Post-buckling of cantilever columns having variable cross-section under a combined load

Post-buckling of a cantilever column is examined under a combined load consisting of a tip-concentrated load and a distributed axial load, through dynamic formulation. The formulation of the problem is based on the moment–curvature relationship. The two-point boundary value problem described by the governing equations is dependent on the frequency parameter and the two load parameters. The buckling loads are those loads at which the eigencurve, namely, the load versus frequency curve of the column meets the load axis. A simple and reliable iterative procedure to convert the two-point boundary value problem into an initial value problem is followed and solved the non-linear differential equations utilizing a fourth-order Runge–Kutta integration scheme. To demonstrate the potentiality of the adopted numerical scheme, linear vibration frequencies of truncated, tapered cantilever wedges and cones are determined and compared with the published analytical and test results. Buckling and post-buckling loads of a simply supported stepped column are obtained and compared with the published test results. The loads and deflections of non-uniform cantilever columns are obtained for various slopes at the tip. The interaction of load parameters for a free–free truncated conical column has also been examined. The numerical results indicate that the path represented by the two load parameters turns out to be nearly a straight line.     

轴心受压H型截面钢柱火灾行为的试验研究

本文对4根H型截面钢柱进行了火灾行为的试验研究。全部火灾试验采用自行研制的火灾试验炉,试验结果表明炉子性能稳定,使用方便。试验采用足尺试验形式,柱长3300mm。钢柱轴心受压,其中两个限制轴向变形,另两个不限制轴向变形。柱两端采用单向刀口支座,允许钢柱绕强轴转动。钢柱试验中考虑荷载大小和是否限制轴向变形两个因素。通过试验,得出了钢柱在火灾下的侧向变形和轴向变形随温度变化情况。试验证明:钢柱受火时,轴向变形明显的分为膨胀阶段和压缩阶段。压缩阶段很短,一旦进入压缩阶段,钢柱很快破坏。钢柱受到的外加荷载越大,其极限温度越低。限制轴向变形的钢柱极限温度降低。试验研究为今后钢结构火灾行为研究提供了依据。     

Estimating deflection of a simple beam model using fiber optic bragg-grating sensors

In this paper, we develop a method to estimate the bridge deflection using fiber optic Bragg-grating (FBG) strain sensors. For most structural evaluation of bridge integrity, it is very important to measure the geometric profile, which is a major factor representing the global behavior of civil structures, especially bridges. In the past, because of the lack of appropriate methods to measure the deflection curve of bridges on site, the measurement of deflection has been restricted to just a few discrete points along the bridge, and the measuring points have been limited to the locations installed with displacement transducers. However, by applying classical beam theory, a formula is rearranged to estimate the continuously deflected profile by using strains measured directly from several points. In addition, FBG strain sensors, which are electromagnetic, noise-free and multipoint measurable, are employed to obtain flexural strains more accurately and stably. The regression analysis is performed to obtain a strain function from the measured strain data. Finally, the deflection curve can be estimated by applying the strain function to the formula. An experimental test has also been carried out to verify the developed method.     

梁中非线性弯曲波传播特性的研究

研究了梁中的非线性弯曲波的传播特性，同时考虑了梁的大挠度引起的几何非线性效应和 梁的转动惯性导致的弥散效应，利用Hamilton变分法建立了梁中非线性弯曲波的波动方程. 对该方程进行了定性分析，在不同的条件下，该方程在相平面上存在同宿轨道或异宿轨道， 分别对应于方程的孤波解或冲击波解. 利用Jacobi椭圆函数展开法，对该非线性方程进行 求解，得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解，讨论了这些解存 在的必要条件，这与定性分析的结果完全相同. 利用约化摄动法从非线性弯曲波动方程中导 出了非线性Schr\"{o}dinger方程，从理论上证明了考虑梁的大挠度和转动惯性时梁中存在 包络孤立波.     

