Natural vibrations of a cylindrical shell reinforced with rectangular plates

This paper outlines a technique of determining the natural frequencies and modes of an elastic structure consisting of a cylindrical shell and noncrossing rectangular plates inserted into it. The influence of the position, number, and thickness of the plates on the natural frequencies and modes is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 89–96, March 2006.     

Thermoelastoplastic Stress-Strain State of Rectangular Plates

A technique is proposed to solve a thermoplastic problem for rectangular plates of varying thickness with arbitrary boundary conditions at all edges. The technique is based on the hypothesis of rectilinear element, the theory of simple loading, and the method of complete systems __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 53–63, October 2005.     

Thermomechanical Postbuckling of Imperfect Moderately Thick Plates on Nonlinear Elastic Foundations*

ABSTRACT

A postbuckling analysis is presented for a moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading, and resting on a softening nonlinear elastic foundation. The cases of (1) thermal postbuckling of initially compressed plates and (2) compressive post-buckling of initially heated plates are considered. The initial geometrical imperfections of the plates are taken into account. Formulations are based on Reissner-Mindlin plate theory, considering first-order shear deformation effects, and including plate-foundation interaction and thermal effects. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples include the performance of perfect and imperfect, moderately thick plates resting on softening nonlinear elastic foundations. Typical results are presented in dimensionless graphical form.     

The finite element technique for predicting the natural frequencies,mode shapes and damping values of filamentary composite plates

This article presents the numerical method for predicting the natural frequencies, mode shapes and damping values of filamentary composite plates. This method is based on finite element technique, using damped element and allowing transverse shear deformation. For the example of this technique, the theoretical results comparing with experimental values of carbon fibre and glass fibre reinforced plastics plates (mid-plane symmetric) are provided. The dynamic properties of these laminates are discussed. Finally, a simple graphic technique to estimate the natural frequencies and damping values is suggested.     

Large amplitude free vibrations of irregular plates placed on an elastic foundation

A unified method for determining the lowest natural frequency of large amplitude free vibrations of thin elastic plates of any shape and placed on elastic foundation is given. The conformal mapping technique is introduced and Galerkin's method is used to calculate approximate values of the lowest natural frequency. Time periods for circular, square and cornered plates placed on elastic foundation have been determined for simply supported and clamped edge boundary conditions. Practical values have also been determined experimentally. The results are presented in the form of graphs and they are compared with other known results.     

Experimental and theoretical predictions of first-ply failure strength of laminated composite plates

Experimental and theoretical methods are presented to study the first-ply failure strength of laminated composite plates under different loading conditions. An acoustic emission technique is used to measure the energy released in the plates during the failure process. The first-ply failure strength of the plates is then identified via the energy vs load diagrams which are constructed on the basis of the measured acoustic emissions. A finite element analysis, which is constructed on the basis of the layerwise linear displacement theory, and the Tsai–Wu failure criterion are used to predict the first-ply failure strength of the plates. The comparison between the experimental and theoretical results shows good agreement.     

Elastic Critical Buckling of Welded Thin Steel Rectangular Plates∗

A theoretical approach for the study of the effect of residual stresses due to welding on the elastic critical buckling behavior of thin steel rectangular plates is described. A finite difference technique is utilized for the determination of in-plane residual stresses due to a weld, and the Rayleight-Ritz method is used for the critical buckling problem, with stresses due to external loads being superimposed on the residual stresses. A number of illustrative examples are included, showing the possible detrimental effect of residual stresses due to welding. An approximately linear relationship is shown to exist between the square of the natural frequency of lateral vibration and the drop in buckling strength, for certain loading conditions     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF FULLY BACKED SANDWICH PLATES UNDER LOCALIZED IMPULSIVE LOADING

An analytical model is developed to assess the elastic-plastic dynamic response of fully backed sandwich plates under localized impulse load.The core is modeled as an elastic-perfectly plastic foundation.The top face sheet is treated as an individual plate resting on the foundation.The elastic-plastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique.The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed.The model can be used to predict the impulse-induced local effect on fully backed sandwich plates.     

