The influence of preform on the modes of vibrating beams

A theoretical analysis is presented of a vibratory system in which it is possible to eliminate an unwanted mode of vibration by using that mode as an initial deformation of the system. The analysis shows that this is possible in straight beams with end restraints in axial deformation. The mathematical problem leads to an eigenvalue problem of a type not normally encountered. In the paper examples are given for the changes in eigenfrequency and mode shape produced by the initial preformed shape of the beam for cases where the preform is proportional to a mode of the straight beam and when the preform is unrelated to any mode. The analysis shows that, while elimination of a mode in the strict sense is not achieved, the results can be interpreted for practical purposes in this way.     

Axisymmetric seismic response of a thick circular plate supporting many rods by modal synthesis

Dynamic response of a thick, horizontal, circular plate supporting a large number of slender rods subjected to uniform boundary motion in the vertical direction has been studied by synthesizing component modes of continuous substructures. The excitation considered corresponds to the vertical component of boundary movement produced by earthquake disturbances and the axisymmetric response problem was solved. Mindlin theory was used to formulate the component equations of the plate which is treated as the main component in a modal synthesis technique. The slender rods, which are attached vertically to the plate, are handled as branch components. Vibration modes of a classical thin plate were used as the initial displacement functions for the Mindlin plate. These functions were subsequently modified by a component mode improvement process to obtain plate modes. System modes were generated by combining the improved plate modes with component modes of rods. Numerical results for the natural frequencies and time-history response of the coupled system are compared with those given by a three-dimensional finite element method.     

Natural frequencies and modes of rhombic mindlin plates

The natural frequencies and mode shapes of thin and moderately thick rhombic plates are obtained using a 9-noded Lagrangian quadrilateral isoparametric plate element based on Mindlin's theory. The effects of rotatory inertia are included. Plates with a wide range of skew angles and boundary conditions are considered and wherever possible the present results are compared with earlier published work.     

Seismic design and testing of buckling‐restrained braces with a thin profile

A thin‐profile buckling‐restrained brace (thin‐BRB) consists of a rectangular steel casing and a flat steel core that is parallel to a gusset plate. A thin configuration reduces the width of the restraining member and thus saves usable space in buildings. However, deformable debonding layers, which cover the steel core plate in order to mitigate the difference between the peak tensile and compressive axial forces, provide a space for the steel core to form high mode buckling waves when the thin‐BRB is under compression. The wave crests squeeze the debonding layers and produce outward forces on the inner surface of the restraining member. If the restraining member is too weak in sustaining the outward forces, local bulging failure occurs and the thin‐BRB loses its compression capacity immediately. In order to investigate local bulging behavior, a total of 22 thin‐BRB specimens with a ratio of steel core plate to restraining steel tube depth ranging from 0.3 to 0.7 and axial yield force capacities ranging from 421 kN to 3036 kN were tested by applying either cyclically increasing, decreasing, or constant axial strains. The restraining steel tube widths of all the specimens were smaller than 200 mm and were infilled with mortar with a compressive strength of 97 MPa or 55 MPa. Thirteen of the 22 thin‐BRB specimens' restraining members bulged out when the compressive core strains exceeded 0.03. A seismic design method of the thin‐BRB in preventing local bulging failure is proposed in this study. Test and finite element model (FEM) analysis results suggest that the outward forces can be estimated according to the BRB compressive strength, steel core high mode buckling wavelength, and the debonding layer thickness. In addition, the capacity of the restraining member in resisting the outward forces can be estimated by using the upper bound theory in plastic analysis. Both the FEM analysis and test results indicate that the proposed method is effective in predicting the possibility of local bulging failure. Test results indicate that the proposed design method is conservative for thin‐BRB specimens with a large steel core plate to restraining steel tube depth ratio. This paper concludes with design recommendations for thin‐BRBs for severe seismic services. Copyright © 2015 John Wiley & Sons, Ltd.     

