Mid-frequency Analysis Research Articles

Feature Recognition of Abstract Art Painting Multilevel Based Convolutional Ancient Recognition Neural Network Method

Art can be used to spread an inspirational message to encourage people and accomplish great things in life. The art of communication among people can be a mode of communication to concentrate on common issues to improve humankind. The challenging characteristics in art painting include such as degradation, cracking, and flaking is considered an essential factor. In this paper, the Multilevel Based Convolutional Ancient Recognition Neural Network Method (M-CARNNM) has been proposed to incorporate experts’ suggestions, helping artists envisage how the ancient painting may have looked after restoration. Mid-frequency analysis is introduced to reinforce the rough estimation of complete images by adding missing regions and the nearest neighbor pixels to match the maps. A domain-specific pyramid network is used to capture various space context amounts. Experimental results effectively predict the proposed method for large areas of lack of information and produce controllable vector graphics, photographic painting, and high-frequency results.

Medium-Frequency Vibration Analysis of Timoshenko Beam Structures

Medium-frequency (mid-frequency) vibration analysis of complex structures plays an important role in automotive, aerospace, mechanical, and civil engineering. Flexible beam structures modeled by the classical Euler–Bernoulli beam theory have been widely used in various engineering problems. A kinematic hypothesis made in the Euler–Bernoulli beam theory is that the plane sections of a beam normal to its neutral axis remain planes after the beam experiences bending deformation, which neglects shear deformation. However, previous investigations found out that the shear deformation of a beam (even with a large slenderness ratio) becomes noticeable in high-frequency vibrations. The Timoshenko beam theory, which describes both bending deformation and shear deformation, would naturally be more suitable for medium-frequency vibration analysis. Nevertheless, vibrations of Timoshenko beam structures in a medium frequency region have not been well studied in the literature. This paper presents a new method for mid-frequency vibration analysis of two-dimensional Timoshenko beam structures. The proposed method, which is called the augmented Distributed Transfer Function Method (DTFM), models a Timoshenko beam structure by a spatial state-space formulation in the [Formula: see text]-domain. The augmented DTFM determines the frequency response of a beam structure in an exact and analytical form, in any frequency region covering low, middle, or high frequencies. Meanwhile, the proposed method provides the local information of a beam structure, such as displacement, shear deformation, bending moment and shear force at any location, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated in numerical examples, where the efficiency and accuracy of the proposed method is demonstrated. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are examined through comparison of the Timoshenko beam and Euler–Bernoulli beam theories.

A Chebyshev convex method for mid-frequency analysis of built-up structures with large convex uncertainties

PurposeThis paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties.Design/methodology/approachBased on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM.FindingsCCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method.Originality/valueThe proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.

Stochastic hybrid perturbation technique-based smoothed finite element-statistical energy method for mid-frequency analysis of structure–acoustic systems with parametric and nonparametric uncertainties

At present, the most widely used mid-frequency method, i.e., the hybrid finite element-statistical energy analysis method (FE/SEA), still holds potential flaws, e.g., low accuracy and ignoring uncertain factors. In order to eliminate these problems, a generalized smoothing finite element statistical energy analysis method (SFE/SEA) is first proposed in this work, which is constructed based on the edge-based gradient smoothing technique, thus reducing the dispersion error in the deterministic calculations. Second, on the basis of the proposed SFE/SEA, the parametric uncertainty models will be introduced, combining the second-order random interval perturbation method and the random interval moment method, etc.; thus, a mid-frequency analysis method (SHPSFEM/SEA) considering both parametric uncertainties (both the random and interval variables) and nonparametric uncertainties is proposed, to effectively analyze the probability and interval characteristics of the random structural–acoustic coupled systems. Moreover, for the interval parameters with wide variation range, the subinterval perturbation method (S-SHPSFEM/SEA) is introduced by dividing the large interval parameters into small interval parameters. The proposed methods are compared with the Monte Carlo simulations of the hybrid FE/SEA model. The high accuracy and efficiency of the proposed methods are verified by two numerical examples.

A modal impedance-based statistical energy analysis for vibro-acoustic analysis of complex systems having structural uncertainty

A modal impedance-based statistical energy analysis for point, line, and area connected complex structural-acoustic systems is introduced. The proposed methodology is applied to perform mid- and high-frequency vibro-acoustic analysis of a cabinet model. The cabinet is composed of several composite plates with local mass variability simulating structural uncertainty, isotropic beams, and an acoustic enclosure. The method uses point mobilities, which are determined using modal parameters obtained by finite element method, to define line and area mobilities via dimension reducing principle. The methodology presented here is successfully verified by several numerical and experimental Monte Carlo computations. With this study, conventional statistical energy analysis is improved for mid-frequency vibro-acoustic analysis of complex systems.

