On the Discretization of Distributed-Parameter Systems with Quadratic and Cubic Nonlinearities

Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance ( _n ) and subharmonic resonance of order one-half ( 2 _n ), where is the excitation frequency and _n is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches.     

Determination of critical molecular weight for entangled macromolecules using the tensile strength data

The multivariable power dependence of polymer properties on molecular characteristics (Dobkowski, 1981) has been applied to molecular weight dependence of tensile strength, and the known equation of Flory (1945) has been extended taking polydispersity of polymers into account. Constant parameters of the relevant regression equations have been calculated using experimental data on tensile strength and molecular weight averagesM _n andM _w of polystyrene (PS) and polycarbonate (PC). Then, the critical molecular weight for entanglementsM _c has been obtained from the following relationship:A=K M _cwhereA and are parameters of the extended Flory equation for the tensile strength, and the constantK = 2 is assumed for linear polymers. It has been found thatM _c of injection and compression moulded PS is equal to 34000 and 37350g/mole, respectively, whileM _c of injection moulded PC equals to 5000 g/mole. The values ofM _c calculated from the polymer tensile strength are consistent with published data obtained by other methods and with the computer modeling calculations. Branched polymers have only qualitatively been discussed. Dimensionless equations have been proposed for tensile strength characteristics for polymer materials.The described procedure can be suggested as applicable to various polymers for the determination of theirM _c values. However, more experimental data on another polymer materials will be necessary to support hitherto obtained results.The essential part of a lecture presented during the NATO Advanced Study Institute Rheological Fundamentals of Polymer Processing, Alvor, Portugal, 26 September–7 October 1994     

Nonlinear analysis of the forced response of a beam with three mode interaction

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies,_n . Three mode interaction (₂ 3₁ and _{3 1} + 2₂) is considered and its influence on the response is studied. The case of two mode interaction (₂ 3₁) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.     

不连续岩石梁的失稳解析

本文根据不连续岩石梁的物理力学特性提出了无拉力岩石梁的力学解析模型。根据Ｆｒｅｅｂｏｄｙ法及Ｃａｓｔｉｇｌｉａｎｏ定量导出了不连续梁各物理量的求解方程式。进而采用挠度增量δｍａｘ＾ｉ＋１＝δｍａｘ＾ｉ＋Δδ↑－的逐次解析方法，求解了不连续梁的失稳问题，得出了与Ｆ．Ｄ．Ｗｒｉｇｈｔ的试验值相吻合的结果。探讨了不连续岩石梁在不同荷载条件下的失稳特性。     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS (Ⅱ)

When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H ∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H ∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part (Ⅰ)of the paper. The modal synthesis method for computation of the optimal H ∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).     

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。     

Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise

Geometrically non-linear deformation of axially extensional Timoshenko beams subjected mechanical as well thermal loadings were characterized by a system of 7 coupled and highly non-linear ordinary differential equations, which results in a complicated two-point boundary-value problem. By using shooting method this kind of problem can be numerically solved efficiently. Based on the above-mentioned mathematical formulation and numerical procedure, analysis of large thermal deflections for Timoshenko beams, subjected transversely non-uniform temperature rise and with immovably pinned–pinned as well as fixed–fixed ends, is presented. Characteristic curves showing the relationships between the beam deformation and temperature rise are illustrated. Especially, the effects of shear deformation on the bending and buckling response are quantitatively investigated. The numerical results show, as we know, that shear deformation effects become significant with the decrease of the slenderness and with the increase of the shear flexibility.     

断层活动性评价中关于测年资料的引用

断层活动性评价是研究区域构造稳定性的基础,它直接影响到水工建筑物本身的抗震安全。目前,对于断层活动性评价较常用的方法就是有关断层样品的年龄测试,这是比较直观的定量方法之一。但由于测年方法有多种,同一样品用不同的测年方法测得的结果有时偏差很大,哪种结果更为可靠始终是众多学者所关心的问题。本文对在水利水电工程断层活动性评价中关于断层年龄引用方面存在的一些问题进行探讨,并结合溪洛渡工程对研究区的马边—盐津断裂、莲峰断裂和金阳断裂进行了断裂活动性分析与评价。     

岩爆与围岩分类

岩爆是高地应力条件下完整脆性硬质围岩失稳的一种表现型式,岩爆烈度如何影响围岩类别尚不清楚,探索岩爆与围岩分类的关系,对准确判别高地应力条件下的围岩类别有着重要意义。本文以某深埋隧洞围岩分类为依据,对我国水利水电地下洞室围岩分类中岩爆烈度与围岩类别的关系、岩爆判别指标的选取等问题进行了探讨。     

纤维板增强钢筋砼缺口梁承载力试验研究

通过对8组24根碳纤维薄板增强钢筋混凝土梁进行三点弯曲试验，探讨碳纤维薄板增强钢筋混凝土缺口梁的破坏过程、极限承载力及其影响因子．研究结果表明：1)碳纤维薄板增强钢筋混凝土缺口梁总是沿着纤维薄板与混凝土的界面发生剥高破坏；2)与无增强梁相比，增强梁的极限来载力可以提高20％一40％．而且当纤维薄板贴长Lc与两支点间距离S之比为0．57左右时增强效果最明显；3)缺口对梁的破坏模式影响较大，而对梁的极限承载力影响不大(下降10％-15％)．