Simulating the fluid forces and fluid-elastic instabilities of a clamped–clamped cylinder in turbulent axial flow

In this paper, the fluid forces and the dynamics of a flexible clamped–clamped cylinder in turbulent axial flow are computed numerically. In the presented numerical model, there is no need to tune parameters for each specific case or to obtain coefficients from experiments. The results are compared with the dynamics measured in experiments available in the literature. The specific case studied here consists of a silicone cylinder mounted in axial water flow. Computationally it is found that the cylinder loses stability first by buckling. The threshold for buckling is in quantitative agreement with experimental results and weakly nonlinear theory. At higher flow speed a fluttering motion is predicted, in agreement with experimental results. It is also shown that even a small misalignment between the flow and the structure can have a significant impact on the dynamical behavior. To provide insight in the results of these fluid–structure interaction simulations, forces are computed on rigid inclined and curved cylinders, showing the existence of two different flow regimes. Furthermore it is shown that the inlet turbulence state has a non-negligible effect on these forces and thus on the dynamics of the cylinder.     

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.     

Concentrated-impact loading of circular plates

Solution to the impulsive motion of a clamped circular plate due to concentrated axisymmetric impact has been obtained. Experiments were conducted on a clamped circular-plate model under half-sine-pulse loads with several pulse durations. Experimental results are compared with the numerical results.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

On the response of MEMS resonators under generic electrostatic loadings: experiments and applications

Nonlinear Dynamics - We present an investigation of the dynamic behavior of an electrostatically actuated clamped–clamped microbeam, under the simultaneous excitation of primary and...     

Classical and nonlinear buckling analyses of spherical sandwich shells

The buckling and initial postbuckling behavior of clamped shallow spherical sandwich shells with dissimilar face sheets under a uniform pressure is studied. The numerical results show that the buckling and initial post-buckling behavior of clamped shallow spherical sandwich shells with dissimilar face sheets is similar to that of the corresponding homogeneous shell.     

Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions

The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The governing differential equation has been solved using Rayleigh-Ritz technique. The frequency equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.     

Multimode vibration suppression with passive two-terminal distributed network incorporating piezoceramic transducers

The design of an inductance/capacitance two-terminal distributed passive electric network for simultaneously controlling several flexural modes of vibration is discussed. The efficiency of the network to annul multimode vibrations of simply supported, clamped–clamped and cantilever beams is demonstrated.     

均布载荷作用下带边缘大波纹膜片的非线性弯曲

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有硬中心的带边缘大波纹膜片的非线性弯曲问题．应用积分方程方法，获得了具有夹紧固定和滑动固定两种外边界的膜片的特征关系，即荷载-中心挠度曲线．作为算例，给出了夹紧固定膜片中的应力分布．     

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

通过把固支边上的边界位移函数作为状态变量引入状态方程,得到了含固支边矩形单层与叠层厚板的精确解. 在求解过程中,将非齐次状态方程的求解变为齐次状态方程的求解,省略了求解待定常数的中间过程,使求解过程变得简单. 所得到的解能够严格满足固支边界条件,在同一材料层内不需作分层处理,因而更加精确. 此外,对固支边的应力提出了新的计算方法,能够得到更精确的边界应力. 算例表明,本文解比现有精确解收敛快,与有限元解吻合的更好,尤其是在固支边处体现得更加明显.     

Determination of the microscale stress–strain curve and strain gradient effect from the micro-bend of ultra-thin beams

A simple method is established to determine the microscale uniaxial stress–strain curve from the load and deflection data for a doubly clamped beam. The method is based on the fact that, for beam deflection much larger than the beam thickness, the axial stretching dominates the deformation in the doubly clamped beam and the doubly clamped beam behaves like a simple plastic hinge. The microscale uniaxial stress–strain curve, together with the cantilever beam experiments, is used to determine the strain gradient effect in Au thin beams. The effect of finite rotation is also discussed.     

