Infinite Plate Model Research Articles

Vibration Analysis of Coupled Multilayer Structures with Discrete Connections for Noise Prediction

It is often necessary to calculate the vibration of noise from multilayer structures comprising several substructures coupled with discrete connections. A dynamic flexibility method (DFM) is adopted to decouple the multilayer substructures, which allows the interface forces among the substructures to be directly solved using a linear equation of deformation compatibility. The structural vibrations and power flows into each substructure can then be calculated. To illustrate the use of the DFM, a coupled train–track–bridge system for urban rail transit traffic is investigated as a case study. Two infinite plate models are used to model the U-shaped bridge substructure to improve the computing efficiency compared with the finite element models in calculating high-frequency vibration. The applicability of the infinite plate models is discussed in terms of various rail positions on the bridge, the thickness of the rail support blocks, and multiple wheels that interface with the rail. The results show that the Mindlin plate model has similar accuracy but much greater computing efficiency than the finite element models. With the vibration results from the DFM, the associated wheel–rail noise and structure-borne noise from the bridge are then calculated together with a 2D acoustic model. Good agreement is observed between the predicted noises and the measured data.

Relationship between sound radiations resulting from airborne-sound and point-force excitations of a double-leaf infinite elastic plate

This paper presents an expanded theory for relating airborne-sound-excited and force-excited sound radiations from solid structures. Although the reduction of these two types of sound radiation is a fundamental issue in noise-control engineering, each of them has been historically treated as a separate issue. The reduction in the former is normally called airborne sound insulation and separated from the latter, especially in architectural acoustics. A previous study (M. Yairi et al., J. Acoust. Soc. Am., 140, 453–460 (2016)) established a fundamental relationship between the sound radiations from random-incidence sound-excited and point-force-excited vibrations of a single-leaf infinite elastic plate. A conversion function that relates the two excitation cases was presented in a simple closed form, not including the parameters of the plates, which included of only the specific impedance and the acoustic wavenumber of the medium surrounding the plate. In this paper, the applicability of the conversion function is expanded from a single-leaf infinite elastic plate model to a double-leaf infinite elastic plate model. The sound radiation from a double-leaf infinite elastic plate driven by random-incidence sound and that driven by point-force excitation are theoretically investigated. The conversion function derived from the present model successfully relates the two excitation problems at all analyzed frequencies and has been shown to agree with the previously established single-leaf theory.

Effective elastic thickness in the Central Andes. Correlation to orogenic deformation styles and lower crust high-gravity anomaly

Global studies have assessed the importance of elastic thickness (Te) on orogenic evolution, showing that the style and nature of upper crustal shortening are influenced by the inherited lithospheric strength. Thus, pioneer works have identified that the upper crustal deformation style in the easternmost sector of the Central Andes in South America are related to the elastic thickness (Te). There, the thick-skinned and pure-shear style of Santa Bárbara system was initially related to the existence of low Te values. In contrast, the thin-skinned and simple-shear style of deformation in the Subandean system involves high Te values. However, more recent Te studies in the Central Andes present conflicting results which lead to question this straightforward relation. Results from these studies show a strong dependence on the applied methodology hampering the general understanding of the lithospheric thermo-mechanical state of the Central Andes. To contribute to this issue, we perform a high-resolution Te map, using forward modeling by solving flexural equation of infinite plate model in two dimensions. To achieve this, the crust-mantle interface was calculated using a high-resolution gravity anomaly dataset which combines satellite and terrestrial data, and an average density contrast. Additionally, the gravity anomaly and the foreland basin depth in the Central Andes were best predicted by considering that lower crustal rocks fill the space deflected downward in the plate model. The obtained Te values show an inverse correlation with previous heat flow studies, and a strong spatial correlation with the styles and mechanisms of deformation in the easternmost sector of the Central Andes. In the Santa Bárbara system Te values less than 10 km predominate, whereas in the Subandean system high Te values were observed. Such high values correlate with the orogenic curvature and with an shallower gravity Moho zone, which breaks the regional trend of the Central Andes. This shallower gravity Moho is linked to a high-gravity anomaly located in the east part of the Eastern Cordillera and Subandean system. These results are also correlated with a high-velocity zone in the upper mantle previously found by receiver functions studies. This correlation could indicate changes in the properties of the lower crustal rocks that justify the shallower gravity Moho zone and explain in part the highest Te values.

