The vibration and post-buckling of geometrically imperfect,simply supported,rectangular plates under uni-axial loading,part I: Theoretical approach

The work described in this paper constitutes the theoretical part of a theoretical and experimental study of the post-buckling and vibration of simply supported rectangular plates having slight initial curvature (geometrical imperfection) and subject to uni-axially applied, in-plane, compressive loads. The experimental part, and the comparison with theoretical predictions, is given in a second paper. The Rayleigh-Ritz approach, with a deflection function formulation for both the in- and out-of-plane behaviour of the plates, is used since this permits the convenient modelling of various types of in-plane boundary conditions, including those encountered in the experimental study. A concept of connection coefficients, introduced to reduce the computational effort involved, is described. In order to illustrate the applicability of the theoretical approach, a number of square plates having various sets of in-plane boundary conditions and degrees of initial imperfection are treated. Graphical results are presented showing the variation of the lateral central deflection and the fundamental natural frequency of vibration with applied in-plate loads varying from zero to several times the lowest critical buckling load. Where possible, comparison is made with values available in the literature and excellent agreement is achieved. The results presented appear to suggest that an approximately linear relationship exists between a load-frequency parameter and the central deflection of the plates considered, for a substantial in-plane loading range.     

Tensile fracture analysis of V-notches with end holes by means of the local energy

This paper deals with investigating brittle fracture in V-notches with end holes under mode I loading. Thirty-six fracture test results, reported most recently in the literature on a new notched disk-type specimen, namely the Brazilian disk containing central VO-shaped notch made of polymethyl-metacrylate, were theoretically predicted by means of the well-known brittle fracture criterion, namely the strain energy density over a critical control volume which embraces the notch edge. A very good agreement was shown to exist between the experimental and theoretical results.     

Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells

Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.     

三合板的一般弹性理论

一.引言 本文所指之三合板是一种轻质板材,在航空工业上近年来有广泛的应用。板由三层材料构成:外层为二硬薄钣(金属薄钣),夹心为较轻软之材料(如泡状醋酸赛璐珞、软木、或蜂巢状金属材料)。前者称为表钣,后者称为夹心,表钣与夹心胶合成一综合板。三合板之形变与应力之计算在十多年来曾引起力学家与工     

Non-linear axisymmetric transient analysis of orthotropic thin annular plates with a rigid central mass

The geometrically non-linear, axisymmetric transient elastic response is determined of cylindrically orthotropic thin annular plates with a rigid central mass subjected to a uniformly distributed load on the plate as well as a central load on the rigid mass. The dynamic analogue of the von Kármán equations in terms of the normal displacement w and the stress function Ψ are employed. The displacement w and stress function Ψ are expanded in finite power series and the orthogonal point collocation method in the space domain and the Newmark β scheme in the time domain are used. The response of isotropic and orthotropic, clamped as well as simply supported, annular plates with a rigid central mass, subjected to step function and sinusoidal pulse loads, has been calculated for two values of the annular ratio. The influence of the mass ratio and the magnitude of the step load on the deflection response has been determined. The effect of mass ratio, amplitude and duration of sinusoidal pulse on the deflection response has also been studied.     

Vibration studies on some integral rib-stiffened plates

Results from a theoretical and experimental comparison study of the vibrations of four integrally machined rib-stiffened plates are presented. Two plates had one rib-stiffener and two plates had two rib-stiffeners. The finite element method was used for the theoretical predictions and real-time laser holography was used for the experimental verifications. The first twenty-four vibration modes were predicted and measured for each plate, and detailed comparisons are presented. Reasonably good quantitative agreement was obtained in all cases for both frequencies and mode shapes.     

The flexural vibration of welded rectangular plates

A theoretical and experimental study of the effect of weld runs on the flexural vibrational characteristics of the common structural element, the rectangular plate, is described. A finite difference technique is utilized for the determination of the in-plane residual stress pattern due to the weld(s) and the Rayleigh-Ritz method, with beam characteristic functions, is used for the out-of-plane vibration analysis. The theoretical approach presented is applicable to rectangular plates of any practical aspect ratio, having any combination of out-of-plane boundary conditions for which beam functions may reasonably be used and subject to one or more weld runs parallel to any edge. Theoretical and experimental results for a number of specific plates are presented, demonstrating the effects of welding on the plate vibration and the capability and accuracy of the analytical approach in predicting these effects. Included is a study of the effect of using the full residual stress pattern as derived from the finite difference analysis, the effect of neglecting certain stress components and the effect of using simplified stress patterns developed primarily for the stress and buckling analysis of long plates.     