Generalization of Seide’s problem by the regulated stochastic linearization technique

In this paper, the nonlinear random vibration of a uniform beam clamped at both of its ends is investigated by the regulated stochastic linearization technique. A closed system of nonlinear algebraic equations for linearization coefficients is obtained using the frequency–response function matrix. Root mean-square response of maximum deflection of the beam that is obtained from the present technique is subsequently compared with that furnished by the conventional linearization. The numerical results show that the regulated stochastic linearization technique constitutes an excellent alternative to the classical linearization scheme for analyzing responses of the clamped–clamped beam.     

Buckling reliability evaluation of a clamped beam with random imperfections subjected to axial impact using probability density evolution method

Based on the generalized probability density evolution theory, the joint probability density function of impact responses and random factors, that is, random initial imperfection and load intensity for a clamped beam, is derived. And a Total Variation Diminishing (TVD)-based numerical scheme is employed to obtain the numerical solutions. With given threshold values, the dynamic reliability is assessed in terms of a bilateral displacement criterion. Two numerical examples are then presented to demonstrate the proposed method. One is a clamped beam with random initial perfections subjected to a deterministic impulse load, and another is a clamped beam with a deterministic initial imperfection subjected to impact loading with a random amplitude. The predicted dynamic reliability is in good agreement with the result by Monte Carlo method.     

Elasticity solution of clamped-simply supported beams with variable thickness

This paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differefitial equations and the boundary conditions attwo ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated.     

Determination of the complex shear modulus of structural adhesives using a doubly clamped sandwich beam

A method is described for calculating the complex shear modulus of structural adhesives from dynamic test data on a doubly clamped sandwich beam in which the adhesive is contained as a thin layer. The accuracy of the technique is validated by finite-element analysis. Values of modulus obtained using the doubly clamped beam technique are found to be in excellent agreement with values obtained from dynamic tests on bulk specimens of an epoxy adhesive.     

矩形板屈曲问题的一个小波解

利用Wavelet-Galerkin法分析了四边固支与四边简支矩形板的屈曲问题.以小波作为基函数表示板的挠度,推导出屈曲系数及屈曲模态的计算过程.数值计算给出了不同边长比的矩形板的屈曲系数及屈曲半波数.与传统的三角函数作基函数的Galerkin法及有限元法结果比较,结果表明在一定条件下小波可以作为试函数解决结构力学的屈...     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅱ)—RECTANGULAR PLATES WITH TWO ADJACENT CLAMPED EDGES

In this paper,applying the method of reciprocal theorem,we give the distributions ofthe amplitude of bending moments along clamped edges and the amplitude of deflectionsalong free edges of rectangular plates with two adjacent clamped edges under harmonicdistributed and concentrated loads.     

Some observations in the vortex-turning behaviour of noncircular inclined jets

An experimental comparison was conducted for Re = 2,500, free elliptic and rectangular jets inclined at 30° and 60° along major or minor planes. Regardless of the jet base geometry, minor-plane inclined jets produced vortex roll-ups that remain inclined. In contrast, major-plane inclined jets produce significantly stronger vortex-roll-up turning behaviour. Interestingly, major-plane inclined rectangular jets exhibit strong vortex-overturning behaviour, where the vortex-roll-up inclination exceeds the 0° incline angle considerably. Vortex-turning extents and rates are compared between major-plane inclined elliptic and rectangular jets here and support present qualitative observations. Closer inspections reveal that the lack of axis-switching phenomenon in major-plane inclined rectangular jets allows vortex-overturning behaviour. In addition, jet centreline deflection is most sensitive in minor-plane inclined jets, where increasing the incline angle leads to a decrease and an increase in the elliptic and rectangular jet deflection, respectively.     

四边固支矩形薄板自由振动的哈密顿解析解

在哈密顿体系中利用辛几何方法求解了四边固支矩形薄板自由振动问题的解析解。首先,从基本方程出发,将问题表示成Hamilton正则方程,然后利用辛几何方法导出本征值问题,从而得到本征函数解,使之满足边界条件;再由方程组有非零解的条件,最终推导出四边固支矩形薄板的自振频率方程,得到频率的解析解。计算了不同长宽比情况下四边固支矩形薄板的频率,结果与已有文献完全一致。该解法有望推广至更多尚未得到解析解的矩形板的振动问题。