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Francesco Sorge 《Meccanica》1995,30(4):397-403
A simplified approach to sandwich plate free vibrations, based on the superposition method, can provide approximations to the lowest modes for various boundary conditions, showing a characteristic influence of the bending-shear stiffness ratio.
Sommario Un'analisi semplificata delle vibrazioni naturali di pannelli sandwich in diverse condizioni di vincolo, con il metodo di sovrapposizione degli effetti, consente l'individuazione approssimata dei modi più bassi, mostrando un comportamento vibratorio caratteristico al variare del rapporto tra le rigidezze di flessione e taglio.相似文献
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《International Journal of Solids and Structures》2006,43(21):6329-6346
The fitting of the flexural velocity branch by means of the Padé approximation is examined. Its use for free isotropic plates is elaborated and compared to other approaches. The flexural-velocity expansion into power series, which underlies the Padé implementation, is detailed. The generalization for fluid-loaded plates and inhomogeneous plates is outlined, and the impact of anisotropy is discussed in some detail. 相似文献
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A. Bayón F. Gascón R. Medina F.J. Nieves F. Salazar 《European Journal of Mechanics - A/Solids》2011,30(3):423-431
In this work the flexural vibration of a free cylinder of any aspect ratio is analysed. A general solution by powers series of the coordinates is proposed here to represent the displacements, with restrictions on the powers of the radial coordinates which prevent potential energy and stress singularities at the axis of the cylinder. By means of an analytic method, it is concluded that certain points of the cylinder have no axial motion. As a result of the pure transverse movement and of the fact that the cylinder bends, it is inferred that the axis is extended. Furthermore, in the symmetric modes, the points situated at the centres of the bases are displaced in the same direction and sense, and hence the distance between them does not vary in time. Flexural natural frequencies are numerically calculated by Ritz’s method with the general solution series proposed. Since the series used are more adequate, convergence is better than with classic series. The results are verified by FEM. Some consequences are extended to a rectangular plate, whose points of the middle surface vibrate transversally in the double-symmetric mode. In order to verify the theoretical results, a set of experiments with a laser interferometer is carried out. The experimental frequencies agree with the theoretical values. 相似文献
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Small mass impacts on composite structures are common cases caused by hailstones and runway debris. Small mass impactors usually result in a wave controlled local response, which is independent of boundary conditions. This response occurs before the reflection of waves from the boundaries and cannot be modeled by large mass drop weight tests. An elasto-plastic contact law, which accounts for permanent indentation and damage effects, was used here to study small mass impact on laminated composite plates. By comparing with results from the Hertzian contact law, it was found that damage can change the dynamic response of the structure significantly with increasing impact velocity. Due to smaller contact force generated for the case of using elasto-plastic contact, the central displacement of the plate is also less than the one using Hertzian contact law. The linearized version of the contact law was then used to derive the closed-form approximations of the contact force, indentation and plate central displacement for the impact loading of composite laminates. The threshold velocity for delamination onset under small mass impact was predicted analytically based on the obtained peak contact forces by combining with an existing quasi-static delamination threshold load criterion. A good agreement was found between the predicted threshold values and published experimental results. 相似文献
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Summary In this paper a nonlinear vibration theory which includes the effects of transverse shear deformation and rotatory inertia is formulated for rectilinearly orthotropic circular plates using Berger's method. A solution to the governing equations for rigidly clamped plates is obtained on the basis of a single-mode approach by use of Galerkin's method and numerical Runge-Kutta procedure. A good agreement is found between present results and those obtained by a more accurate theory for nonlinear static and dynamic cases. Numerical results indicate significant influence of these effects on the vibration behaviour of moderately thick plates, especially high-modulus composite plates. These effects, however, are not so significant for the radius-to-thickness ratio greater than 10.
