Bilinear Characteristics Research Articles

Approximate analytical determination of vibrodiagnostic parameters of the presence of a crack in an elastic body under superharmonic resonance

We discuss an approximate analytical method for calculating the main parameter of nonlinearity of vibration of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force, under a strong 2nd-order superharmonic resonance.

菱刈鉱山におけるＳｕｂｌｅｖｅｌ Ｏｐｅｎ Ｓｔｏｐｉｎｇ（ＳＬＯＳ）導入に関する研究

The Hishikari Mine is the only major gold mine operating in Japan, whose production rate in 2008 was around 184,000 tonnes with the average gold grade of 42.8 g/t. The gold veins are extracted mainly by drifting and bench stoping with backfill. Blasted waste rocks are generally used as backfill materials and crushed waste rocks with cement (cemented rock fill) are used for larger stopes. In order to extract the KE-2 vein with wider mineralization and lower grade, being closely located to the narrower KE-3 vein with higher gold grade, we have studied the applicability of the sublevel open stoping (SLOS) with cemented rock fill through in-situ measurements of rock mass displacements and numerical stress analyses for evaluating the stability of the KE-2 large SLOS stopes and interaction with the KE-3 bench stopes.We have used a bi-linear stress-strain characteristics of backfill for modeling the nonlinear compaction of cemented rock fill, whose stiffness increases with wall displacements of the backfilled stopes. The non-linear compaction may affect support characteristics of backfill, the present paper, therefore, incorporates the two-stage/bi-linear compaction modeling of backfill in FLAC3D in order to analyze the supporting effects of the cemented rock fill and to investigate the required backfill quality and mining sequence for more stable and steady operations of the KE-2 and KE-3 stopes.

The Bilinear Characteristics of Muscle-Skeletomotor System and the Application to Prosthesis Control

The Bilinear Characteristics of Muscle-Skeletomotor System and the Application to Prosthesis Control

Physical characteristics of polyimide films for flexible sensors

Physical characteristics of polyimide films, including optical, micro/nano mechanical, and thermophysical characteristics were investigated using a photometric, a nanoindentation, and a thermomechanical analyzer for applications in flexible sensors. Experimental results show that UV light cannot transmit into the polyimide films. The transmittances, with a maximum of about 86%, at VIS and near IR lights decrease with increasing PI film thicknesses. The mechanical characteristics were determined using tensile, bending moment, and nanoindentation testing. The stress–strain curve approximated bilinear characteristics, the load–unload bending moment exhibited hysteresis, and nanoindentation generated elastic energy dissipation in the loading–unloading region. Nanoindentation showed an almost uniform hardness and a reduced Young’s modulus of about 0.181±0.03 and 3.21±0.06 GPa, respectively, when the penetrating depth was more than about 2 μm. Thermophysical characteristics were greatly influenced on 8.3 and 25 μm specimens due to the higher relaxation of thin PI films. The thermal expansion remained steady when the thickness was over 50 μm. The results show that PI films have potential in flexible sensing and higher temperature fabrication.

Implementing broadcast encryption scheme using bilinear map and group characteristic

This paper introduced a novel method for implementing broadcast encryption. Our scheme takes advantages of bilinear map and group characteristic, and shifts most of the storage overhead to the public device instead of storing in the tamper-proof device which is a major problem on current implementation. Furthermore, the broadcast keys in our scheme could be reused periodically resulting in more operational efficiency.

Seismic base‐isolation by use of a telescoping stepping mechanism

AbstractA new base‐isolation mechanism corresponding to a variance of the stepping A‐shaped frame is proposed and its seismic performance is investigated numerically for strong ground accelerations with peak values in the range from 0.5 to 1g. In its simplest two‐dimensional form, the system consists of a frame with two telescoping legs pinned at the apex at a sharp angle. The legs are attached to the foundation through a spring and a damper acting in parallel. Both the springs and viscous dampers have bilinear characteristics that make them very stiff in compression but very soft in tension. As the structure rocks sideways, the length of the loaded leg remains essentially constant while the length of the unloaded leg increases. When the ground acceleration changes direction, the process is reversed. The resulting system has three main characteristics: (i) as the structure steps on a rigid leg, the maximum acceleration that can be transmitted to the superstructure is limited to a value which is approximately independent of the amplitude of the ground motion; (ii) there is a systematic lifting of the superstructure with kinetic energy being systematically transformed into potential energy during the strong phase of the ground motion; and (iii) the system is slowly self‐centering at the end of the earthquake. The seismic performance of the system is evaluated for a tall bridge pier and for a smaller frame that could be used in a multi‐story building. The results obtained for the 1940 El Centro ground motion scaled to 1g and for the near‐field Rinaldi ground motion recorded during the Northridge earthquake show that substantial reductions of the absolute acceleration can be obtained with reasonable relative displacements of the superstructure and small strokes in the isolation devices. Copyright © 2004 John Wiley & Sons, Ltd.

