Nonlinear supersonic flutter of panels considering shear deformation and rotary inertia

Nonlinear supersonic flutter of panels is studied for end conditions of simply supported, clamped and partial restraint against rotation by a unified approach. The effect of shear deformation and rotary inertia on nonlinear flutter boundary is studied for various thicknesses of panel.     

Frame response to a harmonic excitation,taking into account the effects of shear deformation and rotary inertia

The Timoshenko beam theory is used to compare experimental and analytical results in a steel frame subjected to a harmonic excitation. The very good agreement between the experimental and the theoretical results proves the usefulness of this ‘exact’ method over other methods as the finite elements.     

Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned ends

The method of multiple scales is used to analyze the nonlinear vibrations of a beam with pinned ends. The formulation incorporates the effects of the transverse shear deformation as well as the rotary inertia on the large amplitude vibration behaviour. A uniformly valid higher second-order perturbation solution is obtained. The predictions of nonlinear frequencies at different beam parameters are given. The influences of shear and rotary inertia are significant in the case of moderately thick and short beams undergoing large amplitude vibrations.     

An efficient, conforming axisymmetric shell element including transverse shear and rotary inertia

A conforming, two-node conical element is presented incorporating both transverse shear deformation and rotary inertia effects. The success of the formulation is based on the C⁰ continuity shape functions that, in addition to providing full kinematic compatibility, satisfy the interdependent variable interpolation requirement. This requirement points toward a particular dependence of the kinematic variable interpolations which allow for the satisfaction of the Kirchhoff constraint everywhere in the element domain. There exists an internal degree-of-freedom reduction achieved by means of a continuous shear constraint condition. In the derivation of element matrices, Hamilton's principle is invoked with Gaussian quadratures ensuring exact integration throughout. Excellent convergence characteristics and high accuracy results attainable with the element are demonstrated in static and free vibration problems for thin and moderately thick plates and shells.     

Dynamic stability of bars considering shear deformation and rotatory inertia

Dynamic stability of bars including shear deformation and rotatory inertia are investigated in this paper using finite element formulation for various slenderness ratios. Stability and frequency parameters and instability regions for these bars for various end conditions and slenderness ratios are presented. A master dynamic stability curve covering all the end conditions and slenderness ratios of the bar is presented in the non-dimensionalized form.     

3-D beam element of composite cross section including warping and shear deformation effects

In this paper a boundary element method is developed for the construction of the 14 × 14 stiffness matrix and the nodal load vector of a member of arbitrary homogeneous or composite cross section taking into account both warping and shear deformation effects. The composite member consists of materials in contact each of which can surround a finite number of inclusions. To account for shear deformations, the concept of shear deformation coefficients is used. In this investigation the definition of these factors is accomplished using a strain energy approach. Seven boundary value problems are formulated and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the shear deformation coefficients is accomplished from stress functions using only boundary integration. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The influence of the warping effect especially in composite members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the analysis of a space frame. Moreover, the discrepancy of both the deflections and the internal forces of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect, especially in thick walled cross section members.     

Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation

A new horizontally curved three-noded isoparametric beam element with or without an elastic base throughout its length, is formulated, in which the same set of parabolic shape functions in natural coordinates is used to interpolate beam geometry as well as displacements at any point of the beam. The formulation includes shear deformation effects and is also capable of accounting for torsional loading. The elastic base is assumed to offer distributed vertical reaction and torque at any point of the beam proportional to the vertical deflection and angle of twist respectively at that point. Development of the stiffness matrix is presented. A two point Gaussian quadrature rule has been followed for the necessary numerical integration. Numerical results for a few sample problems have been presented and comparison with the analytical solutions indicates the suitability of the element.     

Finite deformation of a rotating orthotropic cylinder with linear elasticity

The effects of finite deformation upon a rotating, orthotropic cylinder with linear elasticity is investigated. The governing equation and boundary conditions form a non-linear two-point boundary-value problem. A numerical integration technique is used in conjunction with the related initial-value problem and Newton's method to obtain approximate solutions. The problem and method of solution provide an example for treatment of non-linear boundary conditions. The stresses induced by finite deformation and the influence of the degree of orthotropy are studied.     

Optimization of anisotropic composite panels with T-shaped stiffeners including transverse shear effects and out-of-plane loading

A two-step method to optimize anisotropic composite panels with T-shaped stiffeners, including a new formulation of the transverse shear properties and an approximation of the ply contiguity (blocking) constraints as functions of the lamination parameters is provided. At the first step, a representative element of the stiffened panel (superstiffener) is optimized using mathematical programming and lamination parameters subjected to combined loading (in-plane and out-of-plane) under strength (laminate or ply failure), buckling and practical design constraints. Ply blocking constraints are imposed at this step to improve convergence towards practical laminates. At the second step, the actual superstiffener’s laminates are obtained by using a genetic algorithm. Results, for the case considered, show that the inclusion of transverse shear effects has an associated 2.5% mass penalty and that neglecting its effects might invoke earlier buckling failure. In addition, the influence of designing for failure strength at laminate or ply level is assessed.     

风力机叶片大挠度挥舞振动特性分析

分析了风力机叶片大挠度挥舞振动特性.基于Hamilton原理,建立了叶片大挠度挥舞振动控制方程,其中非稳态气动力由Greenberg公式得出.使用瑞利-利兹法求解振动特征问题,得到振动的频率和无阻尼模态函数.基于得出的模态函数,使用Galerkin方法将控制偏微分方程离散,得到模态坐标方程.将振动位移分解为静态位移和动态位移,得到了静态位移和动态位移方程,考查了入流速度比对静态位移和气动阻尼的影响,并对大挠度挥舞振动动态响应进行了分析,得到如下结论：大挠度挥舞振动静态位移沿叶片展向随入流速度比的增大而增大,叶尖处位移最大；当入流速度比较小时,振动为小振幅的周期运动,入流速度比较大时,振动为大振幅的拟周期运动.     

