Stress analysis of flexible noncircular cylindrical shells with hinged edges for different critical loads

An analytic nonlinear boundary-value solution is found and used in analysis of the precritical and postcritical stress states of a flexible long cylindrical shell with variable curvature and hinged longitudinal edges under nonuniform loading __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 43–50, February 2006.     

考虑固体域几何非线性的固液耦合系统瞬态有限元分析

本文基于理想可压缩流体压力传输方程及增量型ＴｏｔａＩＬａｇｒａｎｇｉａｎ列式，建立了考虑固体域几何非线性的固液耦合系统有限元方程，并开展了非线性分析工作。本文的方法可用于流体域远大于固体域，从而可仅仅研究固体域非线性响应的情况。由于流体域每个节点仅有一个未知量（压力），故流体域的计算规模得以大大减缩。同时，因为本文方法仅需对固体域进行非线性分析，故显著地简化了固液耦合非线性问题的求解工作。本文的方法亦可用于三维分析。     

Nonlinear deformation of a particulate material in complex stress state

An algorithm is proposed to determine the effective deformation properties and stress-strain state of particulate composite materials with physically nonlinear components and complex stress state. The laws that govern the deformation of particulate composites are studied. A particulate composite is considered a two-component material of random structure. Its effective properties are determined by conditional averaging. The nonlinear equations that incorporate the physical nonlinearity of the components are solved by the method of successive approximations. The relationship between macrostresses and macrostrains is established. The effective deformation properties of a particulate composite as a function of the volume fractions of the components and stress state are studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 50–60, March 2006.     

初曲矩形薄板的非线性动力屈曲研究

对两参数冲击载荷面内压缩作用下初曲矩形薄板的非线性动力屈曲问题进行了理论研究。首先采用双重余弦函数的组合确定了面内冲击矩形薄板的艾雷应力函数和中面力的分布；其次根据伽辽金法求得了初曲矩形薄板非线性动力屈曲问题的控制方程，基于巴拿赫压缩映象原理，采用逐次逼近方法求解了该控制方程。最后，应用本文发展的理论，给出了面内两参数冲击载荷作用下初曲矩形薄板动力屈曲响应的计算实例，计算结果与已有的实验结果较吻合     

Dynamic modeling and modal truncation approach for a high-speed rotating elastic beam

Summary  In the classical finite element analysis of beams, the nonlinear terms of deformation are ignored due to the linearization of deformation based on the assumptions of structural dynamics. Since the number of generalized coordinates is large in flexible bodies when using the finite element method (FEM), the modal truncation approach (MTA) is usually used for improving computational efficiency, and only lower-order transverse modes are chosen. In this paper, dynamic modeling and application of the MTA to a high-speed rotating beam are studied. The foreshortening displacement is included in the longitudinal displacement, therefore the dynamic modeling takes account of the effect of geometric nonlinearity. Equations of a rotating beam are obtained and the FEM and MTA are used for discretization. The applicability of the MTA to a high-speed rotating elastic beam is verified. The comparison of the results obtained by the FEM and MTA shows that in the case of a high-speed rotation, the centrifugal force can excite high-order transverse modes. Since using lower-order transverse modes for modal truncation obviously can cause error, addition of more transverse modes may improve the result. Furthermore, a coupling effect between axial and transverse displacements is revealed. It is shown that in the case of a sudden change of the axial displacement, the inclusion of the axial modes can significantly improve the response. Received 10 April 2001; accepted for publication 26 March 2002 This work was supported by the National Science Foundation of China (19832040) and the National Education Ministry of China (2000024818), for which the authors are grateful.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.     

An experimental and analytical study of autoparametric resonance in a 3DOF model of cable-stayed-beam

Autoparametric interaction and the associated phenomenon of amplitude saturation are experimentally observed in a physical model of cable-and-beam structure. In this system, the horizontal beam is fixed at one end and supported at the other end by an inclined taut cable. The longitudinal axes of beam and cable are in a vertical plane. Three natural frequencies of the system are approximately of the ratio 1:1:2. This is a combination of two conditions that are very likely to occur in relatively long-span, multi-stay-cable bridges, namely, 1:1 tuning and 1:2 superharmonic tuning. While the beam is vertically excited with sufficiently large force near a primary resonance, the cable vibrates horizontally at half of excitation frequency. The beam also vibrates horizontally at half-frequency, as well as vertically. As the vertical excitation on the bean is further increased in amplitude, the vertical vibration amplitude gets saturated instead of increasing proportionately. A 3DOF analytical model of the structure is also derived, where the finite motion of the cable introduces geometric nonlinearities in quadratic and cubic forms. The system parameters having been carefully measured from the experimental model, steady-state solutions of the coupled nonlinear equations of motion are obtained, by the perturbation method of multiple time scales. Agreement between experimental observation and analytical prediction is very good, both qualitatively and quantitatively. Very good agreement is found also in the case of horizontal excitation of the beam, where effects of linear and nonlinear interaction are apparent.     

The equations of an inverted pendulum with an arbitrary number of links and an asymmetric follower force

This paper formulates a problem for and gives the differential equations of plane-parallel motion of an inverted n-link pendulum subject to an asymmetric follower force applied at the upper end via a spring. The physical nonlinearities of springs are taken into account. The possible mechanisms of energy dissipation are described __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 106–114, May 2007.     

Vibration control of piezoelectric beam-type plates with geometrically nonlinear deformation

This paper presents a wavelet-based approach of deformation identification and vibration control of beam-type plates with geometrically nonlinear deflection using piezoelectric sensors and actuators. The identification is performed by transferring the nonlinear equations of identifying deflection into a system of solvable nonlinear algebraic equations in terms of the measurable electric charges and currents on piezoelectric sensors. After that, a control law of negative feedback of the identified signals of deflection and velocity is employed, and the weighted residual method is chosen to determine control voltages applied on the piezoelectric actuators. Due to that the scaling function transform is like a low-pass filter which can automatically filter out high-order signals of vibration or disturbance from the measurement and the controller employed here, this control approach does not lead to the undesired phenomenon of control instability which is generated by the spilling over of high-order signals. Finally, some numerical simulations are carried out to show the efficiency of the proposed approach.     

弹性地基上间断中厚矩形板的非线性静力分析

研究弹性地基上带传力杆的间断中厚矩形板的非线性静力特性。荷载在传力杆中的传递由竖向弹簧模拟,其弹簧刚度取决于传力杆的特性以及杆与板间的相互作用。根据能量变分原理,考虑地基耦合效应,建立了双参数地基上带传力杆的间断矩形中厚板的非线性静力控制方程。构造出一组满足所有边界条件的试探函数,应用伽辽金法对该组非线性方程进行求解。数值算例中,讨论了传力杆参数、板的结构参数及地基参数对弹性地基上间断矩形中厚板的非线性静力特性的影响。