Spectral Displacement Research Articles

Approximate Seismic Lateral Deformation Demands in Multistory Buildings

An approximate method to estimate the maximum lateral deformation demands in multistory buildings responding primarily in the fundamental mode when subjected to earthquake ground motions is presented. This method permits a rapid estimation of the maximum roof displacement and of the maximum interstory drift for a given acceleration time history or for a given displacement response spectrum. A multistory building is modeled as an equivalent continuum structure consisting of a combination of a flexural cantilever beam and a shear cantilever beam. The simplified model is used to investigate the ratio of the spectral displacement to the roof displacement and the ratio of the maximum interstory drift ratio to the roof drift ratio. The effect of the distribution of lateral forces along the height of the building and of the ratio of overall flexural and shear deformations is examined. Lateral deformation demands of a 10-story steel building computed with the simplified method when subjected to various earthquake...

Nonlinear procedures for seismic evaluation of buildings

New static and dynamic displacement-based procedures have been developed by the Federal Emergency Management Agency (FEMA) for the seismic evaluation and design of buildings. The static procedures calculate displacements in yielding buildings as the product of an elastic spectral displacement and coefficients Ci. Mean elastic and mean inelastic displacements are assumed to be equal for elastic periods, T0, greater than the characteristic site period, Tg. The data presented in this paper and elsewhere support this assumption for values of the strength ratio greater than or equal to 0·20. For T0 ≤ Tg, mean inelastic displacements can substantially exceed mean elastic displacements for all values of the strength ratio; FEMA 273 accounts for this observation by the coefficient C1. However, the FEMA 273 cap on C1 (= 1·5) is not sufficiently conservative and should be increased to 3·0 for the analysis and design of modern construction. The effects of stiffness degradation, strength deterioration and pinching are represented in FEMA 273 by the coefficient C2. The values assigned to C2 appear to be most reasonable. Nonlinear dynamic analysis is being widely used to estimate maximum deformations and displacements in buildings. The values calculated for the maximum deformations and displacements will be dependent upon the means used to characterize structural damping in the building frame. Although structural damping is routinely implemented through a damping constant (or matrix), such an implementation will overestimate the effects of structural damping in a yielding building and underestimate maximum deformations and displacements. Structural damping should be characterized by the target damping ratio (typically 5% of critical) at the point of maximum displacement. Copyright © 1999 John Wiley & Sons, Ltd.

DISPLACEMENT DESIGN SPECTRA

Recent developments in displacement-based design methodologies have increased the need for reliable displacement design spectra, especially in long periods. The design spectra proposed in Eurocode 8 are assessed, using recent attenuation relationships that predict response spectral ordinates based on European data, as well as five selected European strong motion accelerograms. To identify possible trends in long-period spectral displacements, several high-quality digital recordings from the 1995 Hyogoken-Nanbu (Kobe) earthquake were collected and studied. Based on the differences recognised, possible modifications for the design spectrum to take into account in future revision of Eurocode 8 are proposed.

Effect of a non-linear boundary layer on the radiation from earthquakes and underground nuclear explosions

A constitutive equation in the immediate source region is postulated. It is proposed that between the permanently deformed source volume and the linear zone there exists a microfractured boundary layer having the constitution of a five-parameter Murnaghan solid that exhibits both geometrical finite strain and physical cubic terms in the energy density function. Waves excited by the source carry the signature of the boundary layer into the linear zone, all the way to the far field. The mathematical realization of this programme consists of the application of the longwave Born–Rayleigh approximation to the Landau–Goldberg equation. The perturbed field, governed by an additional force system, is represented as a multipole expansion of eigenvector spherical harmonics of the unperturbed background field. Our solution aims at the spatial characteristics of the 3-D perturbed field (e.g. radiation patterns, amplitude amplification, etc.) together with its frequency-content features. The results show, in general, that for every spatial mode with indices (ℓ1, m1) fed into the non-linear boundary layer system, there emerges in the elastic zone the output modes (ℓ1±2s, 2m1), s=0,2,4,…. Compressional and shear modes generate each other (‘mode crossing’), and spatial field harmonics of lower and higher orders than originally existed in the primary field appear. In addition, one encounters the expected frequency doubling in the spectral displacements of the first-order perturbation. Detailed calculations are made, especially for dipolar sources, which include explosion (ℓ1=0,m1=0) and shear dislocations (ℓ1=2, m1=0,1,2). It is revealed that the boundary layer tends to amplify the source field by a factor that may reach 4 for explosions in pre-existing cavities and 2 for earthquakes. Hence, the amplification will effectively limit the true seismic decoupling of underground nuclear explosions to a limiting value of under 70 and tend to boost the true seismic moments of earthquakes. In the latter case the non-linear theory suggests the introduction of two new source parameters: a virtual radius, r0, associated with the yield limit of rocks, and a larger radius associated with the elastic limit of rocks. It is shown that for shear dislocations, the fault's area is interpreted geometrically as a virtual spherical surface of radius r0. As long as small finite strains are assumed inside a thin boundary layer, scrambling of the wavefield (that is displacement amplification, generation of higher-degree multipoles and mode crossing) is the most conspicious physical perturbation, independent of any non-classical modification of the constitutive law. In this sense, the salient gross features of our final results are model-independent. Our results serve as a bridge between the microscopic and macroscopic theories of fracture and hopefully pave the road towards a dynamical theory of earthquake-source mechanisms.

Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index

We present a graphic method of analyzing the spectral displacements of a long-period fiber grating as a function of ambient index. Mode dependence of the maximum displacement, disappearance of a particular resonance peak, and spectral behavior when the ambient index is larger than that of the cladding material are investigated and compared with experimental results.

A spectral displacement study of the binding constants of cyclodextrin–hydrocarbon and –fluorocarbon surfactant inclusion complexes

The spectral displacement technique with phenolphthalein as the chromophore has been used to obtain 1:1 equilibrium binding constants (K2) for a homologous series of hydrocarbon (hc) (CnH2n+1COONa, n = 5–13) and fluorocarbon (fc) anionic surfactants (CnF2n+1COONa, n = 3–8) with β-cyclodextrin (β-CD). The magnitude of K2 increases as the alkyl chain length increases in each homologous series. K2 values in the ranges of 102–105 M−1 and 101–104 M−1 were obtained for the β-CD–fc and for the β-CD–hc surfactant complexes, respectively. The different binding affinity of β-CD with hc and fc surfactants is discussed in terms of such physicochemical properties of the guest species as hydrophobicity, geometrical size, conformational effects, molecular polarizability, and solvation of the head group. Keywords: spectral displacement, phenolphthalein, cyclodextrin, surfactant, binding constant.

SEISMIC DESIGN AND RESPONSE OF BARE AND MASONRY-INFILLED REINFORCED CONCRETE BUILDINGS. PART II: INFILLED STRUCTURES

The effects of masonry infills on the global seismic response of reinforced concrete structures is studied through numerical analyses. Response spectra of elastic SDOF frames with nonlinear infills show that, despite their apparent stiffening effect on the system, infills reduce spectral displacements and forces mainly through their high damping in the first large post-cracking excursion. Parametric analyses on a large variety of multi-storey infilled reinforced concrete structures show that, due to the hysteretic energy dissipation in the infills, if the infilling is uniform in all storeys, drifts and structural damage are dramatically reduced, without an increase in the seismic force demands. Soft-storey effects due to the absence of infills in the bottom storey are not so important for seismic motions at the design intensity, but may be very large at higher motion intensities, if the ultimate strength of the infills amounts to a large percentage of the building weight. The Eurocode 8 provisions for designing the weak storey elements against the effects of infill irregularity are found to be quite effective, in general, for the columns, but unnecessary and often counterproductive for the beams.

Fiber Sagnac interferometer temperature sensor

A modified Sagnac interferometer-based fiber temperature sensor is proposed. Polarization independent operation and high temperature sensitivity of this class of sensors make them cost effective instruments for temperature measurements. A comparison of the proposed sensor with Bragg grating and long-period grating fiber sensors is derived. A temperature-induced spectral displacement of 0.99 nm/K is demonstrated for an internal stress birefringent fiber-based Sagnac interferometer.

The Cr 2O 72−CrO 42−HCrO 4− system revisited

The electronic spectra of aqueous Cr VI solutions in the pH range 3–11 have four isosbestic points, located at 246, 293, 338 and 441 nm. These positions are independent of the total concentration of Cr VI. The existence of the isosbestic points indicates that only two species are present, namely CrO 4 2− and Cr 2O 7 2−, and that HCrO 4 − is spectrophotometrically undetectable. This conclusion is further supported by factor analysis, which gives the number of linearly independent species in solution to be two, and also by the method of spectral displacement. At the isosbestic points absorbance in linear in total Cr VI concentration. In this sense Beer's law is valid, and the results can be used for analytical purposes.

Spatial and spectral response of a Fabry–Perot interferometer illuminated by a Gaussian beam

A generalized study has been done of the transmission characteristics of a Fabry-Perot interferometer (FPI) illuminated by a Gaussian light beam impinging on it at normal and non-normal incidence. The theoretical approach is based on a plane-wave, angular-spectrum representation of both the incident Gaussian beam and the transmitted beam. Expressions are obtained for the FPI instrumental function and for the spatial distribution of the transmitted beam. Numerical results are presented for the FPI maximum transmission, effective finesse, and spectral displacement of the interference maximum.

