Excitation Power Spectral Density Research Articles

In-plane spin excitation of skyrmion bags

Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current (AC) magnetic field, we investigate the spin-wave modes of skyrmion bags, which behave differently from the clockwise (CW) rotation mode and the counterclockwise (CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion–inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.

A two-step weighting regularization method for stochastic excitation identification under multi-source uncertainties based on response superposition-decomposition principle

Excitation identification has received considerable attention because of its importance in safety assessment and structural design. This paper proposed a power spectral density (PSD) identification method for stationary stochastic excitations considering multi-source uncertainties in load fluctuations, material dispersions and measurement noises. Based on the traditional inverse pseudo-excitation method, a two-step weighting regularization strategy is creatively developed to reduce the amplification effects of the uncertainties in the transfer matrix and measurements on reconstructed results near natural frequencies. Especially, to enhance the generalizability of regularization operations, a weighting matrix is defined based on the interval-quantized deviation analysis of pseudo excitations and then an improved Tikhonov regularizing operator is defined given the features of the weighting transfer matrix and pseudo responses. Next, the response superposition-decomposition principle is performed to determine the boundaries of excitation PSD and two uncertainty propagation methods are developed. To guarantee the accuracy and efficiency of uncertainty analysis, the adaptive reduced-dimension Chebyshev model is adopted to characterize the nonlinear response-parameter relationships, and the first-order Taylor series approximation is used to describe the linear response-excitation relationships. Eventually, two numerical examples and one experimental example are discussed to demonstrate the feasibility of the developed approach. The results suggest its promising applications in complicated structures and loading conditions.

A hybrid genetic algorithm-neural network model for power spectral density compatible ground motion prediction

In this paper, the utility of power spectral density (PSD) in ground motion prediction for hazard analysis is examined. The main advantage of PSD is that the area under PSD of excitation gives the energy of the excitation and it is structure independent. The PSD of ground motion from past earthquakes and properties of PSD in terms of spectral moments are studied. 1487 accelerograms from 25 major past earthquakes with magnitude ranging from 4.9 to 7.9 taken from the ‘Pacific Earthquake Engineering Research Centre – Next Generation Attenuation’ database are considered. PSD of past ground motion data is used to form a hybrid genetic algorithm-neural network based attenuation relationship with magnitude of earthquake, Joyner-Boore distance and shear-wave velocity. PSD compatible time histories are generated using the proposed model. An application of the proposed model is demonstrated by developing a uniform hazard power spectral density for Delhi with a return period of 2500 years.

Shaker Testing with Simultaneous Control of PSD and FDS

Abstract The fatigue damage spectrum (FDS) model characterizes how the damage potential is distributed over the excitation frequency range, similarly to how the power spectral density (PSD) characterizes the distribution of the excitation level. However, reproducing the operational PSD during in-house shaker testing does not necessarily mean that the FDS would be also reproduced because some unusually distinctive peaks, higher than those in a signal generated from the PSD, occur in vibrations of automobiles and railway vehicles. Presence of these peaks in real operational vibrations and their absence in the PSD-based random testing is the reason why the shaker testing FDS obtained by the ordinary PSD control is different in shape and usually lies below the operational FDS. It is shown in this paper that the FDS shape as a function of frequency can be controlled by manipulating some of the IFFT phases instead of making all of them random. Since the phase manipulation does not affect the excitation PSD, the FDS and the PSD can be controlled simultaneously, which is demonstrated for an example of operational vibrations of an automobile. This new concept of shaker testing with the PSD+FDS control can also be used for accelerated testing when the FDS target needs to be artificially increased. It can be done without scaling up the PSD, thereby avoiding concerns about the test exaggeration factor being too high.

Finite element analysis and experimental investigation of beer bottle‐turnover boxes transport unit under random vibration excitation

AbstractThis paper investigates the dynamic response of the transport unit of beer bottle‐turnover boxes under the random vibration excitation by using the experiments and finite element (FE) analysis and provides an analytical method of random vibration for a contact nonlinear transport unit with a jumping body through a case study. The acceleration power spectral density (PSD) of the bottle in a single‐layer transport unit and in a bottom layer of a two‐layer transport unit is unimodal; however, that on a top layer of the two‐layer transport unit is basically bimodal. The acceleration response of the bottle in the bottom layer is mainly controlled by a peak frequency and the corresponding excitation PSD near the peak frequency and that on the top layer by two peak frequencies and the corresponding excitation PSDs. The critical stress is located at the bottom and shoulder for the bottle and in the reinforcement area of the bottom plate or at the side‐stiffening plate for the turnover box. A different shape of an excitation spectrum results in a large difference in stress response. The FE results are basically in agreement with the experiments.

