Analyticity and causality of the three-parameter rheological models

In this paper the basic frequency response and time response functions of the three-parameter Poynting-Thomson solid and Jeffreys fluid are revisited. The two rheological models find application in several areas of rheology, structural mechanics and geophysics. The relation between the analyticity of a frequency response function and the causality of the corresponding time-response function is established by identifying all singularities at ω=0 after applying a partial fraction expansion to the frequency response functions. The strong singularity at ω=0 in the imaginary part of a frequency response function in association with the causality requirement, imposes the addition of a Dirac delta function in the real part in order to make the frequency response function well defined in the complex plane. This external intervention, which was first discovered by P.A.M. Dirac, has not received the attention it deserves in the literature of viscoelasticity and rheology. The addition of the Dirac delta function makes possible the application of time domain techniques that do not suffer from violating the premise of causality

The engineering merit of the “Effective Period” of bilinear isolation systems

This paper examines whether the “effective period” of bilinear isolation systems, as defined invariably in most current design codes, expresses in reality the period of vibration that appears in the horizontal axis of the design response spectrum. Starting with the free vibration response, the study proceeds with a comprehensive parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations. The study employs Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method. When the response history of the bilinear system exhibits a coherent oscillatory trace with a narrow frequency band as in the case of free vibration or forced vibration response from most pulselike excitations, the paper shows that the “effective period” of the bilinear isolation system is a dependable estimate of its vibration period; nevertheless, the period associated with the second slope of the bilinear system is an even better approximation regardless the value of the dimensionless strength of the system. As the frequency content of the excitation widens and the intensity of the acceleration response history fluctuates more randomly, the paper reveals that the computed vibration period of the systems exhibits appreciably scattering from the computed mean value. This suggests that for several earthquake excitations the mild nonlinearities of the bilinear isolation system dominate the response and the expectation of the design codes to identify a “linear” vibration period has a marginal engineering merit

Transverse versus longitudinal eigenperiods of multispan seismically isolated bridges

This paper is motivated from the wider need in system identification studies to identify and interpret the eigenvalues of seismically isolated bridges from field measurements. The paper examines the transverse eigenvalues of multispan bridges which are isolated in both transverse and longitudinal directions at all supports including all center piers and end-abutments. The paper shows that regardless of the value of the longitudinal isolation period of the deck, the length of the bridge and the number of spans, the first transverse (isolation) period is always longer than the longitudinal isolation period of the deck. This result cannot be captured with the limiting idealization of a beam on continuously distributed springs (beam on Winkler foundation) which yields the opposite result–that the first transverse period is always shorter than the longitudinal isolation period. This fundamental difference between the response of a flexural beam supported on distinct, equally spaced springs and that of a beam supported on continuously distributed springs has not received the attention it deserves in the literature of structural mechanics-dynamics. Finally, the paper shows that the first normalized transverse eigenperiod of any finite-span isolated deck follows a single master curve and the solutions from all configurations are self-similar and are not dependent on the longitudinal isolation period or on whether the deck is isolated on elastomeric or spherical sliding bearings

Size versus slenderness: Two competing parameters in the seismic stability of free-standing rocking columns

When a free-standing column with a given base becomes taller and taller, there is a competition between the increase in its size (more stable) and the increase in its slenderness (less stable). This paper investigates how these two competing phenomena affect the stability of tall, slender, free-standing columns when subjected to horizontal and vertical ground shaking. The main conclusion of the paper is that the outcome of this competition is sensitive to local details of the ground shaking and the dominant frequency of a possible coherent, distinguishable pulse. The often observed increase in stability due to increase in height (despite the increase in slenderness) may be further enhanced due to a sudden transition from the lower mode of overturning with impact to the higher mode of overturning without impact. The paper proceeds by offering a simple mathematical explanation why the vertical ground acceleration has a marginal effect on the stability of a slender, free-standing column; and concludes that the level of ground shaking that is needed to overturn a tall free-standing column of any size and any slenderness is a decreasing function of the length scale, apTp^2, of the dominant coherent acceleration pulse normalized to the base-width of the column

Time and frequency domain identification of seismically isolated structures: advantages and limitations

This paper investigates the effectiveness of widely used identification methods to identify the response of seismically isolated structures supported on bearings with bilinear behavior. The paper shows that while both time domain and frequency domain methods predict with high accuracy the modal characteristics of structures isolated by linear isolation system, their performance degrades appreciably when the isolation system exhibits bilinear behavior even when its strength assumes moderate values (say 5% of the weight). The paper also shows that the natural period of isolated structure that results from bilinear isolation systems can be satisfactorily predicted with wavelet analysis

