Stability of parametric vibrations of hybrid composite plates

In this paper, the dynamic stability of laminated hybrid composite plates subjected to periodic uniaxial stress and bending stress is studied. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunctions transforms. Based on Bolotin's method the regions of dynamic instability of laminated hybrid composite plates are determined by solving the eigenvalue problems. The effects of layer thickness ratio, layer number, core material and load parameter on the dynamic instability of laminated hybrid composite plates are investigated and discussed.     

Nonlinear Theory of Dynamic Stability for Laminated Composite Cylindrical Shells

ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎｃｏｍｐｏｓｉｔｅｃｙｌｉｎｄｒｉｃａｌｓｈｅｌｌｓａｒｅｕｎｄｅｒｔｈｅａｃｔｉｏｎｏｆｄｙｎａｍｉｃｌｏａｄｉｎｇ ,ｔｈｅｙｍａｙｆａｌｌｉｎｄｙｎａｍｉｃｂｕｃｋｌｉｎｇｏｒｄｙｎａｍｉｃｉｎｓｔａｂｉｌｉｔｙ .Ｉｆｔｈｅｄｙｎａｍｉｃｌｏａｄｉｓｓｕｄｄｅｎｌｙａｐｐｌｉｅｄ ,ｏｒｉｔｉｓｃｈａｎｇｉｎｇｉｎｓｔａｎｔａｎｅｏｕｓｌｙ ,ｓｕｃｈａｓｉｍｐｕｌｓｉｖｅｌｏａｄｉｎｇ ,ｔｈｅｎ ,ｄｙｎａｍｉｃｂｕｃｋｌｉｎｇｗｉｌｌｈａｐｐｅｎｆｏｒｔｈｅｓｈ…     

Nonlinear dynamic response of piezoelastic laminated plates considering interfacial damage effects

This paper presents a nonlinear model for cross-ply piezoelastic laminated plates containing the damage effect of the intralayer materials and interlaminar interfaces. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement, and electric potential on the interfaces are depicted by three shape functions, which are formulated according to solutions about three equilibrium equations and conservation of charge. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage are presented. Then using the finite difference method and the Newmark scheme, an analytical solution is presented. In numerical examples, the effects of different damage models, damage evolution, amplitude and frequency of electric loads on the nonlinear dynamic response of piezoelectric laminated plate with interfacial imperfections are investigated.     

An analysis of the post-buckling of laminated plates of symmetric cross-ply

ＡＮＡＮＡＬＹＳＩＳＯＦＴＨＥＰＯＳＴ－ＢＵＣＫＬＩＮＧＯＦＬＡＭＩＮＡＴＥＤＰＬＡＴＥＳＯＦＳＹＭＭＥＴＲＩＣＣＲＯＳＳ－ＰＬＹＷｅｎｇＺｏｎｇｙｉ（翁宗诒）（ＲｅｃｅｉｖｅｄＭａｒｃｈ６,１９９５,ＣｏｍｍｕｎｉｃａｔｅｄｂｙＺｈｏｕＣｈｅｎｇｔ...     

具损伤压电智能层合中厚板的非线性动力稳定性分析

基于各向异性损伤理论和压电理论，采用能量法和Lagrange方程，建立了具损伤压电智能层合中厚板在参数激励下的非线性运动控制方程，应用增量谐波平衡法，求解了具损伤压电智能层合中厚板的非线性动力稳定性问题。算例中，分析了损伤参数和压电效应对压电智能层合板非线性动力稳定性的影响，揭示了力电耦合效应的内在特征，并与有关文献的结果进行了比较。     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

具损伤压电智能层合板的动力分析

基于应变能等效原理、高阶剪切变形理论和Hamilton变分原理,考虑复合材料铺设层内的损伤效应,建立了具损伤压电智能层合板的运动控制方程,并运用Galerkin方法进行求解.数值算例中,讨论了损伤效应、厚跨比及压电层厚度与层合板总厚度之比对四边简支压电智能层合板自由振动频率的影响和外部控制电压对其动力响应的影响.     

Nonlinear dynamic stability of composite laminated plates

Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection,support conditions and ply-angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.     

