Rectangular Steel Plate Research Articles

Use of Fiber-optic Strain Sensors and Holder Exponents for Detecting and Localizing Damage in an Experimental Plate Structure

The vibration-based structural health monitoring paradigm is predicated on the practitioner's ability to acquire accurate structural response data and then to use that information to infer something about the structure's health. Here the authors combine advances in both sensing and signal analysis and demonstrate the ability to detect damage in a simple experimental structure. A distributed network of nine fiber-optic strain sensors is used to acquire time series data from a rectangular steel plate where damage is considered as a cut of varying lengths. Both the sensors and the associated optical hardware are described. A new feature, Holder continuity, is then introduced as a means of identifying the presence and location of the cut length. This particular metric is derived from the field of nonlinear dynamics and is based on a phase space description of a structure's dynamic response. Specifically, the authors compute the Holder exponent which quantifies the differentiability of the functional relationship between an ‘undamaged’ and a ‘damaged’ structural response. As damage is incurred, this relationship is expected to degrade. Both univariate and multivariate applications of the method are presented. The metric shows sensitivity to damage comparable to that exhibited by the plate's modal frequencies, a traditionally used feature in health monitoring applications.

20416 磁気浮上薄鋼板に対する浮上補助用永久磁石の最適配置に関する基礎的検討(材料力学(2))

In the thin steel plates which are used in many industrial products, including automobiles, flaws on the plate surface and peeling during the surface treatment process are induced due to the use of many rollers in the conveyance process. These flaws lead to the deterioration of the quality of the plate surface. To solve this problem, the authors proposed a device for controlled levitation of rectangular sheet steel by means of a hybrid actuator using five electromagnets and thirty permanent magnets. For fundamental consideration we have reported concerning the optimal placement of permanent magnets using free - free beam with 2 permanent magnets. In this study, we attempt to determine the optimal placement and number of a thin rectangular steel plate that reduce the deflection.

Array technology for bending wave field analysis in constructions

In this paper it is shown that array technology is an essential tool for the quantitative analysis of bending wave fields in elastic, solid constructions. The advantages can be compared with those of array-based acoustic wave field analysis in free air as well as in enclosed spaces. In contrast to acoustic waves, bending waves are highly dispersive, i.e., their propagation velocity depends strongly on frequency. A convolution operation is introduced as a preprocessing step, removing the dispersion from the bending waves, such that their propagation properties become highly similar to that of acoustic waves. After this transformation, multidimensional acoustic wave field analysis methods can be successfully applied to bending wave fields, using the large technology portfolio in acoustic imaging. The new analysis method is applied to simulated bending wave fields and to real measurements on a rectangular steel plate. The proposed method is demonstrated on bending wave fields, but it can be applied to any type of dispersive wave phenomenon.

Identification of welding residual stresses in rectangular plates using vibration responses(*)

A novel hybrid numerical/experimental identification procedure for the assessment of welding-induced residual stresses in rectangular plates is proposed and evaluated. This procedure explores the influence of the stress state on the dynamic responses of structural components, according to the so-named stress-stiffening effect. The technique consists in using a set of experimental natural frequencies of the welded plate and a mathematical model relating the residual stresses to the natural frequencies to formulate an optimization problem. The cost function represents the differences between the experimental and model-predicted dynamic responses and the design variables are interpreted as parameters of the mathematical model describing the stress distribution over the plate. A parameterized stress model suitable to the case of welding residual stresses is presented in terms of a differential equation that relates an Airy's stress function to the plastic strains resulting from the welding process. From this stress function, the stress components σx, σy and τxy (assuming plane stress state) are computed. Genetic Algorithms are used to solve the numerical optimization problem. To demonstrate the feasibility of the method, it is used for the assessment of residual stresses generated by TIG (GTAW) welding of a thin rectangular steel plate, for which experimentally measured natural frequencies and numerically computed residual stress distributions are available in the literature.(*) A preliminary version of this article has been presented in the 17th International Congress of Mechanical Engineering, promoted by Brazilian Society of Mechanical Sciences and Engineering, São Paulo, Brazil, 2003.