Comment on "Relation between Persistent Currents and the Scattering Matrix"

Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function. Instead of piecewise constant persistent current of free electrons on the plane one has a current which varies linearly with the flux and is antisymmetric with regard to all time preserving values of $\alpha$ including $1/2$. Different self-adjoint extensions of the problem and role of the resonance are discussed.

Order statistics of functionals of strong ground motion for a class of renewal processes

In this paper, probability distribution functions are derived for the order statistics of various functionals of strong ground motion at a site. These functionals can be: Modified Mercalli Intensity (MMI), peak ground acceleration (PGA), Fourier spectral amplitudes of acceleration, response spectrum amplitudes (spectral displacement, pseudo-spectral velocity and pseudo-spectral acceleration), and amplitudes of the peaks (local maxima and local minima) in the time historyof the response of SDOF and MDOF structures at the site. Three parameters of the response of a structure are considered: displacement, shear force and bending moment at each level (storey) of the structure. The earthquake sources contributing to the risk of ground motion at the site are a number of point, area or volume sources, each with defined frequency of occurence-magnitude relationship. The magnitudes of the possible events at these sources are discretized, and the occurrence of events of different magnitudes are assumed to be statistically independent. For each magnitude, it is assumed that the eartquakes occur in a Poissonian sequence or in a renewal process which is a generalization of the Poissonian. For these assumptions, the probability distribution functions are presented for the number of earthquakes, n, during which a given level of site or structural response is exceeded during the exposure time, and for the return period of the exceedances. For example, for single-degree- of-freedom: (SDOF) or multi-degree-of-freedom structures, (MDOF) n can be the number of earthquakes during which the response of a storey will exceed a given level at least m times(m = 1, 2, 3,…) during the exposure time. These probability distribution functions can be used to extend the concept of uniform probability functionals to more than one exceedance. A more important application is to generalize the uniform probability functionals method of site response (uniform probability Fourier or response spectra) to uniform probability envelopes of displacement, shears and bending moments of a given structure. The uniform probability envelopes can be for exceedance at least once during at least one earthquake, or, in general, for exceedance at least m times per earthquake ( m = 1, 2,…) during at least n earthquakes. In other words, during at least n earthquakes at least m peaks in the response can be higher than the specified level. Such uniform probability envelopes can be used (1) to define new design guidelines for building codes based on cost-benefit analysis; (2) to construct more refined probability distribution functions for the damage and total economic losses caused by earthquakes; and (3) to develop planning and decision strategies on strengthening and retrofitting existing buildings.

Effects of tuned mass dampers on random response of bridges

The effectiveness of tuned mass dampers (TMDs) in reducing random response of simple bridges is studied using the finite element method. Optimum tuning parameters as suggested by Den Hartog are used in the present study. The developed model is based on the method of complex matrix inversion to calculate response characteristics within a cut-off frequency range. Two illustrative examples with different cases of TMD arrangements are solved by the present analysis to study their sensitivity and suitability in reduction of random responses. A comparative study of response power spectral density and mean square displacement of different cases reveal that the efficiency of a particular TMD arrangement depends primarily on the nature of eigenfrequency distribution of structure.

Critical Base Excitations of Structural Systems

A critical excitation is one that maximizes chosen response quantities subject to constraints related to duration and energy imposed on the excitation. A study of the response of single- and multi-degree-of-freedom systems subjected to critical base excitations is presented. The effect of damping and duration of excitation on the peak response is studied. The critical peak relative displacement, relative velocity, and absolute acceleration are related to one another in the same manner as the spectral displacement, velocity, and acceleration are related in earthquake response spectra. Objective functionals for maximizing response of multi-degree-of-freedom systems are developed. Examples illustrating system behavior are included, and a comparison is made of peak critical responses with peak responses from a strong-motion earthquake.

The Gecko visual pigment: The anion hypsochromic effect

The 521-pigment in the retina of the Tokay gecko ( Gekko gekko) readily responds to particular physical and chemical changes in its environment. When solubilized in chloride deficient state the addition of Class I anions (Cl −, Br −) induces a bathochromic shift of the absorption spectrum. Class II anions (NO − 3, IO − 3, N − 3, OCN −, SCN −, SeCN −, N(CN) − 2), which exhibit ambidental properties, cause an hyposochromic shift. Class III anions (F −, I −, NO − 2, CN −, AsO − 3, SO 2− 4, S 2O 2− 3) have no spectral effect on the 521-pigment. Cations appear to have no influence on the pigment absorption and Class I anions prevent or reverse the hypsochromic shift caused by Class II anions. It is suggested that the spectral displacements reflect specific changes in the opsin conformation, which alter the immediate (dipolar) environment of the retinal chromophore. The protein conformation seems to promote excited-state processes most in the native 521-pigment state and least in the presence of Class II anions. This in turn suggests that the photosensitivity of the 521-pigment is controlled by the excited rather than by the ground-state properties of the pigment.