Free vibration of a circular plate elastically restrained along some radial segments

An analysis is presented for the free vibration of a circular plate restrained against deflection along radial segments. With the reaction forces acting on the segments regarded as unknown harmonic loads, the stationary response of the plate to these loads is expressed by the use of the Green function. The force distributions along the segments are expanded into Fourier series with unknown coefficients, and the homogeneous equations for the coefficients are derived by restraint conditions on the supports. The natural frequencies and the mode shapes of the plate are determined by calculating the eigenvalues and eigenvectors of the equations. The method is applied to circular plates supported along several radial segments located at equal angular intervals, the natural frequencies and the mode shapes of the plates are calculated numerically and the effect of the supports is discussed.     

光学薄膜的光热偏转信号分析

本文给出了透明基体上的单层薄膜在激光辐照下的温度分布和光热形变偏转信号的理论表达式。通过数值计算,分析了偏转信号与薄膜参数、基体参数以及调制频率之间的关系,用反射式光热偏转装置对光学薄膜的光热偏转信号进行了实验研究。结果表明,理论计算和实验结果是一致的。     

Experiments on plane overvolted discharges in N2, and comparison with calculations

In this paper experimental and theoretical results for the development of overvolted discharges in N₂ between a plane-parallel gap are described. By suitable initial conditions laterally extended (plane) discharges can be realized instead of the usually observed filamentary streamers. In this discharges which were large in diameter compared with the gap distance, a quantitative comparison of the experimental results with one dimensional calculations is possible. It is shown that the discharges can be described by the well-known build-up theory of instationary discharges but an additional far-reaching electron generating mechanism (gas ionizing radiation) must be included. The development of our discharges is compared with that of the streamer.     

On the toughening mechanisms of MoSi<Subscript>2</Subscript> reinforced Si<Subscript>3</Subscript>N<Subscript>4</Subscript> ceramics

The toughness increment occurring in Si₃N₄-based composites due to the addition of MoSi₂ particles was compared to the predictions of theoretical models based on the combination of residual stresses and crack deflection toughening mechanisms. A direct application of theoretical models led to a substantial discrepancy between predicted and observed values. For this reason, the basic parameters of the theoretical models were experimentally evaluated. The residual stresses were assessed by measuring the strain in the reinforcing particles by X-ray diffraction. Moreover, the MoSi₂ interparticle distance was calculated by image analysis and the crack paths were analyzed in order to check the actual extent of crack deflection. The overall toughness increase recalculated as the sum of the newly estimated values of residual stresses and crack deflection contributions, was shown to be in good agreement with the experimental results. PACS 81.05.Je; 81.40.Np     

A quantum mechanical study of the He,H-, He-He and He-H systems

This paper applies the methods for treating diatomic molecules described in papers I and II of this series, to the interation of two normal helium atoms and the interaction of a normal helium atom and a hydrogen atom. The results are compared to the experimental results of Amdur and referred to other theoretical results where they exist. The results on the He-H interaction are in fair agreement with Amdur's experimental work. The repulsive potential of two normal helium atoms disagrees with Amdur's experimental results at the distances between 1 and 2 angstroms. The helium atom and negative hydrogen ion are also discussed.     

Inner shell ionization by heavy,charged particles and associated energy loss of the projectile

The process ofL- andM-shell ionization of atoms by heavy, charged particles is analysed in detail by a semiclassical, time-dependent perturbation method. The target electrons are described by non-relativistic hydrogenic wave functions. For the projectile is assumed a well-defined straight-line path. The Coulomb deflection and the screening is partially taken into account. The theoretical values of the total cross section is in reasonable agreement with experimental values. The condition of validity for the semi-classical method is shown to be fulfilled for all non-relativistic projectile energies. The projectile energy loss by ionization is further shown to be of negligible importance for the resolution of magnetic spectrographs used in nuclear structure physics.     