简支梁振台的理论解及位移测试

利用由机械振动理论推导出的等截面简支梁的理论解,推导出了带集中质量的简支梁振动台的理论解,并通过分析动态条件下简支梁的位移与应变之间的关系,证明了:在动态条件下梁的位移与应变之间存在很好的正比关系。利用梁的位移与应变之间正比关系,如果在梁上适当位置粘贴应变片,通过测试应变就能准确地测得梁的动态位移。本文通过实例证明了该方法确实可行,理论解与实测结果非常吻合。这为简支梁的动态测试提供了有效而简便的方法。     

From crack deflection to lattice vibrations—macro to atomistic examination of dynamic cleavage fracture

A set of cleavage experiments with strip-shaped single-crystal silicon specimens subjected to three-point bending is reported. The experiments enabled examination of the relationships between the dynamic energy release rate, the velocity, the orientation-dependent cleavage energy, and the cleavage plane of propagation.Dynamic crack propagation experiments show that when a [0 0 1] silicon single crystal is fractured under three-point bending at ‘parallel’ velocity (directly measured at the bottom surface of the specimen) of up to , it prefers to cleave along the vertical (1 1 0) plane, while when the specimen is fractured under the same conditions but at a velocity higher than , it cleaves along the inclined (1 1 1) plane. At intermediate velocities, the crack will deflect from the (1 1 0) plane to the (1 1 1) plane. Crack velocity was determined by the initial notch length. The local (calculated) velocity of deflection between the cleavage planes ranges from , for a crack propagating on the (1 1 0) plane in the direction, to about , for a crack on the (1 1 0) plane, but in the [0 0 1] direction.It is suggested that the cause of the deflection phenomenon is the anisotropic, velocity-dependent cleavage energy, resulted phonon radiation caused by anisotropic, velocity-dependent lattice vibrations. We have studied the effect of material properties and propose selection criteria to explain the deflection phenomenon: the crack will deflect to the plane of least-energy, for which G−Γ_i(V)=max, or to the plane with maximum crack tip velocity, V_i(Γ)=max.     

Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate

Based on the von Karman plate theory of large deflection, we have derived a non-linear partial differential equation for the vibration of a thin orthotropic plate under the combined action of a transverse magnetic field and a transverse harmonic mechanical load. The influence of the magnetic field is due to the magnetic Lorentz force induced by the eddy current. By employing the Bubnov-Galerkin method, the non-linear partial differential equation is transformed into a third-order non-linear ordinary differential equation. The amplitude-frequency equations are further derived by means of the multiple-scale method. As numerical examples for an orthotropic plate made of silver, the influence of the magnetic field, orthotropic material property, plate thickness, and the mechanical load on the principal resonance behavior is investigated. The higher-order effect and stability of the solution are also discussed.     

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.     

Numerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing

This article presents numerical simulations of the limit-cycle oscillation (LCO) of a cropped delta wing in order to investigate the effects of structural geometric and material nonlinearities on aeroelastic behavior. In the computational model, the structural part included both the geometric nonlinearity that arises from large deflections, and the material nonlinearity that originates from plasticity. The Euler equations were employed in the fluid part to describe the transonic aerodynamics. Moreover, the load transfer was conducted using a 3-D interpolating procedure, and the interfaces between the structural and aerodynamic domains were constructed in the form of an exact match. The flutter and LCO behaviors of the cropped delta wing were simulated using the coupling model, and the results were compared with existing experimental measurements. For lower dynamic pressures, the geometric nonlinearity provided the proper mechanism for the development of the LCO, and the numerical results correlated with the experimental values. For higher dynamic pressures, the material nonlinearity led to a rapid rise in the LCO amplitude, and the simulated varying trend was consistent with the experimental observation. This study demonstrated that the LCO of the cropped delta wing was not only closely related to geometric nonlinearity, but was also remarkably affected by material nonlinearity.     

关于亚纯函数增长级的一个注记

研究了无穷级亚纯函数f与亚纯函数g在某个角域上具有分担集S = {a1,a2,a3}的增长级关系.