Dispersion and damping analysis of orthotropic composite plate in mid frequency based on symplectic method

A semi-analytical method is used to investigate the dispersion and damping characteristics for rectangular thin orthotropic composite plates in mid frequency analysis. A symplectic eigenproblem is formed whose solution gives analytically the dispersion equation and the wave shape for any combination of simple boundary conditions along the plate edges. The damping capacity of each wave component is obtained using the strain energy theory. In the numerical examples, the dispersion and damping characteristics are calculated and analyzed for orthotropic composite laminated plates with three different combinations of boundary conditions. Comparison of the present results with the Rayleigh-Ritz results and the finite element results validates the effectiveness of the present method. Based on the damping analysis in the wave domain, the thresholds of mid frequency and high frequency vibration characteristics of the composite plate are illustrated. The relationship between the wave components in the present method and the modal modes in the modal method is also explained.

Hybrid Evidence Theory-based Finite Element/Statistical Energy Analysis method for mid-frequency analysis of built-up systems with epistemic uncertainties

Considering the epistemic uncertainties within the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model when it is used for the response analysis of built-up systems in the mid-frequency range, the hybrid Evidence Theory-based Finite Element/Statistical Energy Analysis (ETFE/SEA) model is established by introducing the evidence theory. Based on the hybrid ETFE/SEA model and the sub-interval perturbation technique, the hybrid Sub-interval Perturbation and Evidence Theory-based Finite Element/Statistical Energy Analysis (SIP-ETFE/SEA) approach is proposed. In the hybrid ETFE/SEA model, the uncertainty in the SEA subsystem is modeled by a non-parametric ensemble, while the uncertainty in the FE subsystem is described by the focal element and basic probability assignment (BPA), and dealt with evidence theory. Within the hybrid SIP-ETFE/SEA approach, the mid-frequency response of interest, such as the ensemble average of the energy response and the cross-spectrum response, is calculated analytically by using the conventional hybrid FE/SEA method. Inspired by the probability theory, the intervals of the mean value, variance and cumulative distribution are used to describe the distribution characteristics of mid-frequency responses of built-up systems with epistemic uncertainties. In order to alleviate the computational burdens for the extreme value analysis, the sub-interval perturbation technique based on the first-order Taylor series expansion is used in ETFE/SEA model to acquire the lower and upper bounds of the mid-frequency responses over each focal element. Three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.

Fuzzy interval Finite Element/Statistical Energy Analysis for mid-frequency analysis of built-up systems with mixed fuzzy and interval parameters

This paper introduces mixed fuzzy and interval parametric uncertainties into the FE components of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model for mid-frequency analysis of built-up systems, thus an uncertain ensemble combining non-parametric with mixed fuzzy and interval parametric uncertainties comes into being. A fuzzy interval Finite Element/Statistical Energy Analysis (FIFE/SEA) framework is proposed to obtain the uncertain responses of built-up systems, which are described as intervals with fuzzy bounds, termed as fuzzy-bounded intervals (FBIs) in this paper. Based on the level-cut technique, a first-order fuzzy interval perturbation FE/SEA (FFIPFE/SEA) and a second-order fuzzy interval perturbation FE/SEA method (SFIPFE/SEA) are developed to handle the mixed parametric uncertainties efficiently. FFIPFE/SEA approximates the response functions by the first-order Taylor series, while SFIPFE/SEA improves the accuracy by considering the second-order items of Taylor series, in which all the mixed second-order items are neglected. To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions. The FBIs are eventually reconstructed by assembling the extrema solutions at all cut levels. Numerical results on two built-up systems verify the effectiveness of the proposed methods.

Hybrid Chebyshev Interval Finite-Element and Statistical Energy Analysis Method for Midfrequency Analysis of Built-Up Systems with Interval Uncertainties

AbstractThe hybrid Chebyshev interval finite-element/statistical energy analysis (CI-FE/SEA) method is proposed as an improved method of mid-frequency response analysis for built-up systems with interval parameters, in which the Chebyshev series approximation theory is incorporated into the hybrid FE/SEA method. In the resultant hybrid CI-FE/SEA model, the uncertainty in the SEA subsystem is modeled by a nonparametric ensemble and dealt with hybrid FE/SEA equations analytically, whereas the uncertainty in the FE subsystem is modeled in terms of interval variables. Truncated Chebyshev series are used to approximate the average energy response and cross-spectrum response of the hybrid interval FE/SEA systems. The bounds of the truncated Chebyshev series with respect to the interval parameters are calculated through use of a Monte Carlo simulation. To compare the proposed hybrid CI-FE/SEA method with the conventional Taylor series based method, the hybrid second-order interval perturbation finite-element/sta...