求解薄板频率特性的边界元法解析研究

根据弹性薄板理论和振动理论,运用边界元法(BEM)分析了薄板弯曲自由振动的频率特性,从薄板自由振动的微分方程式出发,采用动态基本解推导出其相应的边界积分方程式,计算中对边界积分方程进行缩减,应用频率扫描的方法研究薄板的动态特性,准确、有效地得到了其相应的固有频率、给出的数值算例证明了本文的方法简单、可行,且具有良好的解析计算精度。     

薄钢板剪力墙抗震性能试验研究

通过4个薄钢板剪力墙和1个钢筋混凝土框架的试验，研究了薄钢板剪力墙在低周往复荷载作用下的刚度、承载力、延性和耗能性能。试验表明，利用薄钢板剪力墙在低周往复荷载作用下的刚度、承载力、延性和耗能性能。试验表明，利用薄钢板剪力墙作为抗侧力构件是可行的。在钢筋混凝土框架中设置薄钢板可有效地增加刚度，承载力和耗能性能。     

Free vibration and transient response of thick and thin plates using the finite element method

An isoparametric quadrilateral plate bending element is used for the free and forced vibration analysis of both thick and thin plates. Plates of rectangular, circular and triangular planform are analysed and excellent results are obtained. The element performance is assessed by comparison with analytical solutions based on Mindlin's thick plate theory, three-dimensional elasticity solutions and solutions based on thin plate theory.     

On stochastic near-critical oscillations in the upper mantle

The problem of the determination of thermomechanical conditions in the upper mantle under a moving lithospheric plate at a given shear stress does not have a unique solution. Given a fixed heat flux from the lower mantle, two types of motion are possible in the mantle: subcritical (slower and colder) and supercritical (faster and hotter). In this work, it is shown that, if these modes are rather close to each other (in the near-critical state of the mantle), transitions from one mode to another and backward are possible. The calculated period of a change in the mantle state amounts to ～0.3 Myr for the Pacific plate. The oscillatory regime of the mantle state can manifest itself in the activity pulsations of hotspots located near fast separating mid-ocean ridges.     

Why did Arabia separate from Africa? Insights from 3-D laboratory experiments

We have performed 3-D scaled lithospheric experiments to investigate the role of the gravitational force exerted by a subducting slab on the deformation of the subducting plate itself. Experiments have been constructed using a dense silicone putty plate, to simulate a thin viscous lithosphere, floating in the middle of a large box filled with glucose syrup, simulating the upper mantle. We examine three different plate configurations: (i) subduction of a uniform oceanic plate, (ii) subduction of an oceanic-continental plate system and, (iii) subduction of a more complex oceanic-continental system simulating the asymmetric Africa-Eurasia system. Each model has been performed with and without the presence of a circular weak zone inside the subducting plate to test the near-surface weakening effect of a plume activity. Our results show that a subducting plate can deform in its interior only if the force distribution varies laterally along the subduction zone, i.e. by the asymmetrical entrance of continental material along the trench. In particular, extensional deformation of the plate occurs when a portion of the subduction zone is locked by the collisional process. The results of this study can be used to analyze the formation of the Arabian plate. We found that intraplate stresses, similar to those that generated the Africa-Arabia break-up, can be related to the Neogene evolution of the northern convergent margin of the African plate, where a lateral change from collision (Mediterranean and Bitlis) to active subduction (Makran) has been described. Second, intraplate stress and strain localization are favored by the presence of a weakness zone, such as the one generated by the Afar plume, producing a pattern of extensional deformation belts resembling the Red Sea-Gulf of Aden rift system.     

Free vibrations of simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness and elastically restrained edges against rotation using Rayleigh-Ritz method

This paper addresses the free transverse vibrations of thin simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness with elastically restrained edges against rotati...     