Damage detection using multivariate recurrence quantification analysis

Recurrence-quantification analysis (RQA) has emerged as a useful tool for detecting subtle non-stationarities and/or changes in time-series data. Here, we extend the RQA analysis methods to multivariate observations and present a method by which the “length scale” parameter ε (the only parameter required for RQA) may be selected. We then apply the technique to the difficult engineering problem of damage detection. The structure considered is a finite element model of a rectangular steel plate where damage is represented as a cut in the plate, starting at one edge and extending from 0% to 25% of the plate width in 5% increments. Time series, recorded at nine separate locations on the structure, are used to reconstruct the phase space of the system's dynamics and subsequently generate the multivariate recurrence (and cross-recurrence) plots. Multivariate RQA is then used to detect damage-induced changes to the structural dynamics. These results are then compared with shifts in the plate's natural frequencies. Two of the RQA-based features are found to be more sensitive to damage than are the plate's frequencies.

Controlling system dimension: a class of real systems that obey the Kaplan-Yorke conjecture.

The Kaplan-Yorke conjecture suggests a simple relationship between the fractal dimension of a system and its Lyapunov spectrum. This relationship has important consequences in the broad field of nonlinear dynamics where dimension and Lyapunov exponents are frequently used descriptors of system dynamics. We develop an experimental system with controllable dimension by making use of the Kaplan-Yorke conjecture. A rectangular steel plate is driven with the output of a chaotic oscillator. We controlled the Lyapunov exponents of the driving and then computed the fractal dimension of the plate's response. The Kaplan-Yorke relationship predicted the system's dimension extremely well. This finding strongly suggests that other driven linear systems will behave similarly. The ability to control the dimension of a structure's vibrational response is important in the field of vibration-based structural health monitoring for the robust extraction of damage-sensitive features.

INELASTIC BUCKLING OF RECTANGULAR STEEL PLATES USING A RAYLEIGH–RITZ METHOD

The paper presents a Rayleigh–Ritz based non-discretization method of analysis for the inelastic local buckling of rectangular steel plates subjected to applied in-plane axial, bending and shear actions with various boundary conditions. Use is made of the pb-2 representation of the displacement function as the product of a domain polynomial and a boundary polynomial. The constitutive model for the plate is an adaptation of the von Mises yield criterion and the associated flow rule presented in an infinitesimal form, and which leads to an incremental and iterative method of solution. The convergence and accuracy of the solutions are demonstrated, and it is shown that the method of analysis is computationally feasible for the solution of inelastic bifurcative plate instability problems. A parametric study is then undertaken for a range of plate boundary conditions under various regimes of applied loading.

DUCTILE STEEL CONNECTIONS FOR SEISMIC RESISTANT PRECAST BUILDINGS

Welded connections are extensively used by the precast concrete industry to ease construction. When the seismic resistance and ductility of a building incorporating precast concrete elements needs to be assured, the connections should be carefully designed and constructed to avoid undesirable structural performance. This paper discusses aspects related to an analytical and experimental programme conducted to investigate the response of a connection detail for coupling precast concrete walls in low to medium rise buildings. The connection consists of a rectangular steel plate with a concentric circular perforation. In this way, a weak but ductile link is introduced in the system. Using the principles of capacity design, the walls can be designed as if coupled and with energy dissipation taking place in the connection. Simplified expressions are presented to evaluate the shear stiffness and the yield and ultimate strength of the perforated steel plates, based on theory and the experimental data collected during the test.

Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions

Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads and under various boundary conditions is presented. Theoretical formulations are based on Reddy's higher order shear deformation plate theory and include the thermal effects due to temperature rise. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The temperature field considered is assumed to be uniform in the XY plane and through the plate thickness. The plate may be clamped or simply supported on two opposite edges with the remaining others being either free, simply supported or clamped. A semi-numerical approach, which makes use of multi-parameter perturbation technique , one-dimensional differential quadrature approximation and Galerkin method, is employed to calculate the nonlinear bending of the plates. Numerical results for silicon nitride/stainless steel rectangular plates are given in dimensionless graphical forms . The roles played by the constituent volume fraction index, temperature rise, character of out-of-plane boundary conditions and in-plane constraints, width-to-thickness ratio as well as plate aspect ratio are studied.

Noncontact Vibration Control of a Magnetic Levitated Rectangular Thin Steel Plate.

Noncontact vibration control of a magnetic levitated rectangular thin steel plate was studied experimentally. We fabricated equipment which enables the generation of elastic vibration via forced input of disturbance to a levitated thin steel plate, so that the suppressive effect on the elastic vibration could be examined. Two models of the steel plate, a single-degree-of-freedom model and a continuous model, were considered in this study. By applying the optimal control theory to the each model, the superiority of the models with respect to the suppressive effect of elastic vibration was examined. Furthermore, suboptimal control was applied in which spillover of elastic vibration was considered, the experimental results obtained using the optimal control and the suboptimal control were compared, and the applicability of these controllers was discussed.

