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doi: 10.1002/eqe.4290160303pmid: N/A
A simple rule is derived to combine, within the framework of a complex mode superposition, the maximum modal responses of systems such as soil‐structure and structure‐equipment systems, for which closely spaced natural frequencies are likely, and for which, because of the large difference in the damping values of their various components, the assumption of an orthogonal damping matrix may lead to significant errors. The rule constitutes the generalization of Rosenblueth's rule for systems with closely spaced natural frequencies and classical modes, and is expressed in terms of their complex mode shapes and natural frequencies. Its derivation is based on the theory of a complex modal analysis for systems with non‐classical modes of vibration and on Rosenblueth's original derivation. As in this original derivation, earthquake ground motions are modelled as a stationary white noise process, but the formulae obtained under this assumption are modified later on to account for the transient nature of actual earthquakes. A numerical example is presented to illustrate the application of the rule, and a comparative study with numerical integration solutions is performed to assess its accuracy. In this comparative study, it predicts the numerical integration solutions with an average error of 0.3 per cent.
doi: 10.1002/eqe.4290160304pmid: N/A
The paper presents a dynamic response analysis of vertically excited liquid storage tanks including both liquid‐tank and liquid‐soil interaction. The system considered is a thin‐walled, elastic cylindrical shell entirely filled with an incompressible and inviscid fluid, resting on a flexible foundation over an elastic halfspace with frequency dependent stiffness and damping parameters. The problem is treated analytically by the generalized‐coordinate approach and then solved numerically using the complex frequency response analysis. For one special tank, natural frequencies and equivalent damping ratios are evaluated and compared with those corresponding to a rigid ground. The maximum dynamic pressure is calculated using the response spectra of the 1976 Friuli earthquake. A parameter study is carried out to show the great influence of variable soil stiffness upon the damping ratio of the shell‐liquid‐soil system.
Grandori Guagenti, E.; Molina, C.; Mulas, G.
doi: 10.1002/eqe.4290160305pmid: N/A
Recent studies show that, in some seismogenetic areas, strong earthquakes occur rather predictably. Their pattern of occurrence, however, cannot be interpreted according to a classic model of seismic risk analysis. It is shown that semi‐Markov models are capable of interpreting predictable behaviour and, in particular, the types suggested by the Slip Predictable Model, the Time Predictable Model and the Characteristic Earthquake Model. A number of general properties are demonstrated, dealing with return periods, waiting times, damage cost, stationary and variable characteristics of seismic risk analysis. The case of Friuli is then examined and its semi‐Markovian interpretation is discussed. This interpretation is compared with others which also are possible, and the consequences for the computation of hazard and risk terms are evaluated.
Zerva, Aspasia; Ang, Alfredo H‐S.; Wen, Y. K.
doi: 10.1002/eqe.4290160306pmid: N/A
Lifeline systems have been heavily damaged during past earthquakes; this has often been attributed to the effect of differential ground motion at the supports of these long structures. Based on a stochastic model for the ground excitation the responses of pipelines and bridges of various span lengths subjected to either perfectly or partially correlated random input motions in the axial, lateral (i.e. transverse horizontal) and vertical directions are investigated and the significance of the spatial variation of ground motion is examined.
doi: 10.1002/eqe.4290160307pmid: N/A
Low‐frequency errors of a commonly used non‐stationary stochastic model (uniformly modulated filtered white‐noise model) for earthquake ground motions are investigated. It is shown both analytically and by numerical simulation that uniformly modulated filter white‐noise‐type models systematically overestimate the spectral response for periods longer than the effective duration of the earthquake, because of the built‐in low‐frequency errors in the model. The errors, which are significant for low‐magnitude short‐duration earthquakes, can be eliminated by using the filtered shot‐noise‐type models (i.e. white noise, modulated by the envelope first, and then filtered).
doi: 10.1002/eqe.4290160308pmid: N/A
The seismic performance of a steel framed structure equipped with (i) friction damping devices and (ii) base isolators is compared. A parametric study based on energy concepts is performed first using time‐history dynamic analysis to determine the optimum properties of the two systems when excited by an earthquake whose energy is distributed over a relatively broad frequency band (1940 El Centro, N‐S). Using these same properties, the responses of the two structural systems are then examined when excited by earthquakes whose power content essentially is concentrated at the low frequency end of the energy spectrum (1977 Romania, Bucharest, N‐S and 1985 Mexico, SCT E‐W). The results of the study show that, while both systems similarly reduce the response of conventional structures to the California earthquake, the friction damped structure exhibits a superior performance under the low frequency earthquakes. Very large shear forces and displacements are observed when the Romania and Mexico earthquakes are applied to the base isolated structure, indicating that the performance of a base isolated structure depends on the characteristics of the site earthquake. By comparison, friction damped structures are shown to behave favourably under the three earthquakes studied; this suggests that friction damping devices offer a more consistent way of protecting structures during earthquakes.
Wepf, Dieter H.; Wolf, John P.; Bachmann, H.
doi: 10.1002/eqe.4290160309pmid: N/A
For a reservoir with an arbitrary shape of the upstream dam face and of the bottom including an adjacent regular part of constant depth extending to infinity, the hydrodynamic‐stiffness matrix in the frequency domain for a displacement formulation is derived using the boundary‐element method. The fundamental solution takes the boundary condition at the free surface into account. The analytical solution of the semi‐infinite reservoir is used to improve the accuracy. To be able to transform the hydrodynamic‐stiffness matrix from the frequency to the time domain, the singular part consisting of its asymptotic value of ω ∞ is split off. It consists of an imaginary linear term in ω which can be interpreted as a damper with a coefficient per unit area equal to the product of the mass density and the wave velocity. This also applies for a reservoir bottom of arbitrary shape. The remaining regular part of the stiffness matrix is transformed numerically. The corresponding interaction force‐displacement relationship involves convolution integrals. This boundary‐element solution agrees well with analytical results and with those of other numerical procedures based on a time‐stepping method. The method is also applied to an actual earthquake acting on a reservoir with an irregular part with an inclined bottom and a regular part extending to infinity. The results of the analysis in the time domain coincide with those determined in the frequency domain.
doi: 10.1002/eqe.4290160310pmid: N/A
This paper discusses a general technique for vibration control of simple, continuous mechanical systems. The discussion involves giving the expressions for the response of an illustrative element (fixed‐free bars) to a sinusoidal disturbance and then formulating the problem of open‐loop vibration control of this system as a mathematical programming problem. The final step uses numerical optimization techniques to find the control forces. When these techniques are used, the amplitude of the system's steady state response is minimized. The discussion also shows that while this method effectively controls the vibration, it has a great deal of flexibility in accomplishing its stated purpose.
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