用广义协调元分析复合式多层无孔和开孔矩形薄板的振动

复合式多层无孔和开孔矩形薄板是桥梁结构和建筑等结构中的最重要的组成部分。当研究它们的振动问题时,用解析法求解自振频率十分困难,而采用通用的有限元法求解自由度数目多,收敛也比较慢。本文利用三角形薄板广义协调元分析了复合式多层四边简支、四边固定无孔和开孔矩形薄板的自由振动,求出了前几阶频率系数,其结果与用ANSYS软件算出的结果基本接近,当为单层无孔和开孔板时,与文献[8]的结果完全相同,且与文献[10]的解析解吻合较好,证明了本文理论推导及程序编制的正确性,表明广义协调元与有限元相比具有自由度少、精度高、程序简便以及收敛快等优点。     

Thin layer element method for dynamic soil-structure interaction analysis of axi-symmetric structure in submerged soil

The three-dimensional thin layer element method is formulated for the dynamic response analysis of an axi-symmetric structure in submerged soil. Biot's wave equation for fluid-filled porous medium is used in the formulation. The three-dimensional thin layer element method computes the wave numbers and their associated mode shapes, for both Rayleigh waves and Love waves in submerged soil, which define the characteristics of the waves. The submerged condition affects the characteristics of the Rayleigh waves in soil. As a result, it alters substantially the soil-structure interaction stresses if the permeability of the soil is relatively large and, to less extent, the response of the structure. The thin layer element method is far more efficient than the finite element method for analyzing the fluid-filled porous medium, yet capable of taking into account a multi-layered inhomogeneous soil.     

拟协调四节点板弯曲单元在薄板振动分析中的应用

本文以文〔１〕构造的拟协调板弯曲单元为基础，横向剪切应变假设中采用沿厚度二次分布，将其应用于薄板固有振动分析，求解前ｎ阶固有频率，结果表明该单元具有良好的数值特性。     

开洞薄钢板剪力墙低周反复荷载试验研究

薄板墙的滞回曲线在零位移附近有零刚度现象,存在明显的捏缩效应,常规方法是直接采用中厚板或通过强大的加劲体系将薄板转化成中厚板,但这将降低薄板墙的经济性。通过两片开洞薄钢板墙低周反复荷载试验,系统地研究了开洞钢板墙的破坏过程和破坏机理,得到了承载力,侧移刚度,延性和耗能能力等指标。试验结果表明,开洞钢板墙有较高的承载力和侧移刚度,延性和耗能能力很好。开洞不仅可以满足门窗洞口等建筑需求,而且可以减小内填板宽度,调节内填板与框架的刚度比,避免薄板墙的捏缩效应,使构件有更高的安全储备,开洞钢板墙是一种理想的水平抗侧力构件。     

High‐mode buckling responses of buckling‐restrained brace core plates

Cyclic loading tests and finite element analyses on six novel all‐steel buckling‐restrained braces (BRBs) are conducted using different loading patterns to investigate the core plate high‐mode buckling phenomenon. The proposed BRB is composed of a core member and a pair of identical restraining members, which restrains the core member by using bolted shim spacers. The design of the proposed BRB allows the core plate to be visually inspected immediately following a major earthquake. If necessary, the pair of restraining members can be conveniently disassembled, and the damaged core plate can be replaced. Test results indicate that the proposed BRBs can sustain large cyclic strain reversals and cumulative plastic deformations in excess of 400 times the yield strain. Experimental and analytical results confirm that the high‐mode buckling wavelength is related to the core plate thickness and the applied loading patterns. The larger the axial compressive strain is applied, the shorter the high‐mode buckling wavelength would be developed. The buckling wavelength is about 12 times the core plate thickness when the high‐mode buckling shape is fully developed. However, it reduces to about 10 times the core plate thickness when a compressive core strain reaches greater than 0.03. The high‐mode bucking wavelength can be satisfactorily predicted using the proposed method or from the finite element analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Magneto-elastic shear waves in a conducting,infinite plate in vacuum

Summary The influence of an external magnetic field on the propagation of purely transverse waves polarized parallel to the plane faces in a homogeneous, initially unstressed, infinitely conducting, elastic flat plate extending to infinity has been investigated. We have found that such waves can be propagated only if the field is normal to the direction of polarization.The effects are of three fold depending on the inclination of the field to the direction of propagation. When the field is normal, it is to decrease the range of modes in which a disturbance of given frequency can be propagated; when parallel, it is to increase the velocity of each mode without decreasing the range of modes of propagation. In both these cases, the different modes can be classified into symmetric and anti-symmetric modes. In the general case, not only the phase velocity and the range of modes are affected over those of purely elastic case but the symmetric and anti-symmetric types of motion are coupled in every mode.     