Dynamic response of initially stressed functionally graded rectangular thin plates

This paper deals with the dynamic response of initially stressed functionally graded rectangular thin plates subjected to partially distributed impulsive lateral loads and without or resting on an elastic foundation. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The plate is assumed to be clamped on two opposite edges and the remaining two edges may be simply supported or clamped or may have elastic rotational edge constraints. The formulations are based on classical small deflection plate theory, and account for the plate–foundation interaction effects by a two-parameter model (Pasternak-type). A one-dimensional differential quadrature approximation and the Galerkin procedure are employed in the free vibration analysis, and the Modal Superposition Method is used to determine the transient response of the plate structure. A parametric study is carried out. Effects of constituent volume fraction index, foundation stiffness, plate aspect ratio, the shape and duration of impulsive load, as well as the initial membrane stresses on the dynamic response of FGM plates are studied. Comprehensive numerical results for silicon nitride/stainless steel rectangular plates are presented in dimensionless tabular and graphical forms.

Strength of compressed rectangular plates subjected to lateral pressure

This paper presents the results of a parametric study to quantify the effect of lateral pressure on the collapse of square and rectangular steel plates under a predominantly compressive load. The load-shortening behaviour of square and rectangular plates under the combined effect of longitudinal compression and lateral pressure were obtained using a general-purpose non-linear finite element code for different breadth to thickness ratios. Finally design curves are proposed to predict the collapse strength of the compressed plates under lateral pressure.

F-0943 平板を流れる振動エネルギに及ぼす制振材の影響(G10-8 制音・制振)(G10 機械力学・計測制御部門一般講演)

Vibration power flow on a rectangular steel plate where damping material is pasted on a cross part has been measured by means of vibration intensity technique. The test plate is excited at one point while on the other end damping material is made vibration power flow transfer from the excited point to the end. The aim damping material is located between the excited point and the end of damping material. Vibration power absorption ratio of the damping material is obtained from inflow and outflow of power flow. In this case, distribution of power flow on cross section is not uniform in magnitude. The absorption ratio of vibration power depends on frequency and shows a tendency to increase with frequency.

Unilateral buckling of elastically restrained rectangular mild steel plates

This paper considers the elastic unilateral buckling of rectangular mild steel plates that are restrained elastically and subjected to bending and axial actions. A variational formulation of the Ritz method using linear combinations of harmonic functions for the buckling deformations is used to establish an eigenproblem to determine the plate local buckling coefficients. The motivation for the study is the retrofit of reinforced concrete beams by gluing and then bolting steel plates to the sides of the beam. Such plates, when acting compositely with the concrete beam, are subjected to predominantly bending and axial actions which may cause unilateral local buckling. Whereas the bolts provide complete restraint against buckling at discrete points, the glue may also inhibit local buckling between these nodal points since it acts as a continuous elastic restraint. The influence of the glue stiffness, support conditions and plate proportions on the unilateral buckling of such plates are assessed.

Hearing shape.

In 4 experiments, participants listened to suspended occluded objects set into vibration by a pendular hammer. In Experiment 1, participants provided analogue measures of the heights and widths of 3 rectangular steel plates equal in area and weight. The same report method and rectangular dimensions were used in Experiment 2 with 3 plates each of steel, wood, and Plexiglas. Heights and widths were distinguished and perceived in similar proportions to the actual dimensions regardless of material composition. In Experiments 3 and 4, participants successfully identified circular, triangular, and rectangular plates of a single material (Experiment 3) and of 3 different materials (Experiment 4). Discussion focuses on the dependency of perceived dimensions on the physical properties and linear dimensions of the plates and the acoustic structure determined by the solutions to the 2-dimensional wave equation.

Transient finite element analysis of deep penetration laser welding process in a singlepass butt-welded thick steel plate

The laser welding residual stresses and strains in a rectangular thick steel plate are investigated by means of a fully three dimensional finite element analysis. Temperature field and stress–strain field decoupling is assumed to be essential in order to perform an efficient finite element analysis. Moreover, ad hoc constitutive elastoviscoplastic equations have been adapted in order to overcome the unreliable behaviour of rate independent (plastic) constitutive models. Evolution of temperature and stress during the welding process has been numerically simulated as a function of the motion of the travelling laser beam. The results obtained showed also the three dimensional character of stress field due to the typical keyhole form of the molten material under the laser beam, and the relative sound contribution of the stress component along the thickness to the triaxial state of stress, often neglected in previous calculations.