A damping mechanics model and a beam finite element for the free-vibration of laminated composite strips under in-plane loading

A theoretical framework is presented for predicting the nonlinear damping and damped vibration of laminated composite strips due to large in-plane forces. Nonlinear Green-Lagrange axial strains are introduced in the governing equations of a viscoelastic composite and new nonlinear damping and stiffness matrices are formulated including initial stress effects. Building upon the nonlinear laminate mechanics, a damped beam finite element is developed. Finite element stiffness and damping matrices are synthesized and the static equilibrium is predicted using a Newton-Raphson solver. The corresponding linearized damped free-vibration response is predicted and modal frequencies and damping of the in-plane deflected strip are calculated. Numerical results quantify the nonlinear effect of in-plane loads on structural modal damping of various laminated composite strips. The modal loss-factors and natural frequencies of cross-ply Glass/Epoxy beams subject to in-plane loading are measured and correlated with numerical results.     

Isotropic and nematic phase N.M.R. spectra of tellurophen

In molecular beam experiments the preferred spatial orientation or polarization of the rotational angular momentum of reactively scattered molecules can be determined by deflection in an inhomogeneous electric field. The apparatus, experimental method, and analysis procedure are described and illustrated with data obtained for the K + HBr, Cs + HBr, and Cs + HI reactions. The experiments employ a new field design which eliminates the non-adiabatic change of quantization axis that handicapped a previous polarization study. A simple normalization procedure provides ‘reduced deflection profiles’ which are very insensitive to substantial variations in the experimental parameters, including the deflection field strength, beam position in the field, collimating slit widths, dipole moment, and distributions of rotational and translational energy. These reduced profiles yield 2 x> and 4 x>, the first two moments of the probability distribution of polarization, where x is the angle between the rotational angular momentum and the initial relative velocity vector. The experimental results indicate marked polarization, corresponding to 2 x> < 0·10, and agree well with theoretical moments calculated from a statistical phase-space treatment.     

Ground-State Properties ,of C, O, and Ne Isotopes in Hartree——Fock-Bogoliubov Calculation with Gogny Interaction

Ground-state properties of C, O, and Ne isotopes are described in the framework of Hartree-Fock-Bogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing feld arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calcu/ations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree--Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C,O, and Ne isotopes in a previous RHB study.     

Non-linear vibration and postbuckling of isotrophic thin circular plates on elastic foundations

An approximate solution for the large deflection axisymmetric responses of isotropic thin circular plates resting on Winkler, Pasternak and non-linear Winkler foundations is presented. Plates with edges elastically restrained against rotation and -in-plane displacement are considered. Von Kármán type equations in terms of transverse deflection and stress function are employed. A one term mode shape is used to approximate the transverse deflection and Galerkin's method is used to obtain an equation for the central deflection which has the form of a Duffing's equation. Non-linear frequencies, postbuckling response to radial load at the edge and the maximum transient response to transverse step load have been obtained. It is shown that sufficiently accurate results are obtained by this method. Numerical results are presented to illustrate the effect of various parameters.     

A prediction theory of random level distribution based on a generalized difference type of Fokker-Planck equation and its application to environmental noise and vibration,II: Experimental study

In a companion paper [1], a procedure for solving the short time prediction problem in terms of the transition probability distribution has been theoretically derived, for discrete time-sampled data. Explicit algorithms for estimating the non-stationary moment statistics of arbitrary order also have been derived, based on a generalized difference equation of Fokker-Planck type for the conditional probability distributed function, which is central to the theory. In this paper, evidence for the validity and effectiveness of the proposed method is presented, as obtained not only by means of digital simulation but also by using road traffic noise data obtained experimentally in Hiroshima. For several non-stationary random processes simulated by means of random numbers, the theoretical and experimental conditional probability functions are compared. For non-stationary road traffic noise data the theoretically predicted and experimentally determined confidence intervals are compared; in these comparisons several types of conditional probability function and various values of weighting parameter are used in the algorithm. All of the theoretical results show good agreement with the experimental results.     

Ground-State Properties of C, O, and Ne Isotopes in Hartree-Fock-Bogoliubov Calculation with Gogny Interaction

Ground-state.properties of C, O, and Ne isotopes are described in the framework of Hartree-FockBogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing field arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calculations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree-Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C, O, and Ne isotopes in a previous RHB study.     

Large deflection of clamped circular plate and accuracy of its approximate analytical solutions

A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.