibration responses, CPSD and CSD were explicitly expressed using expansion coefficients and polynomial basis. Subsequently, the probability distributions of the structural responses can be effectively calculated in terms of these explicit expressions. Dimension‐reduction integration and Gauss numerical integration were applied to calculate expansion coefficients. The validity of the proposed method was verified by numerical examples, including a single‐degree‐of‐freedom system and a multi‐degree‐of‐freedom system (reinforced concrete shear wall). The results indicate that the proposed method is as accurate as Monte Carlo simulation (MCS), whereas the proposed method requires considerably smaller number of nonstationary random vibration analyses than MCS. Moreover, the nonstationary random vibration analysis of a long‐span cable‐stayed bridge demonstrates that the proposed method is feasible for quantifying the uncertainties of the nonstationary random vibration responses of complex engineering structures with uncertain parameters.

Random free vibration analysis of porous functionally graded cantilever plates

Random free vibration analysis of porous functionally graded cantilever plates

Vibration Analysis of a Roller Bearing Condition Used in a Tangential Threshing Drum of a Combine Harvester for the Smooth and Continuous Performance of Agricultural Crop Harvesting

Testing the reliability of the threshing unit is difficult and thus often neglected before the harvesting season, which can result in breakdown maintenance during peak harvesting time in difficult-to-access areas for sensor mounting. In this paper, the vibration analysis of the threshing condition of the combine harvester was performed by introducing the bracket for inaccessible locations. The Adash A4900 Vibrio M analyzer (Adash spol. s.r.o., Ostrava, Czech Republic) was used for a vibration signal measurement and the DDS Adash software was used for signal processing. The demodulated fast Fourier transform (FFT) root mean square (RMS) (500 Hz–16 kHz) method was used to evaluate the bearing condition and DDS Adash Fault Source Identification Tool (FASIT) technology was used to evaluate other mechanical conditions such as the looseness, misalignment, and unbalance of the threshing unit of the Massey Ferguson series of combine harvesters. Modal and random vibration analyses were performed on the bracket and components and compared to prevent the resonance phenomenon using the Ansys Software (Ansys, Inc., Canonsburg, PA, USA). The constrained modal analysis of the threshing drum was performed to observe the deformation. Decent results were obtained from the method used. The method was again validated by the tangential threshing test bench and successfully determined the bearing fault condition. The method used is an uncomplicated and effective way of performing the bearing analysis of the tangential unit of the combine harvester.

On uncertainty modeling of thermoelastic vibration for porous nanosandwich beams with gradient core based on nonlocal higher order beam model

In the present paper, the size-dependent random thermoelastic vibration analysis of porous nanosandwich beams with gradient core are demonstrated based on the nonlocal higher order beam model. The nonlocal elasticity theory incorporation with the higher order shear deformation theory is used to describe the kinematic and constitutive relations. The governing equations are obtained from minimum potential energy principle. The finite element method is used to solve the governing equations. Three types of the FG sandwich nanobeams with three types of porous cores are taken into account, and the influences of these structures and porosity types on the deterministic and stochastic behavior of sandwich beams are thoroughly discussed. Initially convergence and validation study is preformed to validate the present theoretical model by comparing the present results with the several previous works and Monte Carlo Simulation (MCS). Further, a comprehensive parametric study is performed to demonstrate the influence of the length to thickness ratio, degree of uncertainty in the material properties, nonlocal parameter, porosity distribution type, porosity volume fraction, temperature change, and gradation of material on the deterministic and stochastic behaviors of the FG nanosandwich beams. The developed model and computed results may be useful in the precise and reliable design of the components of nanodevices and systems.