Hybrid finite element/statistical energy method for mid-frequency analysis of structure−acoustic systems with interval parameters

The hybrid Finite Element/Statistical Energy Analysis (FE-SEA) model for mid-frequency analysis consists of two parts: the FE components and the SEA components, which are called as the master system and the subsystem respectively. The hybrid Finite Element/Statistical energy analysis approach is established on the assumption that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. This method has been recently extended to allow the properties of the FE components of built-up structures to be uncertain like interval or probabilistic, and the hybrid model with parametric and non-parametric uncertainties is obtained. By dealing with the non-parametric uncertainty analytically and the parametric uncertainty with Monte Carlo Simulations, the distribution of the responses of the hybrid model can be obtained. In this paper, the interval parametric uncertainty is introduced into the hybrid FE–SEA framework for structure−acoustic systems, and the interval dynamic equilibrium equations are established, thus a hybrid model with non-parametric and interval parametric uncertainties for structure−acoustic systems is obtained; to improve the computational efficiency, the second-order interval perturbation finite element method is introduced into the hybrid FE-SEA framework and the second-order interval perturbation finite element/statistical energy analysis (SIPFEM/SEA) method is proposed. For the structure−acoustic system with interval parameters modeled by FE-SEA, the parameters of FE components are considered as interval parameters instead of deterministic ones, thus the expectations of the second order quantities such as the vibrational energy and the response cross-spectrum in the FE-SEA framework become interval variables, too. In the SIPFEM/SEA, the expectations of the second order response quantities of a structure−acoustic system are expanded with the second-order Taylor series at the nominal values of interval parameters, and for the sake of simplicity and efficiency, the non-diagonal elements of the Hessian matrices are neglected; then by searching the target positions of interval parameters that maximize or minimize the objective functions, the bounds of the vibrational energy and the response cross-spectrum can be obtained. Because of the neglect of the higher order terms of Taylor series, SIPFEM/SEA is limited to the interval analysis with narrow parameter intervals. For larger parameter intervals, the sub-interval perturbation method based on the SIPFEM/SEA is introduced. The proposed methods are illustrated by applications to two example structure−acoustic systems in which the acoustic cavities are modeled by using the interval FE method and the structures are modeled by using the SEA. Reference comparisons are made with the Monte Carlo simulations of the hybrid FE/SEA model. The numerical results verify the accuracy and efficiency of the proposed methods.

Efficient Midfrequency Analysis of Built-Up Structure Systems with Interval Parameters

To improve the efficiency of midfrequency analysis of built-up structure systems with interval parameters, the second-order interval and subinterval perturbation methods are introduced into the hybrid finite element/statistical energy analysis (FE/SEA) framework in this paper. Based on the FE/SEA for built-up structure systems and the second-order interval perturbation method, the response variables are expanded with the second-order Taylor series and nondiagonal elements of the Hessian matrices are neglected. Extreme values of the expanded variables are searched by using efficient search algorithm. For large parameter intervals, the subinterval perturbation method is introduced. Numerical results verify the effectiveness of the proposed methods.

A mode count procedure for mid-frequency analysis of complex vibro-acoustic systems

Satellites and space equipment are exposed to high diffuse acoustic fields during the launch process that are able to excite the structure. The use of adequate techniques to model the structure response to the acoustic loads is a fundamental task during the design and verification phases. Currently, the efforts are focused in the mid-frequency range that in this paper is defined as the frequency range in which a combination of models is required. To select the most accurate modelling technique in each frequency band, this paper proposes a procedure based on the modal count of each subsystem. The procedure is applied in an ordinary satellite case and the frequency response continuity and agreement with experimental results are shown.

Vibrations, energies, and power flows in complex systems.

A general numerical method, the so-called Fourier spectral element method, is described for the dynamic analysis of complex structures. When applied to structural problems, this method treats a complex structure as an assembly of fundamental structural components such as beams and plates. Over each component, the basic displacement is sought directly in the form of a modified Fourier series which is mathematically guaranteed to converge absolutely at every field or boundary point. The Fourier coefficients are considered as the generalized coordinates and determined using the Rayleigh–Ritz method. Since this method does not involve any assumption or simplification, it is broadly applicable to the whole frequency range usually divided into low-, mid-, and high-frequency regions. Additionally, because the system model is mesh- and grid-free, a smooth transition between the different frequency regions can be automatically accomplished by switching on/off the statistical processes and/or the spatial- and frequency-averaging features. This method is particularly suitable for mid-frequency dynamic analysis of complex systems. The relationships are investigated between component energies and power flows. It is shown that the spatial- and frequency-averaging processes may not be appropriate for the mid-frequency analysis because the important dynamic characteristics of a system tends to be eliminated.

Midfrequency acoustic radiation analysis.