Fatigue failure and G rms –N curve of corrugated paperboard box

As a kind of transport packaging, the corrugated paperboard box is widely used in logistics. During transport, the stacked packaging units are subjected to random vibration induced by vehicles. Thus, the random dynamic force will be exerted to corrugated paperboard box continuously. As the shipping distance increases, there will be cumulative fatigue damage within the corrugated paperboard box, which will weaken the mechanical property (stiffness) and the protective value of the corrugated paperboard box. Therefore, the dynamic damage and fatigue failure of corrugated paperboard box are crucial for the design of corrugated paperboard box. This article aims to develop the acceleration root mean square-life curve of corrugated paperboard box. At first, the accelerated random vibration test method was developed by the theory analysis according to the damage equivalent principle of a specified point within the corrugated paperboard box. Then, the random vibration experiments were conducted on the loaded corrugated paperboard box by taking white noise as excitation power spectral density. In the experiments, the acceleration transmissibility curve was recorded periodically. Relative stiffness was taken as the indicator to detect the cumulative damage and assess the structural integrity of the corrugated paperboard box. The stiffness reduction 20%, 30%, and 40% were taken as fatigue failure criteria to develop the curves. Results show that both the Basquin type and exponential function type are in good fitting with the curve of the corrugated paperboard box. The index b of the Basquin type is between 8.16 and 11.01, and b′ of the exponential function type between 21.19 and 26.84. The study provides reference for the accelerated random vibration test of corrugated paperboard box.

An advanced algorithm to study the effect of uncertainties on the stochastic performance of high-pier bridge under earthquake

A hybrid method combining the stochastic pseudo excitation method (SPEM) and the response surface method (RSM) was presented to handle the effect of both random characteristics of power spectral density of excitation and uncertain parameters. Based on basic principle of pseudo excitation method (PEM), an optimized algorithm was proposed to be SPEM. The effects of the uncertainties of structure and excitations could be considered through SPEM, thus directly acquiring the whole sampling results of random vibration of uncertain structural system. To reduce the cost of computing the total number of required finite element analysis simulations, RSM was adopted to hold calculated sampling results to gain the probability density function (PDF) of random vibration. The proposed method can consider both the effects of random characteristics of power spectrum of random excitations and the uncertainties of target system. Neverthless, Since the proposed method is based on the pseudo excitation method, the SPEM-RSM can handle the stochastic vibration analysis of determine and uncertain structure. In order to verify the accuracy and efficiency of proposed method, taking a single degree of freedom linear uncertain oscillator and a pier construction as two verification cases, the PDF of responses computed by the hybrid method was verified by Monte Carlo method (MCM), and the efficiency of the proposed method was presented. Then, stochastic responses of the railway continuous bridge subjected to earthquake were calculated, several uncertainties are involved in the computation. In addition, sensitivity analysis was solved for uncertain parameters.

Strip/Foil Rolling Mill Stochastic Excitation Model and Its Stability

Based on the stochastic rolling force data from aluminum hot strip tandem mill, the ARMA time series model and the stochastic excitation power spectral density (PSD) model are established, and the stochastic rolling forces excitation model is established by utilizing Levenberg-Marquardt combined with generalized global planning algorithm. A two dimensional stochastic nonlinear dynamical model of rolls is presented considering the stochastic factor of the rolling force. The Hamilton function is also described as one dimension diffusion process by using stochastic average method, the singular boundary theory was taken for analyzing the global stochastic stability of the system, and the system’s stochastic stability was researched by solving the Fokker-Planck-Kolmogorov (FPK) equation. The results show that the stochastic excitation model obtained has significance for analyzing and researching stochastic dynamics characteristics to the system, and also generalized energy H in the range of 0.02 to 0.4, the system’s response has the minimum transition probability density, and the system state is not easy to change, therefore the system generalized energy H should be to limit in this range in the design and operation of the rolling mill.

Method of Modeling the Excitation Spectrum of Train Based on Track Irregularity

A new technique is present in this paper that transforms the railway track irregularity power spectral density of left and right rails into the excitation power spectral density of wheelset of train, compared with the railway track irregularity spectrums of left and right rails which are not the direct inputs of simulation dynamic model of trail. A parameter model is chosen as the model of excitation spectrum and parameters fitting result shows that this model is suitable for the excitation spectrums of traversing, floating and head shaking, and the method present in this paper is effective.

Stochastic Excitation Model of Strip Rolling Mill

The stochastic excitation power spectral density (PSD) model and ARMA time series model are established based on the stochastic rolling force acquisition data, which is processed into stationary, normal and zero mean from a aluminum hot strip tandem mill. Characteristics of rolling force ARMA time series models are discussed by means of random process theory. The rolling forces PSD function of facilitating engineering application is obtained by utilizing Levenberg-Marquardt combined with generalized global planning algorithm, and the stochastic excitation model is established. It provides the basis for the prediction of rolling force.

Nonlinear dynamic analysis of an elastic beam isolator sliding on frictional supports

The dynamic behavior of an elastic beam free to slide on two frictional supports is studied under sinusoidal and random excitations. The beam force–deflection relationship, originally expressed in terms of elliptic functions, is approximated by a polynomial fit of eleventh order. The friction force is modeled in terms of the sliding velocity and the end slope angle. Under sinusoidal excitation, the equation of motion of the system is solved numerically and the solution is utilized to estimate the system transmissibility. It is found that when the excitation frequency is increased beyond resonance, the friction at the sliding supports improves the transmissibility. The dependence of the response on initial conditions establishes the basins of attraction for different values of friction coefficient and excitation parameters. The dependence of the safety integrity factor on excitation amplitude level and friction coefficient reveals that the friction extends the stable region. Under random excitation, the system response statistics are estimated from Monte Carlo simulation results for different values of friction coefficient and excitation power spectral density level. The friction is found to result in a significant reduction of the system response mean square.