层合析参固支边界条件下的不稳定后屈曲分析

为了深入地研究复合材料层板所独具的后屈曲特性,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组,并运用广义傅立叶级数法对其进行求解。重点分析了非对称层板在固支边界条件下的稳定性问题,发现层板在此条件下有可能存在非对称的失稳临界点和不稳定的后屈曲路径,进而构造了简化的物理模型进行解释,指出后屈曲的非对称性是由于结构关于Z轴不对称,而不稳定性是由于固支边界条件阻碍了前屈曲的发生。     

An exact analytical approach for in-plane and out-of-plane free vibration analysis of thick laminated transversely isotropic plates

In this article, the governing equations of motion of thick laminated transversely isotropic plates are derived based on Reddy’s third-order shear deformation theory. These equations are exactly converted to four uncoupled equations to study the in-plane and out-of-plane free vibrations of thick laminated plates without any usage of approximate methods. Based on the present analytical approach, exact Levy-type solutions are obtained for thick laminated transversely isotropic plates and, for some boundary conditions, the exact characteristic equations hitherto not reported in the literature are given. Also, the in-plane and out-of-plane deformed mode shapes are plotted for different boundary conditions. The present solutions can accurately predict both the in-plane and out-of-plane natural frequencies and mode shapes of thick laminated transversely isotropic plates.     

基于局部移动Kriging无网格方法的层合板自由振动分析

利用基于局部移动Kriging插值无网格法对层合板自由振动进行了数值分析,基于一阶剪切层合理论导出了层合板振动的控制方程和边界条件,进一步得到了自由振动的离散化特征方程。由于Kriging插值函数具有Kronecker delta函数性质,可以直接施加本质边界条件。通过本文给出的方法,对不同边界条件、不同跨厚比、不同材料参数和铺设角度的层合板的振动频率进行了计算,均得到满意结果。最后用该方法对层合板的铺设角度进行优化设计,得到了与已有文献完全一致的优化结果。数值结果充分表明了无网格Kriging方法分析层合板自由振动问题的有效性和高精确度。     

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piezoelectric layers are solved with respect to closed and open circuit boundary conditions, an exterior dielectric slab and active control. The natural frequencies and loss factors of the constrained smart composite plates with passive control methods are not notably changed in comparison with those of the constrained composite plates without piezoelectric effects since vibrational energy does not efficiently convert to electrical energy. The loss factors of the composite plates with active constrained damping increase and the natural frequencies have significant variations as the proportional derivative gains increase. Transverse displacement power spectra of the piezoelectric composite plates with active control are compared with those of the piezoelectric composite plates with passive control showing that active control has the best suppression performance of vibrations for the constrained laminated plates with double piezoelectric layers. Radial power spectral density, phase angles and cylindrical-wave power spectral density are calculated. Interesting patterns of wave propagation are explained when plane wave expansion is used to obtain Bessel cylindrical waves.     

复合材料层合板在动集中力作用下的结构声强特性

本文研究了复合材料正交异性层合板在动集中力作用下的结构声强特性。应用MSC/-NASTRAN商业软件计算了复合材料正交异性层合板在动集中力作用下各单元的内力和速度,再应用MATLAB软件得出复合材料层合板的结构声强。算例表明,复合材料正交异性层合板的结构声强流线图与各向同性板存在明显不同的特性。复合材料正交异性层合板的结构声强流线图受边界条件、层合板叠层顺序和层数的影响。从结构声强向量图和流线图可获得关于能量传递路径、源位置和能量汇合点的许多信息。进一步,结构振动产生的噪声可根据上述信息加以控制。     

On the Bending, Vibration and Stability of Laminated Rectangular Plates with Transversely Isotropic Layers

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带压电层的混合层合板的自由振动和动力响应

基于Reddy高阶剪切变形理论和广义Kármán型方程,用双重Fourier级数展开法求得了四边简支带压电层的混合层合剪切板的自由振动及动力响应的解析解,分析中考虑了热/机/电荷载共同作用,并讨论了温度变化、控制电压、铺层方式对固有频率及动力响应的影响。     