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 1. Available and Proposed Methods of Solution

The paper discusses the available analytical methods and the results of investigation of vibrations of elastic bodies with a bilinear asymmetric characteristic of restoring force that simulates the behavior of a local discontinuity in a material in the form of a closing fatigue crack. An approximate analytical method is put forward for the determination of vibrodiagnostic parameters of the vibration process of the nonlinear system under study in the range of weak superharmonic resonances.

BISPECTRAL ANALYSIS OF THE BILINEAR OSCILLATOR WITH APPLICATION TO THE DETECTION OF FATIGUE CRACKS

Damage detection by means of non-destructive testing plays an important role in ensuring the integrity of machine elements and structures. Vibration testing is an effective means of detecting crack development in structures. In this paper the effect of crack closure on the dynamic behaviour of cantilever beams is studied. Since the crack opens or closes depending on the direction of the vibration, the beam exhibits bilinear characteristics. The aim of the paper is to analyze the system response by using bispectral analysis which forms a subset of higher order statistical analysis. The study has been conducted both on simulated and experimental vibration signals. Firstly, a simplified model is employed to simulate the bilinear behaviour of a beam with a closing crack. The model is an oscillator with a bilinear restoring forcing function. The analysis of the forced vibrations of the model is performed by means of the harmonic balance method showing the occurrence of harmonics in the response spectrum which are strictly related to the bilinear nature of the model. Moreover, an experimental test carried out on a straight beam with a fatigue crack is presented. The beam is excited with white noise by means of a vibration shaker. The bispectral analysis performed both on the model and the actual structure shows high sensitivity of the non-linear behaviour of the system: that is to say, to the presence of the fatigue crack in the structure. In particular, the interactions between the frequency components contained in the signal response are analyzed. The results provide a possibility of using the bispectral analysis technique to detect damages in structures.

Characteristic Methods in Thick Diffusive Problems

The performance of characteristic methods (CMs) on problems that contain optically thick diffusive regions is analyzed and tested. The asymptotic analysis holds for moment-based characteristics methods that are algebraically linear; for one-, two-, and three-dimensional Cartesian coordinate systems; and for arbitrary spatial grids composed of polygons (two dimensions) or polyhedra (three dimensions). The analysis produces a theory that predicts and explains how CMs behave when applied to thick diffusive problems. The theory predicts that as spatial cells become optically thick and highly scattering, CMs behave almost exactly like discontinuous finite element methods (DFEMs). This means that there are two classes of CMs: those that fail dramatically on thick diffusive problems and those whose solutions satisfy discretizations of the correct diffusion equation. Most CMs in the latter set behave poorly in general, sometimes producing oscillatory and negative solutions in thick diffusive regions. However, the analysis suggests that certain reduced-order CMs, which use less information on cell surfaces than is readily available, will behave more robustly in thick diffusive regions. The predictions regarding standard CMs are tested by using the linear and bilinear characteristics methods on several test problems with rectangular grids in x-y geometry. The predictions regarding reduced-order CMs are tested by solving x-y test problems on triangular grids using a CM that employs linear functions for cell-interior sources but constants for cell-surface fluxes. In every case the numerical results agree precisely with the predictions of the theory.

Principles of localization in the fracture of quasi-brittle structures

Comparisons between elastic and dissipative truss-like models for systems with bilinear constitutive characteristics reveal useful analogies for computation. In particular, where localization and unloading are concerned, interpretation of a dissipative system in elastic terms generates a global potential function embracing many possible equilibrium states. We invoke the Maxwell stability criterion, based on global rather than local minima of energy, to determine the most likely outcome. Models in one and two dimensions are developed to explore in detail the analytical implications.

Impact Damper with Granular Materials Applied to Self-Induced Vibration.