Nichtlineare Schwingungen orthotroper Kreisplatten
Übersicht Eine Theorie nichtlinearer Schwingungen orthotroper Kreisplatten wird mit der Methode von Berger formuliert, wobei Schubverformung und Drehträgheit berücksichtigt werden. Für eingespannte Platten wird mit dem Verfahren von Galerkin eine numerische Lösung bestimmt und mit bekannten Lösungen verglichen. Die numerischen Ergebnisse zeigen, daß der Einfluß von Schubverformung und Drehträgheit bei mäßig dicken Platten beträchtlich sein kann.相似文献
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A method to determine weak or defective bonding areas within the brazed adjoining contact surfaces of composite ceramic-metal plates is proposed. The plates include voids, as well as hairline cracks in the ceramic layer, caused by the high-temperature brazing process. To detect these flaws, transient flexural waves are generated and transmitted through the plate by means of an attached piezoelectric transducer. These pulses are a narrow band signal generated in the time domain. The characteristic wavelengths corresponding to the narrow frequency spectrum may be larger than the size of the flaw. Dynamic holographic interferometry using a double-pulsed twin-cavity Nd:YAG laser, comprising two independent reference beams, was used to measure the response. The experimental interferograms (phase maps) coincide rather precisely with analytic results derived from Mindlin's plate equations (including effects of shear and rotary inertia). 相似文献
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S. Papargyri-Beskou A.E. Giannakopoulos D.E. Beskos 《International Journal of Solids and Structures》2010,47(20):2755-2766
Gradient elastic flexural Kirchhoff plates under static loading are considered. Their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case. A variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions, classical and non-classical ones. Two circular gradient elastic plates, clamped or simply supported at their boundaries, are analyzed analytically and the gradient effect on their static response is assessed in detail. A rectangular gradient elastic plate, simply supported at its boundaries, is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors. Finally, a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple-stress elasticity theories. 相似文献
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《International Journal of Solids and Structures》2003,40(16):4153-4166
In this paper moderately large amplitude vibrations of a polygonally shaped composite plate with thick layers are analyzed. Three homogeneous and isotropic layers with a common Poisson’s ratio are perfectly bonded and their arbitrary thickness and material properties are symmetrically disposed about the middle plane. Mindlin–Reissner kinematic assumptions are implemented layerwise, and as such model both the global and local response. Geometric nonlinear effects arising from longitudinally constrained supports are taken into account by Berger’s approximation of nonlinear strain–displacement relations. Overall cross-sectional rotations are defined and subsequently a correspondence of this complex problem to the simpler case of a homogenized shear-deformable nonlinear plate with effective stiffness and hard hinged boundary conditions is found. The nonlinear steady-state response of composite plates subjected to a time-harmonic lateral excitation is investigated and the phenomena of nonlinear resonance are studied and evaluated. 相似文献
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Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration. 相似文献
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By means of Berger's approximation, suitable for plates with immovable edges, the geometrically nonlinear problem is considerably simplified. Thermally loaded plates with polygonal planform under hard-hinged support conditions are considered, taking into account the effect of shear in transverse isotropy. The class of symmetric vibrations about the flat plate position is represented by a homogeneous and coupled set of Duffing-oscillators as a result of a multi-mode expansion. A unifying non-dimensional closed-form solution for the corresponding nonlinear natural vibration periods is given, which is independent of the special planform. The individual shape of the plate enters the transformation into real time through the linear natural frequencies, or, equivalently, through the linear eigen-values of an effectively prestressed membrane of the same planform. 相似文献
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Nonlinear equations of motion for orthotropic plates are proposed on the basis of the three dimensional nonlinear theory of elasticity. The resulting plate model provides a high accuracy, which is confirmed by solving the Vlasov static problem of bending a hinge-supported plate under sinusoidal load. 相似文献
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本文给出了对称角铺设复合材料层合梯形板振动特性分析的一种有效方法,可方便地处理具有内部点支承及各种边界支承时矩形、平行四边形、三角形、等腰梯形与非等腰梯形层合板的横向弯曲振动问题. 相似文献
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The large amplitude flexural vibration characteristics of functionally graded material (FGM) plates are investigated here using a shear flexible finite element approach. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The FGM plate is modeled using the first-order shear deformation theory based on exact neutral surface position and von Kármán’s assumptions for large displacement. The third-order piston theory is employed to evaluate the aerodynamic pressure. The governing equations of motion are solved by harmonic balance method to study the vibration amplitude of FGM plates under supersonic air flow. Thereafter, the non-linear equations of motion are solved using Newmark’s time integration technique to understand the flexural vibration behavior of FGM plates in time domain (simple harmonic or periodic or quasi-periodic). This work is new in the sense that it deals with the non-linear flutter characteristics of FGM plates under high supersonic airflow accounting for both the geometric and aerodynamic non-linearities. Some parametric study is conducted to understand the influence of these non-linearities on the flutter characteristics of FGM plates. 相似文献
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Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates 总被引:2,自引:0,他引:2
S. Papargyri-Beskou D. E. Beskos 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(8):625-635
The governing equation of motion of gradient elastic flexural Kirchhoff plates, including the effect of in-plane constant
forces on bending, is explicitly derived. This is accomplished by appropriately combining the equations of flexural motion
in terms of moments, shear and in-plane forces, the moment–stress relations and the stress–strain equations of a simple strain
gradient elastic theory with just one constant (the internal length squared), in addition to the two classical elastic moduli.
The resulting partial differential equation in terms of the lateral deflection of the plate is of the sixth order instead
of the fourth, which is the case for the classical elastic case. Three boundary value problems dealing with static, stability
and dynamic analysis of a rectangular simply supported all-around gradient elastic flexural plate are solved analytically.
Non-classical boundary conditions, in additional to the classical ones, have to be utilized. An assessment of the effect of
the gradient coefficient on the static or dynamic response of the plate, its buckling load and natural frequencies is also
made by comparing the gradient type of solutions against the classical ones. 相似文献