Vibration analysis of concrete bridges during a train pass-by using various models

The vibration of a bridge must be determined in order to predict the bridge noise during a train pass-by. It can be generally solved with different models either in the time domain or the frequency domain. The computation cost and accuracy of these models vary a lot in a wide frequency band. This study aims to compare the results obtained from various models for recommending the most suitable model in further noise prediction. First, train-track-bridge models in the time domain are developed by using the finite element method and mode superposition method. The rails are modeled by Timoshenko beam elements and the bridge is respectively modeled by shell elements and volume elements. Second, power flow models for the coupled system are established in the frequency domain. The rails are modelled by infinite Timoshenko beams and the bridge is respectively represented by three finite element models, an infinite Kirchhoff plate, and an infinite Mindlin plate model. The vibration at given locations of the bridge and the power input to the bridges through the rail fasteners are calculated using these models. The results show that the shear deformation of the bridge deck has significant influences on the bridge vibration at medium-to-high frequencies. The Mindlin plate model can be used to represent the U-shaped girder to obtain the power input to the bridge with high accuracy and efficiency.

A Review of Skin Buckling Theory in Composite Members

This paper provides a comprehensive review of various methods used for skin buckling analysis in composite components. The skin buckling phenomenon is one of the governing criteria in composite design. It is a kind of contact buckling in which partial sections of skin buckle away from the filler material. In general, the problem can be modelled as a thin plate (skin) in unilateral contact with elastic medium (filler material). The theoretical analysis of contact buckling is complicated due to the nonlinearity arising from changing contact regions. To simplify the calculations, the filler material was usually modelled as a tensionless elastic foundation. The skin buckling coefficient varies in terms of the relative foundation stiffness factors. Because the Eigen-value method is not applicable to nonlinear systems, the finite element (FE) method was usually employed for post-buckling analysis, while initial buckling performance was investigated through analytical or semi-analytical methods such as rigid foundation model, infinite plate model and finite plate model. The compressive buckling and shear buckling problems for thin plates resting on tensionless foundations have been solved successfully. However, there are still urgent needs for future research on the topic. For example, the load carrying capacity of the buckling plates needs to be formulated for practical application. Complicated problems with complex loadings and/or corrugated skins need further investigation as well.

Relationship between sound radiation from sound-induced and force-excited vibration: Analysis using an infinite elastic plate model.

Although sound radiation from sound-induced vibration and from force-excited vibration of solid structures are similar phenomena in terms of radiating from vibrating structures, the general relationship between them has not been explicitly studied to date. In particular, airborne sound transmission through walls and sound radiation from structurally vibrating surfaces in buildings are treated as different issues in architectural acoustics. In this paper, a fundamental relationship is elucidated through the use of a simple model. The transmission coefficient for random-incidence sound and the radiated sound power under point force excitation of an infinite elastic plate are both analyzed. Exact and approximate solutions are derived for the two problems, and the relationship between them is theoretically discussed. A conversion function that relates the transmission coefficient and radiated sound power is obtained in a simple closed form through the approximate solutions. The exact solutions are also related by the same conversion function. It is composed of the specific impedance and the wavenumber, and is independent of any elastic plate parameters. The sound radiation due to random-incidence sound and point force excitation are similar phenomena, and the only difference is the gradient of those characteristics with respect to the frequency.

Local buckling of profiled skin sheets resting on tensionless elastic foundations under in-plane shear loading

Abstract In this paper, the local buckling behaviour of profiled skin sheets resting on tensionless elastic Winkler foundations under in-plane shear loadings is studied. The profiled sheets are modelled as thin orthotropic plates with the buckling behaviour being expressed through a group of nonlinear partial differential equations. For very long plates with both ends clamped, the buckling mode is composed of a series of periodically repeating buckling waves and hence an infinite plate model with only one buckle wave is effective to predict the buckling behaviour. The infinite orthotropic plate is further simplified to a one-dimensional mechanical model by assuming a lateral buckling mode function. After solving the governing equations of the one-dimensional model in both contact and non-contact regions, shear buckling coefficients of the system and the related buckling modes are obtained. Fitted formulae for the contact shear buckling coefficients in terms of relative foundation stiffness and skin profile parameters are developed. The analytical solutions are verified through examining extreme cases from previous studies and a series of finite element (FE) models in ABAQUS. Finally, a practical example is given to show the efficiency of the developed method.