A simple yet efficient shot impact damper consists of a bed of granular materials in a container mounted on a primary vibrating system. We have studied the performance of the shot impact damper which is applied to some kinds of vibrating systems subjected to harmonic excitations. This study clarifies the damping performance of the damper when applied to the self-induced vibration system with bilinear characteristics of friction force. The periodic motion of the self-excited vibration accompanied by the impact of the damper mass is determined by theoretical analysis as well as numerical simulation studies which utilize the Willson-θ method. The damping performances are obtained in terms of the damper parameters and self-excitations. The results show that heavier damper mass provides greater damping effect on the fully built-up vibrations, and that a lighter mass is effective at the onset of the vibration. Finally, we determined the optimum clearances under which the response amplitudes are reduced to a minimum for suppressing the vibrations.

Bilinear self-tuning control of a high temperature heat treatment plant

When dealing with industrial systems it is pertinent to consider extending the linear self-tuning framework to include a knowledge of inherent plant nonlinearities. In heat transfer processes, the nonlinearities that arise may be represented by bilinear characteristics. Indeed, when systems exhibit bilinear characteristics it is not unreasonable to consider accommodating the bilinearity into the model structure within an extended self-tuning control framework and, in this respect, novel bilinear self-tuning control strategies are proposed. This paper describes the development of novel bilinear self-tuning pole-placement and generalised predictive control strategies and reports on their effectiveness when applied to an industrial heat treatment furnace. To provide for a realistic comparison, the performances achieved using the bilinear schemes are compared to that achieved when use is made of an existing autotuned industrial PID controller; their respective performances are quantified in terms of a devised measure of effectiveness. The results are very encouraging and indicate that, by adopting the bilinear self-tuning approach, significant potential improvements over existing state of the art controllers are possible.

Mixed Extremum Principles for the Analysis of Trusses with Bilinear Force-Deformation Characteristics*

ABSTRACT Trusses composed of bars with specially formulated bilinear force-deformation characteristics proposed by Logo and Taylor are treated. Mixed extremum principles are derived, based on potential and complementary potential energy, to form the basis for a load history analysis of trusses. Through the choice of appropriate parameters of force-deformation relationships, the classical principles of linearly elastic and perfectly plastic structures can be obtained and the material and/or geometric nonlinearity, postbuckling behavior, and limited deformation capacity of the bars can be taken into consideration. The principles are stated in the form of a constrained, nonsmooth, nonlinear mathematical programming problem and provide a convenient tool for numerical analysis. Their application is illustrated by two numerical examples.

Fiber-Matrix Interface Effects in the Presence of Thermally Induced Residual Stresses

Analytical models are presented and used to explore the mechanics of transversely loaded, high-temperature composites with a thermally induced residual stress field and a vanishingly weak fiber-matrix interface strength. Of specific interest in this investigation is the existence of a distinctive, bilinear characteristic of the transverse stress-strain curve for composites of moderate fiber-volume fractions in which the coefficient of thermal expansion of the matrix is larger than the fiber and the interface strength is vanishingly weak. For such a system, it is found that the “knee” in the predicted transverse stress-strain curve separating the two linear response zones is associated with the load at which compressive residual stresses at the interface are overcome and separation of the matrix and fiber occurs. Before this “knee,” the transverse modulus of the “weak interface” model is predicted to be the same as for a well-bonded system. The effects of fiber and matrix properties, interface friction, and fiber-volume content are examined.

Efficient computation of network sensitivities

A class of methods for generating network functions and their sensitivities, when only one element is allowed to vary, is presented. This class of methods requires either two or three circuit analyses to obtain expressions for the network function and its first order, higher order, and large-scale sensitivities for all values of the variable component. The class of the two circuit analyses methods reduces moderately the computational effort and makes better use of circuit analysis data as compared to the previous methods which employ at least three circuit analysis. The results are applicable to network functions with bilinear characteristics and can be extended to the general class of bilinear systems.

Reliability Analysis of Structures under Seismic Excitation : 1st Report, Magnification Factor of Structures with Bi-Linear Characteristics

地震荷重下の構造物および構造物に取付けられた機器の破壊に対する信頼性を解析するために、大変形に伴う塑性変形の力学特性をBilinear形ヒステリシスで近似し、1自由度、2自由度モデルに対して、フォッカーブランクの方程式を用いて応答を解析し、第2分枝剛性、入力地震波の振幅、系の固有振動数、地震波の卓越周期等の応答および応答倍率への影響を求め、それらの非線形性への影響を調べた。