Benchmark solutions for stochastic dynamic responses of rectangular Mindlin plates

There exist some researches on the benchmark responses of moderately thick plates based on Mindlin theory under static loads. In practice, rectangular Mindlin plates are often subjected to various random excitations. However, the benchmark solutions of analytically stochastic dynamic responses for rectangular Mindlin plates under random excitations were not investigated. In this paper, analytical power spectral density functions and root mean squares for stationary and nonstationary stochastic responses of rectangular Mindlin plates are derived, which provide benchmark solutions for other numerical methods and experimental design. Firstly, based on the closed-form free vibration analyses of rectangular Mindlin plates with two opposite simply supported edges, exact natural frequencies and modal shapes are obtained. Then, the pseudo excitation method is introduced into the decoupled differential equations of motion. By combining the exact solutions of free vibration, the analytical method for random vibration analysis of elastic Mindlin plate is proposed, and the analytical stochastic responses are derived. Due to the low efficiency of the AM based on symbolic operation, the efficient discrete analytical method, which can ensure that the results are exact in the spatial domain, is further developed. Finally, the performance of the proposed approaches is verified by comparing with the commercial software, Monte Carlo simulation, and literature. The remarkable effects of spatial distributions of excitations on the stochastic responses of Mindlin plates are illustrated. The important influences of parameters including relative thickness, elastic modulus, and boundary constraint degree on responses are revealed.

Non-random vibration analysis of rotate vector reducer

Vibration has been and still is a persistent problem to negate the transmission accuracy and service life of rotate vector (RV) reducer, and vibration analysis remains a challenge in industry. It is attributed to the inherent structural characteristics of RV reducer. Acquisition of experimental data on core components is not straightforward. Thus, the probability-based random vibration method is no longer applicable, and vibration problem of RV is yet to be tackled. To this gap, this study proposes a non-random vibration analysis method for RV reducer, which circumvents the demand of a significant amount of experimental data via random vibration analysis method. To start with, an interval process model is introduced to establish the non-random vibration analysis model for RV reducer on the basis of the deterministic vibration model. Non-random vibration analysis method for RV reducer is then proposed by combining the deterministic vibration analysis approach with the interval process theory. The proposed non-random vibration analysis method is exemplified with a RV-20E reducer to analyze the vibration of its core components. The results are verified against Monte Carlo simulation (MCS) method to indicate that the currently proposed method can efficiently evaluate the vibration of core components inside RV reducer subject to uncertain excitation in the premise of compliance to specific design guidance.

Random vibration analysis of vibro-impact systems: RBF neural network method

The recent success of the radial basis function neural networks (RBFNN) method for random vibration analysis of smooth systems fuels in speculations that this approach may be extended to non-smooth problems. However, very little is known on the applicability of this approach to non-smooth systems. This work generalizes the RBFNN method to the randomly excited non-smooth vibro-impact system (VI-S). We first transform the non-smooth VI-S system to a continuous nonlinear system. Then, the solution of the reduced Fokker–Planck–Kolmogorov (FPK) equation for the transformed VI-S is expressed in terms of the RBFNN with Gaussian activation functions. The weights of the RBFNN are determined by solving an optimization problem to minimize the reduced FPK equation residual subjected to the constraint of the normalization condition. Three examples are presented to demonstrate the validity of the suggested scheme. Several remarks on the solution process also presented. All the results confirm the applicability and validity of the RBFNN method in dealing with the randomly excited non-smooth VI-S.

Auxiliary harmonic excitation generalized method for higher-order analysis of linear structure under multiple non-stationary non-Gaussian excitations

In the classical random vibration analysis, the frequency-domain analysis method, especially the time-frequency domain analysis method based on the frequency domain analysis method, is the most commonly analysis method. However, the time-frequency domain analysis method is challenging when dealing with multiple non-stationary non-Gaussian excitations. In this paper, an accurate and efficient auxiliary harmonic excitation generalized method for higher-order analysis of linear structures under multiple non-stationary non-Gaussian excitations is proposed. Firstly, the expression for the higher-order moment spectrum of response is theoretically deduced by the mode superposition method, in which the time-varying generalized impulse response function and the time-varying generalized frequency response function are introduced. Secondly, according to the relationship between the response of harmonic excitation and the time-varying generalized frequency response function, the expression for the high-order moment spectrum of response is reconstructed in terms of the response of harmonic excitation and the higher-order moment spectrum matrix of the excitations, in which the response of the time-varying auxiliary harmonic excitation can be evaluated efficiently based on the time-domain explicit formulation method. Finally, two examples are investigated to verify the accuracy and efficiency of the proposed method.