Boundary, finite, and infinite element methods have proven useful for solving the 3-D acoustic wave equation at low frequencies. For high frequency, localized formulations such as plane-wave and ray-tracing methods have been applied successfully. These methods are impractical, inaccurate, or both for treating midfrequency problems. Low-frequency methods make very large demands on computer processing while high-frequency methods account only for local effects. Full-spectrum methods have been developed which apply interpolation between the low and high ends of the frequency range to estimate the response in the midfrequency. While these methods have provided some insight to trends as one moves toward the midfrequency range, it is not well established that they can reliably solve problems well away from their established limits. For surfaces with features having dimensions close to midfrequency wavelengths, the physics is distinct from those that govern low and high frequencies, and is not merely a linear combination of the two. This presentation reports on research to develop a midfrequency analysis tool that directly addresses the midfrequency physics. The author will identify the challenges in a physics-based method, discuss an approach to address them, and report on simulations exercising the approach.

Wave based method for mid-frequency analysis of coupled vibro-acoustic problem

Conventional element based methods for modeling acoustic problems are limited to low-frequency applications. Recently, wave based method has been developed which is based on the indirect Trefftz approach. In contrast with the finite element method, in which the structural and acoustic domains are discretized into small elements and the dynamic equations are solved within each element using simple, approximate shape functions, the field variable distributions within the entire of the structural or acoustic domains are approximated in terms of wave functions, which are exact solutions of the homogeneous parts of the dynamic equations and particular solutions of the inhomogeneous dynamic equations are added. The contributions of the wave functions are determined by applying the boundary conditions in a weighted residual formulation or least-squares formulation. Then, direct differentiation of the expressions with respect to design variables leads to expressions of the sensitivities. A comparison with the element based method illustrates that the prediction method has a substantially higher convergence rate, which makes the method applicable for accurate coupled vibro-acoustic predictions up to mid-frequency.

A hybrid formulation for mid-frequency analysis of assembled structures

A new formulation able to predict the behaviour of structures in the mid-frequency range is presented in this paper. The mid-frequency field is a hybrid domain for which assembled structures exhibit simultaneously low- and high-frequency behaviours, depending on the material and geometrical properties of different subsystems. Thus, dealing with the mid-frequency field requires simulation methods which are able to account the differences in behaviour of different subsystems. The hybrid formulation is based on the coupling of two different formulations, the finite elements for the low-frequency behaving subparts and a probabilistic formulation, the smooth integral formulation, applied to the high-frequency subsystems. The hybrid method enables to correctly predict the deterministic response of the low-frequency parts which is not affected by randomness, and the smooth trend of the contributions of the high-frequency parts. The paper is concluded with several numerical examples computed for coupled one- and two-dimensional structures.

A basic hybrid finite element formulation for mid-frequency analysis of beams connected at an arbitrary angle

When beams are connected at an arbitrary angle and subjected to an external excitation, both longitudinal and bending waves are generated in the system. Since longitudinal wavelengths are considerably longer than bending wavelengths in the mid-frequency region, the number of bending wavelengths in the beams is considerably larger than the number of longitudinal wavelengths. In this paper, plannar beams connected at arbitrary angles are considered. The energy finite element analysis (EFEA) is employed for modelling the bending behavior of the beams and the conventional finite element analysis (FEA) is utilized for modelling the longitudinal vibration in the beams. Thus, a basic hybrid FEA formulation is presented for mid-frequency analysis of systems that contain two types of energy. The bending vibration is associated with the long members in the system and the longitudinal vibration is associated with the short members. The long members are considered to have high modal overlap and to contain several wavelengths within their dimension, and uncertainty effects are present. The short members contain a small number of wavelengths, and exhibit a low modal overlap. Due to the low modal overlap the resonant frequencies are spaced far apart in the frequency domain, therefore the short members exhibit resonant or non-resonant behavior depending on the frequency of the excitation. In this work, the bending and the longitudinal vibration within the same beam member are treated as a long and as a short member, respectively. A hybrid joint formulation is developed between long and short members. Power reflection and transmission coefficients are derived for each joint. The distribution of the energy throughout the system demonstrates a strong dependency on the power transfer coefficients. Several systems are analyzed by the hybrid FEA and by analytical solutions, and good correlation between them is observed.

A hybrid finite-element formulation for midfrequency analysis of systems with excitation applied on short members

The hybrid finite-element analysis combines conventional finite-element analysis with energy finite-element analysis for midfrequency computations. A hybrid FEA fomulation has been published for systems with excitation applied on long members. [N. Vlahopoulos and X. Zhao, ‘‘A Basic Development of a Hybrid Finite Element Method for Mid-Frequency Computations of Structural Vibrations,’’ AIAA J. 37(11), 1495–1505 (1999).] In this presentation, theoretical developments associated with applying the excitation on short members will be discussed. Validation cases will be presented for several systems by comparing analytical solutions to hybrid FEA results. It will be demonstrated that the resonant behavior of the short members and the interaction between long and short members are captured correctly by the hybrid FEA. [Work supported by the Automotive Research Center established at the University of Michigan by the US Army Tank Automotive Command.]