Stochastic Dynamic Response of Multiply Supported Tuned Subsystems to Nonstationary Seismic Excitation

ABSTRACT Stochastic dynamic response of multiple degree of freedom (MDOF) subsystems that are attached at multiple points to an MDOF supporting structure that is subjected to seismic excitation is obtained by using a modal time domain random vibration approach. An earthquake is modeled as a nonstationary, nonwhite, vector random process that has a realistic spectral shape and finite ground displacement, velocity, and acceleration. Analyses of secondary systems are decoupled from the primary system without loss of accuracy when the cascading assumption is appropriate. This makes the design process of subsystems convenient and efficient. When tuning occurs, cascading assumptions are no longer appropriate. Previously obtained results for the modal properties of combined systems in terms of modal properties of the primary system and subsystems are then utilized. Results account for tuning spatial coupling in terms of stiffness and inertia. Exact analytical expressions are obtained for the elements of the state transition matrix and the evolutionary covariance matrix of various responses. The solution is exact, within the limitations of modal analysis, since all the cross terms between modal coordinates are considered. Finally the capabilities of this approach are illustrated through analysis of an example.

Use of visible spectral displacement method to determine the concentration of surfactants in aqueous solution

A substitution method in which phenolphthalein is displaced from the β-cyclodextrin cavity by the hydrocarbon moiety of a surfactant is used to determine the concentration of the surfactant. The 1:1 complex of phenolphthalein with β-cyclodextrin has an absorbance practically equal to zero in the region of the 550-nm band of the basic form of phenolphthalein. When solute molecules containing an alkyl moiety displace some of the phenolphthalein at a pH of approximately 10.5, the absorbance at 550 nm is significantly increased and serve as a direct measure of the concentration of the solute. The method is useful in determining concentrations of surfactants such as sodium dodecyl sulfate and N, N-dimethyl- N-dodecylamine oxide, which do not contain chromophores.

The effects of cyclodextrins on drug absorption. I. In vitro observations

A two-phase transfer system, water with organic solvent, was used to investigate the effect of cyclodextrins on transport of dissolved lipophilic drugs from the aqueous to the organic layer. Four model drugs, diazepam, medazepam, n-butyl- p-aminobenzoate and n-pentyl- p-aminobenzoate were used. Stability constants of different cyclodextrin complexes were determined by a phase solubility technique or by a spectral displacement technique. It was found that the first-order transport rate constants of the drugs were hardly affected by complexation with β-cyclodextrin. This phenomenon could be explained by displacement of the drug from the cyclodextrin complex by organic solvent near the interface. This process results in a unique system which has a low concentration of free drug in the bulk of the aqueous layer, whereas near the interface a relatively high concentration of free drug exists. It could be demonstrated that the properties of the organic solvent also influenced the transport rate of complexed drug.

Application of Holographic Optical Elements in Optical Memory Devices

Computer generated Holographic Optical Elements (HOE) have been written by e-beam lithography on Al2O3 waveguides. The spectral bandwidth of HOE with Separate Input and Output Couplers (SIOC-HOE) was 0.7 nm compared to more than 9 nm of HOE with Convolved Input and Output Coupler (CIOC-HOE). The beam waist in the focus can be explained in terms of the natural beam waist and the spectral displacement of the focal point. The coupling efficiency of HOEs with beam splitting characteristic could be modeled. An integrated pickup device for an optical storage medium was realized with CIOC-HOEs.

First results from the pisa seismic noise super-attenuator for low frequency gravitational wave detection

The detection of gravitational wave (GW) signals requires the test masses of an interferometric antenna to be carefully made free from seismic noise coming from the suspension point. In this paper we report the first results coming from the Pisa super-attenuator. We have measured both the test mass absolute noise upper limit to be ⩽10 −11/ vm/√Hz for 10< v<200 Hz and the transfer functions (TF). These TF applied to the measured seismic noise spectral displacement should allow in a 3 km long interferometric antenna a maximum spectral strain sensitivity h ̃ <1.9×10 −20 Hz −1 2 at 10 Hz and h ̃ <7.5×10 −19/v 2 Hz −1 2 for v⩾20 Hz; this gives at the Vela (Crab) pulsar frequency the limit h<3×10 −25 ( h<4×10 −26), for 1 year integration time.