STOCHASTIC AND/OR CHAOTIC RESPONSE OF A VIBRATION SYSTEM TO IMPERFECTLY PERIODIC SINUSOIDAL EXCITATION

A single-degree-of-freedom system with one-sided rigid barrier at its equilibrium position is considered. The system is subject to excitation by a sinusoidal-in-time force with random white-noise temporal variations of the excitation frequency. Whilst response analysis had been made previously for the resonant case, i.e. one with expected excitation frequency being close to an even integer multiple of the natural frequency of the system without barrier, the nonresonant case is considered in this paper which is well known to be prone to multiple bifurcations and chaos in the case of perfectly periodic excitation. A simple qualitative explanation of the corresponding phenomenon of frequency multiplication, or "breeding", is provided for this case based on a special piecewise-linear transformation of state variables, which permits to get rid of velocity jump for the transformed velocity. The influence of the imperfect periodicity is then studied by numerical (Monte-Carlo) simulation. It is shown that increasing intensity of the white-noise variations of the excitation frequency, or bandwidth of the excitation power spectral density (p.s.d.), may greatly reduce frequency content of the response with simultaneous increase of the overall response level. The excitation/system bandwidth ratio is identified as a key governing parameter.

Nonlinear random responses of a structure parametrically coupled with liquid sloshing in a cylindrical tank

The nonlinear random interaction of an elastic structure with liquid sloshing dynamics in a cylindrical tank is investigated in the neighborhood of 2:1 internal resonance. Such internal resonance takes place when the natural frequency of the elastic structure is close to twice the natural frequency of the anti-symmetric sloshing mode (1,1). The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. The analytical model involves three sloshing modes (1,1), (0,1) and (2,1). The system response statistics and stability boundaries are numerically estimated using Monte Carlo simulation. The influence of the excitation center frequency, its bandwidth, and the liquid level on the system responses is studied. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. As the liquid depth or the structure spring stiffness decreases, the region of nonlinear interaction shrinks and is associated with a shift of the peak of the structure mean square response toward the left side of the frequency axis.

Combination of Modal Responses Consistent with Seismic Input Representation

The well-known modal superposition method for the evaluation of seismic response by the complete quadratic modal combination rule (CQC) is revisited. The most widely used version of the CQC rule utilizes correlation coefficients derived for white-noise excitation and neglects the influence of peak factor variation on the response. Here a simplified procedure for evaluation of correlation coefficients and peak factors consistent with the power spectral density of seismic excitation is proposed. The procedure is based on an approximate analytic expression for direct evaluation of the power spectral density of the excitation consistent with any prefixed response spectrum, and the evaluation of the consistent correlation coefficients and peak factors by using analytical expressions. The ranges of system dynamic parameters for which the correlation coefficients derived for white-noise excitation are not adequate are pointed out. Then the influence of the assumptions for CQC rule derivation on the evaluation of...

Efficient Optimization Procedure For Minimizing Vibratory Response Via Redesign Or Modification, Part I: Theory

This paper addresses the problem of minimizing the vibrating response via structural modification. The method presented is computationally efficient, and orders of magnitude faster than conventional approaches. Some aspects of the method's efficiency are traceable to specific properties of vibrating structures. The method is based on the assumption of knowledge of the excitation's power spectral density and can handle structures modelled by an incomplete modal model. While the geometric structural changes are represented as mass and stiffness changes, any structural or geometrical parameter can be used. The optimization problem is cast into numerically efficient subsequent stages. Also the response measure, the cost function and the sensitivities with respect to structural parameter change, are calculated by using a very efficient scheme, exploiting the modal decomposition. The problem is formulated directly in terms of physical and geometrical quantities: i.e., section areas, height, width and point mass. Simple constraints ensure realizable structural changes yielding optimal performance. This helps in presenting more viable design options. Examples are deferred to the companion paper, part II.

Structural response to random acoustic excitation

AbstractThe design of aerospace structures necessitates the study of their behaviour in intense acoustic environments. This is more so in recent times due to an increase in power of the vehicles. The present paper deals with an investigation of the response of structures such as flat, stiffened plates to such environments. A peaked type of power spectral density of excitation is assumed, which is more realistic and representative of actual random acoustic excitations than the conventionally assumed white noise type excitations, either ideal or band‐limited. The space correlation of the excitation field is assumed to be unity over the plate surface. Generalized harmonic analysis is used to obtain responses such as auto‐correlation functions and mean square values of both accelerations and stresses. To obtain the response quantities of stiffened plates the approximate method of analysis suggested by Lin12 is used.