TRANSIENT SOUND FIELDS FROM IMPACTED PLATES: COMPARISON BETWEEN NUMERICAL SIMULATIONS AND EXPERIMENTS

A comparison between measured and simulated transient acoustic fields generated by a thin rectangular impacted steel plate is reported. The plate vibration is modelled in the time domain using a finite difference scheme of second-order in time and fourth-order in space (2-4 scheme) and the radiated acoustic pressure is obtained by solving numerically the Rayleigh integral equation by using a simple Boundary Element Method (trapezoidal rule). The simulated results are evaluated in the form of the spatial pressure distribution at times short-after the impact excitation. The measurements are performed using an optical method: pulsed two-reference-beam holographic interferometry. Results in the form of 2-D projections of the acoustic pressure field are obtained and compared with the simulations. A high degree of similarity is found between the measured and simulated sound fields.

The Estimation of the Sound Power Radiating from a Peripherally Fixed Rectangular Plate Subjected to Acoustic Excitation. 1st Report, Derivation of Estimation Formulae and Application to a Plate Subjected to a Normal Plane Acoustic Wave Excitation.

This paper describes the estimation method of sound power radiating from a peripherally fixed rectangular plate which is subjected to a sound excitation. The forced vibration of the plate which is excited by a distributed force has been theoretically solved by using modal analysis with Rayleigh-Ritz method. The basic equation for estimation has then been shown, and the equations of the frequency response of three parameters-total loss factor, radiation loss factor and input power for estimating sound power-have been derived. For a practical instance, the sound power radiating from a peripherally fixed rectangular steel plate, which was excited by the normal plane acoustic wave, has been estimated. The estimated frequency responses of the sound radiation power coincided well with the measured values obtained by the sound intensity method. This proposed method is hence effective to estimate the sound power radiating from a plate subjected to an acoustic excitation.

Strain Measurement with Microsensors

A model is developed for determining the farfield strains in laminated composites from the strain values indicated by a microsensing device embedded inside the material. The microsensing device considered here consists of three elements: a sensor, a circuit chip, and an antenna. The sensor detects changes in the strains in the material surrounding the sensor. The circuit chip processes the sensor signals which are then transmitted, via the antenna, to a receiver located outside of the composite. The sensor and the circuit are powered by electromagnetic waves generated outside the material and transmitted to the antenna. The model proposed provides a means by which the signal emitted by the microsensing device, and picked up by a receiver, is converted to the engineering value of the farfield strain, i.e., to the strain which would exist in the material at the location of the sensor if the sensor were not present. On the basis of the model, two computer codes were written. The first code calculates the influence coefficient matrix, which is the parameter required to convert the sensor strain to the farfield strain; the second gives the farfield strain directly from the measured sensor strain. Tests were performed to verify the model and the computer codes. In these tests, a strain gauge, a rectangular steel plate, and a circular steel disk (simulating the components of a microsensing device) were embedded in a glass/epoxy beam. The sensor strains were measured by the embedded sensor; the farfield strains were measured by two surface mounted sensors. The measured farfield strains were compared to the farfield strains calculated by the present model, and good agreements were found between the measured and calculated farfield strains.

Analysis of plastic buckling of steel plates in shear based on the tresca yield criterion

Plasticity in steel is characterized by an appreciable amount of plastic flow (in the yield plateau range) which precedes strain hardening. The plastic behavior of materials is most pronounced in the material with plastic flow such as mild steel. The author has previously (1993 and 1994) proposed a new idea of the role of plastic flow in the plastic plate buckling under uniaxial compression [Inoue, T. and Kato, B. (1993). Analysis of plastic buckling of steel plates. Int. J. Solids Structures30, 835–856; Inoue, T. (1994). Analysis of plastic buckling of rectangular steel plates supported along their four edges. Int. J. Solids Structures31, 219–230]. The original idea was to find a new torsional mode of plates which had not been noticed by anyone at the instant of buckling. The new mode was based on the concept that plastic strain was created by slips based on the Tresca yield criterion, and gave a significant reduction of the shear modulus. Its analytical solutions for the plastic buckling were compared with test results, and a good agreement in the early plastic zone was obtained. This paper aims to solve analytically the plastic buckling stress of mild steel plates in shear based on the similar concept adopted in the previous papers.