Estimating the “Effective Period” of Bilinear Systems with Linearization Methods, Wavelet and Time-Domain Analysis: From Inelastic Displacements to Modal Identification

This paper revisits and compares estimations of the effective period of bilinear systems as they result from various published equivalent linearization methods and signal processing techniques ranging from wavelet analysis to time domain identification. This work has been mainly motivated from modal identification studies which attempt to extract vibration periods and damping coefficients of structures that may undergo inelastic deformations. Accordingly, this study concentrates on the response of bilinear systems that exhibit low to moderate ductility values (bilinear isolation systems are excluded) and concludes that depending on the estimation method used, the values of the “effective period” are widely scattered and they lie anywhere between the period-values that correspond to the first and the second slope of the bilinear system. More specifically, the paper shows that the “effective period” estimated from the need to match the spectral displacement of the equivalent linear system with the peak deformation of the nonlinear system may depart appreciably from the time needed for the nonlinear system to complete one cycle of vibration. Given this wide scattering the paper shows that for this low to moderate ductility values (say ) the concept of the “effective period” has limited technical value and shall be used with caution and only within the limitations of the specific application

Seismic protection of structures with supplemental rotational inertia

In this paper we investigate the alternative strategy of suppressing ground-induced vibrations with supplemental rotational inertia. The proposed concept employs a rack-pinion-flywheel system that its resisting force is proportional to the relative acceleration between the vibrating mass and the support of the flywheels. This arrangement, known in the mechanical networks literature as the “inerter”, complements the traditional supplemental damping and stiffness strategies used for the seismic protection of structures. The paper shows that the seismic protection of structures with supplemental rotational inertia has some unique advantages; in particular in suppressing the spectral displacements of long period structures –a function that is not efficiently achieved with large values of supplemental damping. The paper shows that this happens at the expense of transferring appreciable forces at the support of the flywheels and proceeds by examining to what extent the finite stiffness and damping of the support of the flywheels affects the dynamics of the system. The proposed concept may be attractive for the seismic protection of bridges given that the rack-pinion-flywheel system strategy can accommodate large displacements

Modal identification of seismically isolated bridges with piers having different heights

This paper investigates the modal identification of seismically isolated bridges when the localized nonlinear behavior from the isolation bearing initiates at different times due to the uneven height of the bridge piers. More specifically, a three-span bridge supported on spherical sliding bearings is examined. Three different states of the same system with different natural periods emerge during an excitation; the linear system (LS), the partially isolated system (PIS) and the fully isolated system (FIS). Firstly, the paper identifies the time intervals that each state performs by using acceleration data. Subsequently, modal identification techniques such as the Prediction Error Method and a time-frequency wavelet analysis are applied on each interval. The LS’ results are dependable compared to the PIS which is a mildly nonlinear system. The results corresponding to the FIS suggest that it is preferable to apply the modal identification techniques on each interval independently, rather than on the entire response signal

Shallow moonquakes database

This is a database with information regarding shallow moonquake events between 1971 and 1976. It also includes useful metrics for each time history, such as the Nyquist Frequency, Arias intensity, Duration D'95, PGA, etc

A review towards the design of extraterrestrial structures: From regolith to human outposts

The design of a permanent human habitat on a planetary body other than the Earth is an idea introduced many decades ago, which became even more significant after the landing of the first humans on the Moon with the Apollo missions. Today’s rampant technological advances combined with ambitious missions, such as the Insight mission on Mars and the Artemis program for the Moon, render the vision of space colonization more realistic than ever, as it constantly gains momentum. There is a considerable number of publications across several disciplines pertaining to the exploration of Lunar and Martian environments, to those planets’ soil properties, and to the design of the first habitable modules. The scope of this paper is to present a meticulous selection of the most significant publications within the scientific areas related to: (a) geotechnical engineering aspects, including the mechanical properties and chemical composition of Lunar and Martian regolith samples and simulants, along with elements of anchoring and rigid pads as potential forms of foundation; (b) ground motions generated by different types of Moonquakes and meteoroid impacts; (c) the different concepts and types of extraterrestrial (ET) structures (generic, inflatable, deployable, 3D-printed), as well as overall views of proposed ET habitats. Apart from the details given in the main text of this paper, a targeted effort was made to summarize and compile most of this information in representative tables and present it in chronological order, so as to showcase the evolution of human thinking as regards ET structures