The response of circular composite plates to underwater blast: Experiments and modelling

We present a new experimental technique to allow laboratory-scale observation of underwater blast loading on circular plates, including dynamic deformation and failure of the plates as well as the sequence of cavitation events in water. The apparatus is used to measure and compare the responses of a quasi-isotropic glass/vinylester composite and of a woven carbon/epoxy plate. Dynamic explicit FE simulations are conducted and their predictions are found in good agreement with experiments. Measurements and FE predictions are used to validate a recently developed theoretical model for the response of elastic orthotropic plates to underwater blast.     

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

A refined higher order shear deformation theory is used to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modeling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Delamination is modeled through the multi-point constraint approach using the transformation matrix technique. For validation purposes, the natural frequencies and the critical buckling loads are computed and compared with three-dimensional NASTRAN results and available experimental data. The effect of delamination on the critical buckling load and the first two instability regions is investigated for various loading conditions and plate thickness. As expected, the natural frequencies and the critical buckling load of the plates with delaminations decrease with increase in delamination length. Increase in delamination length also causes instability regions to be shifted to lower parametric resonance frequencies. The effect of edge delamination on the static and dynamic stability as well as of delamination growth is investigated.     

Thermal postbuckling analysis of moderately thick plates

A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.     

Erratum to: Vibration Analysis of Perforated Plates Using Time-Average Digital Speckle Pattern Interferometry

Digital Speckle Interferometry is a non invasive full-field coherent optical technique used in mechanical vibration measurement. In this research, it is used for tuning resonant frequencies of vibrating plates in order to investigate the dynamical behavior of perforated plates. The plate was excited to resonant vibration by a sinusoidal acoustic source. Fringe pattern produced during the time-average recording of the vibrating plate, for several resonant frequencies were registered. Results of plates fixed at one edge having internal holes and attached masses are presented. Experimental natural frequencies and modal shapes are compared to those obtained by an analytical approximate solution based on the Rayleigh–Ritz method with the use of orthogonal polynomials as coordinate function. A high degree of correlation between computational analysis and experimental results was observed, proving the potentiality of the optical technique as experimental validation of the numerical simulations.     

Optimal Force Transmission by Flexure-Clamped Boundaries

ABSTRACT

Grillages of maximum strength and maximum stiffness and fiber-reinforced plates of maximum strength are considered. Using a technique developed earlier, optimal solutions are given for a large number of boundary shapes. In all problems discussed, the flexural systems are clamped along all boundaries and the loading is given by an arbitrary nonnegative function.     

Stability Problems for Plates with Short-Term Damageability

The problem on stability of plates with microdamages simulated by hollow randomly dispersed micropores is considered. Two approaches are proposed to investigate the stability of plates weakened by microdamages. These approaches are based on models well known from the theory of stability of elastoplastic bodies — the concepts of tangent-modulus loading and continuous loading     

A rapidly converging technique for vibration analysis of plates with a discrete mass distribution

Summary A technique based on the Galerkin approach has been developed for determination of the natural frequencies of rectangular plates with discrete masses added. The technique is applied to the rectangular plates with simply supported and clamped boundary conditions, but no difficulty exists in applying the same method to the plates of various forms with different boundary conditions. The results of this technique applied to one particular case are compared to a solution obtained by an exact method; the comparison shows the two methods to be in excellent agreement.

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Übersicht Es wird eine auf dem Galerkin-Verfahren basierende Methode zur Berechnung der Eigenfrequenzen rechteckiger Platten mit diskreten Einzel-Massen angegeben. Es werden einfach aufgelagerte und eingespannte rechteckige Platten untersucht, jedoch ergeben sich keine Schwierigkeiten bei der Anwendung derselben Methode auf Platten anderer Formen mit anderen Randbedingungen. Für einen Sonderfall werden die Ergebnisse der Berechnungen mit exakten Lösungen verglichen, wobei eine ausgezeichnete Übereinstimmung festgestellt werden kann.