Random Vibration Analysis of Portable Power Supply Container for Radar With U.S. Military Standards

Random Vibration Analysis of Portable Power Supply Container for Radar With U.S. Military Standards

An explicit time-domain method for non-stationary random analysis of nonlinear frame structures with plastic hinges

In this study, a novel approach for random vibration analysis of nonlinear frame structures under seismic random excitations is developed. The explicit time-domain method is improved in this approach by integrating the plastic hinge model, which can simulate the nonlinear behaviors caused by material property changes. Specifically, the hysteretic system’s equation of motion is constructed using auxiliary differential equations that govern the plastic rotational displacements and their corresponding hysteretic displacements. Additionally, by introducing the concept of equivalent excitations, an explicit iteration scheme for solving the equation of the hysteretic system is developed, in which the auxiliary differential equations are solved under the assumption that the plastic rotational velocity changes linearly with time between two adjacent time instants. Finally, by combining the Monte Carlo simulation method and the proposed explicit time-domain method, the non-stationary random responses of nonlinear frame structures can be obtained. As illustrated by numerical examples, the proposed method achieves satisfactory solution accuracy and efficiency when applied to nonlinear frame structures with plastic hinges. Moreover, the proposed iterative method resolves equations involving displacements describing the frame’s global state, plastic rotational displacements, and corresponding hysteretic parameters, introducing a novel concept for solving problems with nonlinear coupled variables of multiple types.

Random vibration analysis of nonlinear structure with pounding tuned mass damper

To mitigate the undesired vibrations of the structure, a cost-effective approach is to set up the nonlinear dynamic vibration absorber (NLDVA) on the structure. As an alternative NLDVA, the Pounding Tuned Mass Damper (PTMD) gathered extensively attention in recent years. However, the random vibration analysis of structure coupled with PTMD still poses a challenge. Besides, there remains an urgent need to construct a more comprehensive recovery coefficient (RC) for the two-stage damping mechanism of PTMD. To fill in this gap, this work involves the nonlinear random vibration of a type of two degree-of-freedom system composing of a main structure (MS) coupled to a PTMD device, in which the collision process of the system is portrayed by a segmented recovery coefficient (RC) model. Specifically, an equivalent system of structure-PTMD is firstly constructed by coordinate transformation. Then, the approximate probability density function (PDF) of equivalent system is performed by combining non-smooth conversion and stochastic averaging method (SAM). Further, the approximate PDF solution of the structure-PTMD can be determined by resorting to Jacobi transformation and verified numerically. Remarkably, the approximate PDF solutions of the system can also be applied to estimate the power spectral density of the system response. Being analytical, the analysis in this work yields results in the closed-form expressions that enable one to acquire new insight into the dynamic features of the structure-PTMD system. Moreover, the proposed scheme will promote the design and application of PTMD in practical projects from a theoretical point of view.