End condition effect on initial buckling performance of thin plates resting on tensionless elastic or rigid foundations

It is well accepted that the non-contact buckling response of long rectangular plates subjected to compressive or shearing loadings is solely dependent on material and section properties, as well as boundary conditions along the two unloaded side edges. In addition, the boundary conditions at the loaded ends do not influence the critical load. The above rule was also applied to the analysis and design of plates in unilateral contact with elastic or rigid mediums although without any reasonable verification. The results contained in this paper reveal that the boundary condition at the loaded edges (end conditions) significantly affects the contact buckling performance. To investigate the end condition effect, a transfer function method is employed herein to study the initial buckling behaviour of thin plates with different boundary conditions resting on tensionless elastic or rigid foundations. For very long plates with both ends clamped, the buckling mode can be considered as a series of periodically repeating buckling waves and an infinite plate model with only one buckle wave being effective to predict the buckling behaviour. However, for long plates with simply supported loaded ends, local effects dominate the buckling mode and the buckling loads can be reduced by up to 18% compared to long plates with clamped loaded ends. Experimental tests and ABAQUS modelling also verify that the critical stresses for plates with simply supported loaded ends are lower than those for plates with clamped loaded ended plates.

Failure Mode Analysis and Performance Optimization of the Hierarchical Corrugated Truss Structure

The theories of elastic plates and Kirchhoff's sandwich plates are used to analyze the failure modes of the second order hierarchical corrugated truss structure, and a plate model is presented. Besides the six competing failure modes obtained in the literature using the elementary elastic beam theory, another five competing failure modes have been identified herein, including the plate buckling, infinitely wide plate buckling, sandwich plate buckling, infinitely wide sandwich plate buckling, and surface wrinkling. Expressions for the compressive collapse strengths of these modes are derived and used to construct collapse mechanism maps for second order trusses, which is effective for selecting the geometries of second order trusses. By comparing with the result of the finite element method (FEM) it is shown that the plate model has higher accuracy than the beam model, and the infinite wide plate model has the highest accuracy when the length-width ratio of the large struts is greater than 1.0. Finally, three optimization models are proposed. The performance of a second order hierarchical corrugated truss structure has been optimized, and the geometric parameters under the optimal performance can be obtained, which can provide a more convenient way to achieve a desired scheme for designers.

Residual Stress Measurements of Cylindrical Parts by Hole Drilling Strain Gage Method

Hole drilling strain gage method is a semi-destructive measurement. The method is most commonly used to measure residual stresses. The relieved strains are measured around the drilled hole, and the residual stresses are estimated by the mechanical relationship between relieved strains and residual stresses as well calibration coefficients. The calibration coefficients indicate the relieved strains due to unit stresses within the hole depth. Finite element method is always used to determine the calibration coefficients, and the analytical model is based on the infinite plate. But the geometrical shape and size of cylindrical part are different from the infinite plate. The relieved strains around the drilled hole are different too. Finite element model of the cylindrical part is constructed to obtain the hole drilling calibration coefficients. The measurement of residual stresses in a cylindrical part subject to axial loading calculated by calibration coefficients of both infinite plate and cylindrical part model are compared to show the difference.

Initial Compressive Buckling of Clamped Plates Resting on Tensionless Elastic or Rigid Foundations

The unilateral contact buckling problem of thin plates resting on tensionless foundations is investigated. Three different plate models are considered. For a plate of limited length on a tensionless elastic foundation, the plate is first simplified to a one-dimensional mechanical model by assuming a buckling mode in terms of transverse coordinates, after which a new method is employed to determine the initially unknown boundaries of the areas in contact. Based on the continuity condition on the borderline between contact and noncontact regions, the buckling mode displacements of the whole plate may be expressed through the critical load coefficient and the first half-wavelength, reducing the buckling problem to two nonlinear algebraic equations with two unknowns. This procedure has been named the transfer function method. For a very long plate with a symmetric buckling mode, an infinite plate model with two half-waves is presented. For a plate on a rigid foundation, a single half-wave buckling model is shown to be appropriate. Comparison of limiting cases with exact solutions and with ABAQUS results showed good agreement. Finally, the influences of aspect ratio and foundation stiffness are presented.