复合材料层合板的二次屈曲和二次分枝点分析

为了研究复合材料层合板的二次分叉特性 ,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层合板在面内载荷作用下的非线性稳定性控制方程组。控制方程组用广义傅立叶级数法进行求解 ,并得到载荷 -挠度曲线。基于分叉理论中的 Lerray-Schaulder定理 ,采用小挠动法 ,直接导出了复合材料层合板的二次失稳方程。研究结果表明 ,非对称层板也可能存在分叉 ,弹性转动支持系数和铺层等因素对二次分叉有很重要的影响。随着弹性系数的增大 ,二次失稳载荷值与初次失稳载荷值之比下降     

Nonlinear vibration of generally laminated anisotropic thick plates

Summary Nonlinear equations of motion of generally laminated anisotropic plates are derived by use of Hamilton's principle. The effects of transverse shear and rotatory inertia are included in the analysis. The equations of motion so obtained readily reduce to those obtained in a recent nonlinear theory of anisotropic plates including transverse shear and rotatory inertia and to the dynamic von Kármán equations of plates. Based on the Galarkin procedure and principle of harmonic balance approximate solutions to the governing equations of generally laminated rectangular plates are formulated for various boundary conditions. Including the effects of transverse shear and rotatory inertia numerical results for the ratio of nonlinear frequency to linear frequency of symmetric angle-ply and cross-ply laminates, unsymmetric angle-ply and cross-ply laminates and an arbitrarily laminated plate are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, thickness-to-span ratio and aspect ratio. Present results are also compared with the existing data.

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Nichtlineare Schwingungen von anisotropen, dicken Verbundplatten

übersicht Die nichtlinearen Bewegungsgleichungen anisotroper, dicker Verbundplatten werden mit Hilfe des Prinzips von Hamilton hergeleitet. Dabei werden die Einflüsse der Schubspannungen und der Drehträgheit berücksichtigt. Mit dem Verfahren von Galerkin und der Methode der harmonischen Balance werden Näherungslösungen für Rechteckplatten bei verschiedenen Randbedingungen gewonnen. Numerische Ergebnisse für verschiedene Materialparameter sind graphisch dargestellt und werden mit bereits bekannten Ergebnissen verglichen.

     

AN EXACT ANALYSIS OF THERMAL BUCKLING OF PIEZOELECTRIC LAMINATED PLATES

In this paper,the governing differential equations of elastic stability problems in ther-mopiezoelectric media are deduced.The solutions of the thermal buckling problems for piezoelectriclaminated plates are presented in the context of the mathematical theory of elasticity.Owing to thecomplexity of the eigenvalue problem involved,the critical temperature values of thermal bucklingmust be solved numerically.The numerical results for piezoelectric/non-piezoelectric laminated platesare presented and the influence of piezoelectricity upon thermal buckling temperature is discussed.     

压电层合板热屈曲问题的精确分析

本文在作者们以前工作的基础上导出了热压电介弹性稳定性问题的控制微分方程，提出了热压电层合板热屈曲问题的数学和学解法。由于最后所得特征值问题的复杂性，热屈曲临界必须数值求解。文中对不同压电材非压电材料层构成的层合板作了具体计算，考虑了压电性对屈曲温度的影响。     

LARGE AMPLITUDE FREE VIBRATIONS OF LAMINATED COMPOSITE PLATES

This paper deals with large amplitude free flexural vibrations of laminated composite plates using a 9-node Heterosis degenerated isoparametric quadrilateral element, including the effects of transverse shear and rotary inertia. The nonlinear dynamic equations of the plates are formulated in von Karman's sense. Amplitude-frequency relationships are obtained through dynamic response history using the Newmark numerical integration scheme. Detailed numerical results based on various parameters are presented for orthotropic laminated plates with different boundary conditions. The rectangular anti-symmetric cross-ply plates show the softening type of nonlinearity for initial small amplitudes. The displacement amplitudes decrease and nonlinear frequencies increase with the increment of time. Supported by the NNSFC (No. 19672033), the National Key Project on Basic Research and Applied Research (PD9521904) and the Doctoral Training Foundation of Education Commission of China(No. 98000304).