Auxetic hexachiral cantilever beams for piezoelectric vibration energy harvesting

This work presents an auxetic hexachiral cantilever substrate for low-frequency vibration energy harvesting applications. Auxetics are materials with negative Poisson’s ratio that develop stresses of the same nature under mechanical loading, which can be advantageously used in designing energy harvesters with enhanced power output. The proposed harvester is fabricated by attaching a piezo patch on a 3D printed polylactic acid hexachiral substrate to convert the mechanical response to electrical output. Experiments are conducted to characterize the vibration and electrical properties of the harvester. A 3D finite element (FE) model is developed and validated with experimental voltage obtained for different electrical resistance. As the first mode generates maximum power, an equivalent single degree of freedom semi-analytical model is formulated and validated with experiments and FE results. The proposed harvester has a natural frequency of 23 Hz with a voltage output of 9.1 V at 250 kΩ. The developed models are used to study the influence of hexachiral geometry, electrical and mechanical loading on the electro-mechanical response. The harvester voltage is influenced by the ligament thickness and is found to increase linearly with an increase in mechanical loading. Further, the enhancement in performance by the addition of hexachiral sub patch to a plain beam is investigated, followed by a comparison with harvesters having plain, hexagonal and re-entrant geometries. The results show that the hexachiral harvester has the lowest first mode frequency with a power output about 20 and 3 times the plain and re-entrant harvesters, respectively. Finally, random vibration analysis of the hexachiral harvester is carried out to evaluate its performance under ambient loading, and the results show that the semi-analytical model is a computationally efficient alternative to study the first mode behavior. The findings of the study demonstrate the potential of the proposed hexachiral harvester for low-frequency applications.

An analysis method for fatigue life of rail vehicle axles considering rotation effect of wheelset

In this paper, the discrepancy between the calculated and actual fatigue life distribution trend of the axles of railway vehicle structures is corrected. The calculations were made using the traditional fixed-axle model in which the wheelset rotation is neglected in random vibration analysis. A correction method is proposed, which is based on the original methods of fatigue life analysis of the axle structure of railway vehicles (i.e. the pseudo-excitation method and finite element model) and according to the characteristics of the symmetrical axle structure and the actual rotational operation state of the railway vehicle wheelset. Taking a locomotive system as an example, the minimum fatigue life calculated by the fixed-axle model is only 0.81 million km. In contrast, the minimum fatigue life calculated by the proposed method is 5.85 million km, which is consistent with the actual fatigue life of the axle. The position of the minimum fatigue life is also consistent with the actual position. The reliability of the proposed method for calculating the random fatigue life of the axle structure is illustrated. The influence and contribution of the prestress generated by axle press-fitting and vehicle serving weight of the railway vehicle acting on the axle on the axle fatigue life were studied. The results show that the prestress has a different influence on the fatigue life reduction of the wheelset. The minimum fatigue life reduction can reach 16.68% when all the prestresses are considered. Therefore, the influence of prestress should be considered in the design of railway vehicle axle structures. The idea of considering prestress should be proposed when revising axle standards.

Random Vibration Analysis of L-type Electric Luggage Conveyor Vehicle Frame

In order to verify the rationality of the designed L-type electric luggage conveyor vehicle frame structure, this paper imports the frame structure of the designed L-type conveyor vehicle into ANSYS Workbench software, conducts modal analysis, and evaluates the performance of the frame by analyzing the inherent frequency and vibration pattern, then uses Matlab to build the simulation model of the airfield pavement, calculates the power spectrum density, and the dynamic response and stress solution of the conveyor vehicle under specific operating conditions, and conducts random vibration The dynamic response and stress solution of the frame under the specific operating conditions are obtained. The results show that the frame of the L-type electric luggage conveyor is less excited by the road surface during the driving process, which will not cause large damage to the structure and is reasonably designed in terms of vibration characteristics.

대형 레이더의 수송 진동 해석을 위한 주요 모드 결정 방법론

Securing the durability of transport vibration for large radars is essential. Transport vibration evaluation is performed via random vibration analysis. The response of random vibrations is determined by the covariance matrix, which is the correlation between the input power spectral density and dynamic characteristics of the radar. Therefore, in this study, the eigen-modes that have a dominant influence on the response are selected by normalizing the covariance matrix. Further, selective mode superposition ensures the accuracy of random vibration analysis. In addition, based on the analysis results, transport vibration durability evaluation for a large radar is performed.

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.