Gate capacitance of back-gated nanowire field-effect transistors

Gate capacitances of back-gated nanowire field-effect transistors (NW-FETs) are calculated by means of finite element methods and the results are compared with analytical results of the “metallic cylinder on an infinite metal plate model.” Completely embedded and nonembedded NW-FETs are considered. It is shown that the use of the analytical expressions also for nonembedded NW-FETs gives carrier mobilities that are nearly two times too small. Furthermore, the electric field amplification of nonembedded NW-FETs and the influence of the cross section shape of the nanowires are discussed.

서태평양에 위치한 해저산들의 3-D flexure 모델링 : 무한지판 모델

The bathymetric and gravity data were obtained in 2001 and 2003 during a survey of seamounts in the northwest of the Marshall Islands, western Pacific. The study areas are located in the Pigafetta Basin which is the oldest part of the Pacific plate and in the Ogasawara Fracture Zone which formed from the spreading ridge between the Izanagi and Pacific plates in the Jurassic. The densities of seamounts and the elastic thickness values of the lithosphere are calculated by using three-dimensional flexure modeling considering the constant sediment layer in the infinite plate model. Very low elastic thickness values (5km), relatively young seamounts, and old lithosphere in the east study area suggest the possibility of the rejuvenation of lithosphere by widespread volcanisms, whereas the elastic thickness values (15km), relatively old seamounts, and young lithosphere of the west study area are suitable for a simple cooling plate model of isotherm. The gravity residuals of OSM6-1 and OSM6-2 suggest the possibility of different load density or elastic thickness. Relatively older OSM6-2 formed on the younger lithosphere with relatively thin elastic thickness, while younger OSM6-1 on the older lithosphere with relatively thick elastic thickness.

Acoustic insulation provided by circular and infinite plane walls

The transmission of sound energy is a complex phenomenon on account of the number and the interdependence of variables involved. In this context the mathematical modelling of this phenomenon becomes difficult. Of the models that have been developed, some of them only take a limited number of variables into account, leading to simplified models such as the Mass Law. Among the simplified methods for evaluating the sound insulation provided by a single panel are those described by Sewell [1], Sharp [2], Cremer [3] and Callister et al. [4]. Novikov [5] used the mass law with the addition of a correction coefficient to study the sound insulation of finite plates, at low frequencies. Osipov et al. [6] studied the sound transmission through a single panel using an infinite plate model and a room–plate–room model. They noticed that at low frequencies the results are strongly influenced by the geometry and the dimensions of the room–wall–room system, in addition to the properties of the panel material. Most of the articles published that take the full coupling between the fluid and the solid structure into account are restricted to low frequencies, because of the computational cost entailed, particularly when modelling closed spaces. This kind of analysis is simpler in the case of circular enclosures, for which analytical solutions can be derived. Other authors in a different context have tackled the study of circular cylindrical shells. Veksler et al. [7] studied the modal resonances of submerged elastic circular cylindrical shells filled with air, when struck by plane harmonic acoustic waves. Their work used a standard resonance scattering theory, and paid special attention to the generation of bending waves. Bao et al. [8] analyzed the various circumferential waves generated when a circular cylindrical shell submerged in a fluid and filled with another fluid is disturbed by a normally incident plane wave. Maze et al. [9], in a related work, analyzed the existence of various guided acoustic circumferential modes in a water-filled tube. ARTICLE IN PRESS

Transient ultrasonic guided waves in layered plates with rectangular cross section

Transient ultrasonic guided waves in anisotropic layered plates with finite and infinite width are presented in this article. A semianalytical finite-element method is adopted to study the guided waves in both infinite- and finite-width elastic plates. Three-noded beam elements in the thickness direction are used in infinite plate model, whereas the cross section of the finite-width plate is represented by nine-noded quadrilateral elements. Propagation in the axial direction is modeled by analytical wave functions. Elastodynamic Green’s functions are derived using modal summation in the frequency–wave number and time–space domains. Results for dispersion and transient analysis of guided waves in infinite nickel plates are presented and compared with those of finite-width plates. Group velocities are calculated and wave arrival times are computed for different plate cross sections. Numerical results show a significant influence of the plate aspect ratio on the dispersion and transient wave response. The complex natures of mode dispersion and propagation due to several mode excitation in finite-width plates require such quantitative analysis to afford easy interpretation. These results play a role of guidance for nondestructive material evaluation.