     

Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout

The elastic buckling behavior of rectangular perforated plates was studied by using the finite element method in this study. Circular cutout was chosen at different locations along the principal x-axis of plates subjected to linearly varying loading in order to evaluate the effect of cutout location on the buckling behavior of plates. The results show that the center of a circular hole should not be placed at the end half of the outer panel for all loading patterns. Furthermore, the presence of a circular hole always causes a decrease in the elastic buckling load of plates subjected to bending, even if the circular hole is not in the outer panel.     

On buckling of cantilever rectangular plates under symmetrical edge loading

The stability of cantilever rectangular plates under the symmetrical edge loading will be studied in this paper by lite varialional calculus. We are going to find out the minimum critical loading for cantilever rectangular plates subjected to various edge loadings symmetrically on a pair of opposite free edges. We’ll discuss the least critical loadings when the buckling of rectangular plates acted on bv a pair of concentrated forces, uniformly distributed loads, locally uniform distributed loads, distributed loads in the form of triangle and a pair of concentrated couples occur respectively.     

Imperfection sensitivity of the post-buckling behavior of higher-order shear deformable functionally graded plates

This paper investigates the sensitivity of the post-buckling behavior of shear deformable functionally graded plates to initial geometrical imperfections in general modes. A generic imperfection function that takes the form of the product of trigonometric and hyperbolic functions is used to model various possible initial geometrical imperfections such as sine type, local type, and global type imperfections. The formulations are based on Reddy’s higher-order shear deformation plate theory and von Karman-type geometric nonlinearity. A semi-analytical method that makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process is used to obtain the post-buckling equilibrium paths of plates with various boundary conditions that are subjected to edge compressive loading together with a uniform temperature change. Special attention is given to the effects of imperfection parameters, which include half-wave number, amplitude, and location, on the post-buckling response of plates. Numerical results presented in graphical form for zirconia/aluminum (ZrO₂/Al) graded plates reveal that the post-buckling behavior is very sensitive to the L2-mode local type imperfection. The influences of the volume fraction index, edge compression, temperature change, boundary condition, side-to-thickness ratio and plate aspect ratio are also discussed.     

磁驱动飞片的一维磁流体动力学数值研究

磁驱动高速飞片技术是近年来发展的一种新型实验技术,在冲击波物理领域得到应用。该过程伴随着磁场扩散,并由此引起焦耳加热,使得飞片加载面的相状态发生变化,这决定了飞片厚度的范围。基于拉格朗日坐标系,利用磁流体动力学方程组、电阻率方程和状态方程数据库,对磁驱动铝飞片进行了一维磁流体动力学数值计算,获得了不同时刻铝飞片密度、温度的剖面分布,得到了磁场扩散速率随加载电流密度的变化关系。文章所选取的电导率方程只考虑到汽化点为止,对于等离子体形成的过程无法描述,如果要精确描述更高电流密度下的驱动过程,需考虑更为普适的电导率方程。磁场扩散速率随加载电流密度的变化存在转折点,在转折点前后可分别用两个线性关系表达式加以刻画。利用这些关系和冲击波物理相关知识,对磁压加载等熵驱动飞片实验样品厚度的选择进行了研究。     

Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using the differential quadrature technique

This paper investigates the behaviour of multilayered composite plates subject to thermo-piezoelectric-mechanical loading. The analysis is performed using the three-dimensional equations of thermo-piezoelasticity and the differential quadrature (DQ) numerical technique. Solutions to the thermo-piezoelectric laminated plates are made possible with the development and implementation of a DQ layerwise modelling technique. The formulation allows different boundary conditions to be imposed at the edges of the plate. Numerical results for different example plate problems are presented, and the effects of the thermo-piezoelasticity and boundary conditions of these problems are investigated. The DQ model predictions are validated with existing results as the comparison reveals good agreement between two.