Modeling and acoustic analysis of irregular sound enclosure by using Chebyshev-variational method

A modeling method for irregular sound enclosures was proposed based on the Chebyshev-variational theory. A rectangular space was first assumed to bound the irregular sound space and the sound pressure in the rectangular space expressed as a triple-Chebyshev series. Next, a coordinate transformation was performed and the Lagrangian functional of the irregular sound space obtained. Finally, the Lagrangian functional was solved under the Ritz method framework, and the enclosure＇s acoustic characteristic equation deduced and the eigenpairs obtained. The accuracy of the present method was validated according to agreement between the present results and finite element results for an enclosure with a curved surface.Furthermore, the acoustic characteristics of a trapezoidal enclosure and an enclosure with an inner groove were investigated. The results showed that the mode shapes of the trapezoidal sound space changed with increased inclination angle and the natural frequencies, except the first order, of the sound space with a rectangular inner groove decreased with increased groove depth.

Crack simulation and probability analysis using irregular truss structure modeling equivalent to a continuum structure

The problems related to agricultural structure engineering for crack simulation and reliability analysis are complicated because its variables contain wide ranges of mean and standard deviation.This paper describes an integrated model to perform crack simulation and reliability analysis of a continuum structure.The structure is assumed to be under a two-dimensional plane stress and the deformation is infinitesimal.A truss structure model that has the same behaviour as a continuum structure was developed using irregular triangle truss components where each element consists of two hinges with an axial degree of freedom at both of their ends.A Monte-Carlo simulation(MCS)was adopted for the reliability analysis.If the length of one side of the irregular triangle mesh is shorter than the thickness of the structure,the slenderness associated with compressive failure needs to be examined only for the short column.For that reason,the failure criterion suitable for the equivalent truss structure model was established by checking only axial stresses acting on truss members.Since nodes of the equivalent truss structure model for the structural analysis in this study consist of hinges,development of plastic hinges that occurred during crack propagation were not considered in this model.To simulate the development of crack,truss members over allowable stresses of tension or compression among truss members with the largest amount of stress at each completed structural analysis time step were sequentially removed.Since irregular triangle meshes have an uncertainty in themselves to compare with regular meshes,the equivalent truss structure model could describe crack propagation more realistically.The failure probabilities of structures under various loads and boundary conditions had good agreement with the analytical solutions directly solved from the limit state equations expressed in the form of moments.

Determination of the coefficient of rolling friction of irregularly shaped maize particles by using discrete element method

The coefficient of rolling friction is a foundation parameter for conducting particles simulation,however,which of irregularly shaped maize seeds is difficult to measure.Furthermore,the coefficient of rolling friction between the simulation particles and the actual seeds is inconsistent due to the shaped difference of model and different position of gravity center.This paper use two methods to determinate the coefficient of rolling friction based on discrete element method(DEM)and physical experiments.Three types of maize models from five different shaped maize samples(including horse-tooth shape,spherical cone shape,spherical shape,oblate shape,irregular shape)were developed with the help of slice modeling and 3D modeling technology.Aluminum cylinder container is used to arrange the simulation experiments of angle of repose with taking the coefficient of rolling friction as independent variables and the simulation angle of repose as target values.After predicting detailed the coefficient of rolling friction(including horse-tooth shape,spherical cone shape,spherical shape,between horse-tooth shape and spherical cone shape,between horse-tooth shape and spherical shape,between spherical shape and spherical cone shape maize models),and forecasting a unified the coefficient of rolling friction among horse-tooth shape,spherical cone shape and spherical shape maize models,two types of materials(aluminum cylinder container and organic glass container)were used to validate the difference the angle of repose between the simulation maize models and actual maize seeds.Results show the relative error of the angle of repose between the maize models controlled by the coefficient of rolling friction through the detailed method and the actual maize seeds is 0.22%,0.33%in aluminum cylinder,organic glass container,respectively.The relative error of the angle of repose between the simulation maize models controlled by the coefficient of rolling friction through the united method and actual maize seeds is 2.47%,2.97%in aluminum cylinder,organic glass container,respectively.Although the difference of the angle of repose between two method is smaller,the detailed method is better.Moreover,From the accumulation process of the angle of repose we found that the difference on the contacts number between maize models and bottom plate,the change curve of the rotational kinetic energy,the potential energy of maize models controlled by the coefficient of rolling friction through the detailed and the united method are evidently.We can choose a better method to predict the coefficient of rolling friction of maize seeds according to the application situation and investigation objective of irregular maize seeds.The results can provide a theoretical basis for designing and optimizing the structure of the seed-metering machine with DEM.

Fraunhofer diffraction of irregular apertures by Heisenberg uncertainty Monte Carlo model

Geometrical optics and the Monte Carlo method are very flexible in dealing with the interaction of light with non-spherical particles, but usually diffraction is not considered. To cover this gap, the Heisenberg Uncertainty Monte Carlo （HUMC） model is applied to calculate separately the diffraction of a ray or a photon. In this paper, we report an improvement of the HUMC model by specifying the phase of the photon subject to the Fraunhofer diffraction condition. After validating the model by comparing its results with analytical results for apertures of simple shapes, the HUMC model is then applied in simulations of Fraunhofer diffraction by apertures of complex shapes, such as those composed of one or two elliptical openings. We have shown that the diffracted intensity distributions of simple apertures obtained by the HUMC model are in good agreement with the results calculated from analytical expressions. The simulations of diffraction by apertures composed of two square or elliptical openings prove that the HUMC model is a powerful and flexible too] for predicting the Fraunhofer diffraction by a complex optical system.