SOUND RADIATION FROM A PLATE INTO A POROUS MEDIUM

A nearby layer of porous sound-absorbing material has previously been shown to be capable of greatly increasing the acoustic power radiated from a vibrating flat plate, and consequently of enhancing the structural damping in the plate. In this paper, a previously published model for sound radiation from a plate of infinite extent, radiating into a semi-infinite region of absorbent, is extended to allow for a finite air gap between absorbent and plate, as well as a finite absorbent thickness. Limited parametric studies are presented here for typical cases, and model predictions are compared to finite-plate predictions and to measured data. It is concluded that the infinite-plate model can be a useful design tool, presenting minimal computational demands.

Low-Frequency Airborne Sound Transmission through Single Partitions in Buildings

The low-frequency (20–250 Hz) airborne sound transmission of single partitions is investigated. Three theoretical models are used for the prediction: an infinite plate model, a baffled plate model and a room-plate-room model. The calculation models are verified by detailed comparisons with experimental results obtained in the laboratory. A parametric study is carried out to examine the influence of the dimensions of the room and the partition. The results demonstrate the strong modal behaviour of the low-frequency sound transmission. As a result, the low-frequency sound insulation depends not only on the properties of the test wall, but also on the geometry and the dimensions of the room-wall-room system.

Low-frequency airborne sound transmission through single partitions in buildings

The low-frequency (20–250 Hz) airborne sound transmission of single partitions is investigated. Three theoretical models are used for the prediction: an infinite plate model, a baffled plate model and a room-plate-room model. The calculation models are verified by detailed comparisons with experimental results obtained in the laboratory. A parametric study is carried out to examine the influence of the dimensions of the room and the partition. The results demonstrate the strong modal behaviour of the lowfrequency sound transmission. As a result, the low-frequency sound insulation depends not only on the properties of the test wall but also on the geometry and the dimensions of the room-wall-room system. In general, the large variation of the low-frequency insulation compromises the accuracy of prediction of the sound insulation in situ.

THREE‐DIMENSIONAL CONSTRAINT EFFECTS ON STRESS INTENSITY DISTRIBUTIONS IN PLATE GEOMETRIES WITH THROUGH‐THICKNESS CRACKS

AbstractThree‐dimensional finite element analyses of through‐thickness cracks in plate geometries are presented. It is shown that the local constraint variation towards the crack tip causes an increase in stress intensity which is neglected in analyses which assume a constant stress state throughout the geometry. This means that stress intensity factors for these types of crack geometries are a factor (1 — v2)‐0.5 higher than generally reported in stress intensity handbooks.Analyses on crack tunnelling situations show that if plane stress dominates the global behaviour, an almost constant stress intensity across the thickness is reached for a relative tunnelling depth of a 2.5% of the plate thickness. For geometries which are not predominantly in plane stress this value will be somewhat larger. Crack front tunnelling does not influence the mean stress intensity across the thickness.Shear lips are shown to reduce the mean equivalent stress intensity (the mode I stress intensity which has the same energy release rate as the actual combined mode I, II and III loading) by a factor equal to the square root of the ratio between plate thickness and projected length of the crack front. This may explain the reduction in crack growth rate caused by shear lips during fatigue crack growth experiments. The reduction of the mode I stress intensity factor is considerably larger, which may cause a further reduction of fatigue crack growth rate for crack growth mechanisms that depend primarily on the mode I crack tip loading.Analyses on CNT and SENB specimens show that the conclusions reached on infinite plate models also hold for real structures. However for an SENB specimen with an uncracked ligament equal to the plate thickness, the overall constraint is larger than that of a pure plane stress situation, and the effect of stress intensity increases due to the constraint transition is less pronounced.

A new approach to the transient analysis of magnetic field with variable transformation based on eigenvalues

A novel approach to the transient analysis of a magnetic field is presented that uses the formulation of a boundary-element model in two-dimensional problems. In order to solve the transient problems, state equations are formed using the boundary element model, and are solved using the variable transformation based on eigenvalues. The computational accuracy of the proposed method is evaluated by an infinite plate model and an infinite cylinder model in which the impressed magnetic flux densities are given by a unit step function and a sinusoidal function respectively. >