Measurements of thermal distortion of composite plates by holographic interferometry

Laser holographic-interferometry technique was used to measure the dimensional changes of graphite-fibre-epoxy-resin laminated plates subject to significant changes of thermal environment. A multiple double-exposure scheme based on the principle of varying incident beam angles was used to record the interference fringes covering large temperature ranges on the same film plate. This feature is highly desirable for industrial applications.     

复合材料层合板壳的非线性热动态响应分析

本文基于高阶剪切变形理论，考虑同天应变和横向剪切应变的影响，对受热复合材料层合板壳的非线性热动态响应进行分析，计及了转动惯量的影响，给出了通用性较好的Ｃ＾０类有限元公式，文中数值算同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性，文中还就层合板的边界条件、纵厚比及铺设角度对非线性热动态响应的影响进行了分析。     

Natural frequencies of thin,rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh–Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or “patch”, carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.     

Improved natural frequencies for plates with a free edge

A simple correction formula is developed for the square of natural frequencies of plates with a free edge. The theory is applied to torsional vibrations of a long plate strip and to vibrations of a circular plate with a free edge and a number of nodal diameters. The paper concludes with the remark that the theory may be extended mutatis mutandis to vibrations of shells with a free edge.     

Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation

The present study is concerned with the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Continuous gradation of the fiber volume fraction is modeled in the form of an m-th power polynomial of the coordinate axis in the thickness direction of the beam. By varying the fiber volume fraction within the symmetric composite beam to create a functionally graded material （FGM）, certain vibration characteristics are affected. Results are presented to demonstrate the effects of shear deformation, fiber volume fraction, and boundary conditions on the natural frequencies and mode shapes of composite beams.     

Stochastic nonlinear bending response of laminated composite plates with system randomness under lateral pressure and thermal loading

In this paper, the effect of sensitivity of randomness in system parameters on the nonlinear transverse central deflection response of laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modelled as basic random variables. A higher order shear deformation theory in the von-Karman sense is used to model the system behavior of the laminated plate. A direct iterative-based C ⁰ nonlinear finite element method in conjunction with the first-order perturbation technique developed by the authors is extended for thermal problem to obtain the second-order response statistics, i.e., mean and variance of the nonlinear transverse deflection of the plate. Typical numerical results of composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and transverse temperature are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The results have been compared with those available in the literature and an independent Monte Carlo simulation.     

Natural frequencies of circular arcs with varying cross section

This paper presents a transter matrix method for conveniently predicting the natural frequencies of circular arcs with varying cross section. The equations of in-plane vibration of an arc are written as a coupled set of first-order differential equations by using the transfer matrix of the arc. Once the transfer matrix has been determined, the natural frequencies and the mode shapes of the vibration are calculated in terms of the elements of the matrix for a given set of boundary conditions at the ends of the arc. The numerical results obtained by the method are compared with the experimental results for free-clamped arcs with tapered breadth, which are in good agreement with each other.     

Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments

This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study.     

Local and global nonlinear dynamics of thermomechanically coupled composite plates in passive thermal regime

Unified 2D continuum formulation of the nonlinear dynamic problem for a von Kármán shear indeformable symmetric cross-ply composite plate in a thermomechanical environment is presented, along with the ensuing reduction procedure ending up to a three-mode discretized model with unknown transverse displacement and membrane/bending temperatures. Systematic numerical analyses in the case of thermal dynamics passively entrained by the solely active mechanical excitations allow to unveil the main features of the nonlinear response, while highlighting fundamental aspects associated with the thermomechanical coupling. Local and global dynamics of a single-layer orthotropic plate are investigated under varying in-plane/transverse excitations or thermal property of the material. Comparison with the response provided by partially coupled models and the uncoupled mechanical oscillator enables to identify situations in which thermomechanical coupling affects the nonlinear response even in the solely passive thermal setting and to frame the relevant effects within known literature results.     

Resonant frequencies of electroelastic vibrations of piezoceramic plates

The harmonic electroelastic vibrations of a thin ring plate are considered. The effect of boundary conditions on the natural frequencies is studied. The asymptotic properties of the frequency spectrum are determined. The dependence of the resonant and antiresonant frequencies and the dynamic electromechanical-coupling coefficient on the relative size of plate is analyzed     

Natural frequencies of a hemispherical shell

An experimental study of the natural frequencies of a hemispherical thin shell with a clamped edge is described. For the particular shell model studied, the four lowest symmetric modes were identified conclusively by establishing the node-line patterns. The associated natural frequencies were found to be in excellent agreement with theoretical predictions. A great number of higher modes were also excited but could not be conclusively identified due to difficulties in establishing the node-line patterns. The symmetric frequency spectrum up to and including the 23rd mode was, however, established by means of a qualitative argument and showed good correlation with the theoretical spectrum. A number of natural frequencies were found to be present in a particular frequency band for the test shell resulting in a severe crowding in this region. This was found to be in agreement with the more general results for hemispherical shells which indicate that the crowding takes place around a frequency parameterp=1.0.     

Analysis of composite laminated plates

In the static and dynamic analysis of composite laminates, a theory for the laminated plates is presented in this paper. Because the deflection W_b which is caused by the classical bending deformation and the deflection W₅ which is caused by the shear deformation are divided from the total deflection W in the theory, this makes it easy to solve the governing equations. In addition, this theory is convenient for the discussion and analysis of the effects of transverse shear deformations on bendings, vibrations and stabilities of laminated plates.     

Natural vibrations of rectangular plates with a through crack

Summary The paper presents a finite element model of the rectangular plate with a through crack. The crack occurring in the plate is nonpropagating and open. It was assumed that the crack changes only the stiffness of the plate, whereas the mass is unchanged. The method of the formation of the stiffness matrix of a finite element for the rectangular, cracked plate is presented. The effects of the crack location and its length on the changes of the eigenfrequencies of the simply supported and cantilever plate are studied. The results of numerical computations are compared with results of theoretical and experimental data presented in the literature.

---

Eigenschwingungen von rechteckigen Platten mit Transverslriß

Übersicht Der Beitrag präsentiert ein Finite-Element-Modell einer rechteckigen Platte mit Transverslriß. Der Riß pflanzt sich nicht fort und bleibt offen. Es wird angenommen, daß der Riß nur die Steifigkeit der Platte verändert, wogegen die Masse konstant bleibt. Eine Methode zur Aufstellung der Steifigkeitsmatrix für ein finites Element der rechteckigen Platte wird vorgestellt. Der Einfluß der Lage des Risses und der Rißlänge auf die Eigenschwingungen der einfach gestützten und freitragenden Platte wird untersucht. Abschließend erfolgt ein Vergleich der numerischen Berechnungen mit den Ergebnissen von theoretischen und experimentellen Literaturdaten.