重叠回线装置下有限导电薄板瞬变电磁响应的一种简化模型

在吸收前人提出的导电薄板等效电流回路模型概念的基础上,应用普通电磁学理论对其瞬变电磁法的过程作了完整的论述,并得到清晰明确的数学表达式,同时指出一次场关断时间与观测异常幅值的关系.在重叠回线装置下,模型解可进一步被简化.通过实例的具体数值计算过程,证明该简化模型为重叠回线装置下有限薄板类地质体瞬变电磁的定量分析提供了一个简捷有效的途径.     

Free vibration analysis of rectangular plates with cutouts allowing for transverse shear deformation and rotary inertia

The energy approach using the variational procedure in conjunction with the finite difference technique has been applied for the Mindlin theory dynamic analysis of rectangular plates with cutouts in which account is taken of the effects of both transverse shear deformation and rotary inertia. This study has clearly demonstrated that the discrepancy with the thin plate theory solutions increases with increasing values of thickness ratio β and the error due to the thin plate assumptions increases particularly for the higher modes. It is also concluded that the effect of a cutout becomes more pronounced as the thickness of the plate approaches the size of cutout.     

The mid-ocean ridge axial valley as a steady-state neck

In this paper the mid-ocean ridge axial valley is modelled as a steady-state lithospheric neck in which lithospheric stretching balances lithospheric accretion. Conversely, the axial high is a steady-state lithospheric bulge. The lithosphere is modelled as a thin plate with a Newtonian rheology. It is shown that an axial valley will occur if the rate of viscosity increase away from the ridge axis is faster than the rate at which accretion decreases. An axial high will occur if the opposite condition holds. This is consistent with the observation that axial valleys occur at low spreading rates and axial highs at high spreading rates. By fitting our model to profiles across the Mid-Atlantic Ridge and the East Pacific Rise and assuming the lithospheric thickness at the ridge axis to be 5 km, we find accretion widths of 6–8 km. We find the width over which there is a significant increase in lithospheric viscosity to be also 6–8 km.     

3-D Simulation of Steady Plate Subduction with Tectonic Erosion: Current Crustal Uplift and Free-Air Gravity Anomaly in Northeast Japan

Free-air gravity anomaly in plate subduction zones, characterized by island-arc high, trench low and outer-rise gentle high, reflects the cumulative effects of long-term crustal uplift and subsidence. In northeast Japan the island-arc high of observed free-air gravity anomaly takes its maximum about the eastern coastline. On the other hand, the current vertical crustal motion estimated from geological and geomorphological observations shows a gentle uplift in the land area and steep subsidence in the sea area with the neutral point near the eastern coastline. Such a discrepancy in spatial patterns between the free-air gravity anomaly and current vertical crustal motion can be ascribed to a change in the mode of crustal uplift and subsidence associated with the initiation of tectonic erosion at the North American-Pacific plate interface. We developed a realistic 3-D simulation model of steady plate subduction with tectonic erosion in northeast Japan on the basis of elastic/viscoelastic dislocation theory. Through numerical simulations with this model we found that simple steady plate subduction brings about the crustal uplift characterized by island-arc high with its maximum about the eastern coastline, while steady plate subduction with tectonic erosion, which is represented by the landward retreat of the plate interface, brings about gentle uplift in the land area and steep subsidence in the sea area with the neutral point near the eastern coastline. Therefore, if we suppose that tectonic erosion started 3–4 million years ago after the long duration of simple steady plate subduction, we can consistently explain both patterns of free-air gravity anomaly and current crustal uplift in northeast Japan.