A finite element analysis of beams on elastic foundation including shear and axial effects

A displacement finite element method for analyzing a beam on continuous elastic foundation is presented. A three-dimensional model which accounts for the effects of both the Filonenko-Borodich and Pasternak foundation models in a consistent and complete way is used. A variational principle is introduced with the slope field due to bending only and the displacement field approximated by independent quantities subjected to variation. Numerical examples illustrate the accuracy of the element, the importance of shear, axial and shear-axial interaction effects associated with continuous elastic foundation, and finally the application of the element to a rotor supported by two hydrodynamic journal bearings.     

Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory

An analytical solution, based on a higher order shear and normal deformation theory, is presented for the cylindrical flexure of piezoelectric plates. The primary displacement terms are expanded in thickness coordinate and an exact nature of electric potential is obtained in actuator and sensing layers. The electric potential function is evaluated by solving a second order ordinary differential equation satisfying electric boundary conditions along thickness direction of piezoelectric layer. A unidirectional composite plate attached with distributed actuator and sensor layers is analyzed under electrical and mechanical loading conditions and comparison of results with exact solution is presented. Results for non-piezoelectric plates are also compared with elasticity and other solutions of cylindrical bending.     

一类含间隙结构振动特性分析

为分析一类含间隙结构的振动特性及为保护特定子结构而预留间隙的合理性,根据其振动试验结果,采用假设模态法的思想,将该类带间隙的非线性结构按其子结构的一阶弯曲模态简化为带间隙的单自由度与二自由度弹簧-质量系统,分析了不同激励条件下间隙对系统动力学响应的影响.分析结果表明:此类结构中,间隙具有阻碍振动传递的性质,预留间隙是合理的.     

Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

In this study, the effect of the centrifugal forces on the eigenvalue solution obtained using two different nonlinear finite element formulations is examined. Both formulations can correctly describe arbitrary rigid body displacements and can be used in the large deformation analysis. The first formulation is based on the geometrically exact beam theory, which assumes that the cross section does not deform in its own plane and remains plane after deformation. The second formulation, the absolute nodal coordinate formulation (ANCF), relaxes this assumption and introduces modes that couple the deformation of the cross section and the axial and bending deformations. In the absolute nodal coordinate formulation, four different models are developed; a beam model based on a general continuum mechanics approach, a beam model based on an elastic line approach, a beam model based on an elastic line approach combined with the Hellinger–Reissner principle, and a plate model based on a general continuum mechanics approach. The use of the general continuum mechanics approach leads to a model that includes the ANCF coupled deformation modes. Because of these modes, the continuum mechanics model differs from the models based on the elastic line approach. In both the geometrically exact beam and the absolute nodal coordinate formulations, the centrifugal forces are formulated in terms of the element nodal coordinates. The effect of the centrifugal forces on the flap and lag modes of the rotating beam is examined, and the results obtained using the two formulations are compared for different values of the beam angular velocity. The numerical comparative study presented in this investigation shows that when the effect of some ANCF coupled deformation modes is neglected, the eigenvalue solutions obtained using the geometrically exact beam and the absolute nodal coordinate formulations are in a good agreement. The results also show that as the effect of the centrifugal forces, which tend to increase the beam stiffness, increases, the effect of the ANCF coupled deformation modes on the computed eigenvalues becomes less significant. It is shown in this paper that when the effect of the Poisson ration is neglected, the eigenvalue solution obtained using the absolute nodal coordinate formulation based on a general continuum mechanics approach is in a good agreement with the solution obtained using the geometrically exact beam model.     

On the -semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam

In this paper, we show that a linear unbounded operator associated with an Euler–Bernoulli beam equation under shear boundary feedback generates a C₀-semigroup in the underlying state Hilbert space. This provides an answer to a long time unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green's function and the verification of the Riesz basis property for the generalized eigenfunctions. As a consequence, we show that this semigroup is differentiable and exponentially stable, which is in sharp contrast to the properties possessed by most feedback controlled beams based on a passive design principle.     

In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach

The buckling analysis of thick composite annular sector plates reinforced with functionally graded carbon-nanotubes (CNTs) is presented under in-plane and shear loadings based on the higher-order shear deformation theory. It is considered that the plate is resting on the Pasternak-type elastic foundation. The overall material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are estimated through the micromechanical model. The governing equations are derived on the basis of the higher-order shear deformation plate theory, and the quadratic form of the energy functional of the system is presented. An efficient numerical method is presented in the context of variational formulation to obtain the discretized version of stability equations. The validation of the present study is demonstrated through comparisons with the results available in the literature and then comprehensive numerical results are given to investigate the impacts of model parameters on the stability of CNT-reinforced composite annular sector plates.     

Parametric instability of a non-prismatic bar with localized damage subjected to an intermediate periodic axial load

The dynamic instability behaviour of a tapered beam with localized zones of damage and subjected to concentrated periodic loads applied at some intermediate point has been studied by using a finite element analysis. The effects of parameters such as extent and position of damage, position of load, the static and dynamic load factors on the vibration and instability behaviour are discussed. The influence of damage on natural frequency is observed to be most intense at some critical position on the beam. The parametric instability regions are influenced by the combined effects of the position of damage and the position of intermediate load on the beam.     

Optimization of a finite dipole array with genetic algorithm including mutual coupling effects

In this article, the genetic algorithm together with a circuit model is applied to optimize the gain of a dipole array by adjusting the dipole element positions. This algorithm can optimize problems globally without any gradient calculations and is especially suitable for large antenna array design. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 379–382, 2000.