• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.647-664
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• 2006

The main purpose of this paper is to investigate the effect of transient stochastic analysis on nonlinear response of earth and rock-fill dams to spatially varying ground motion. The dam models are analyzed by a stochastic finite element method based on the equivalent linear method which considers the nonlinear variation of soil shear moduli and damping ratio as a function of shear strain. The spatial variability of ground motion is taken into account with the incoherence, wave-passage and site response effects. Stationary as well as transient stochastic response analyses are performed for the considered dam types. A time dependent frequency response function is used throughout the study for transient stochastic responses. It is observed that stationarity is a reasonable assumption for earth and rock-fill dams to typical durations of strong shaking.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.669-683
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• 2003

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

• Smart Structures and Systems
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• v.16 no.1
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• pp.141-162
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• 2015

The magneto-rheological visco-elastomer (MRVE) is used as a smart core to control the stochastic micro-vibration of a sandwich plate with supported mass. The micro-vibration response of the sandwich plate with MRVE core and supported mass under stochastic support motion excitations is studied and compared to evaluate the vibration suppression capability. The effects of the supported mass and localized magnetic field on the stochastic micro-vibration response of the MRVE sandwich plate are taken into account. The dynamic characteristics of the MRVE core in micro-vibration are described by a non-homogeneous complex modulus dependent on vibration frequency and controllable by applied magnetic fields. The partial differential equations for the coupled transverse and longitudinal motions of the MRVE sandwich plate with supported mass are derived from the dynamic equilibrium, constitutive and geometric relations. The simplified ordinary differential equations are obtained for the transverse vibration of the MRVE sandwich plate under localized magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of sandwich plates with supported mass is developed based on the Galerkin method and random vibration theory. The expressions of frequency-response functions, response power spectral densities and root-mean-square velocity responses of the plate in terms of the one-third octave frequency band are obtained for micro-vibration evaluation. Finally, numerical results are given to illustrate the large response reduction capacity of the MRVE sandwich plate with supported mass under stochastic support motion excitations, and the influences of MRVE parameters, supported mass and localized magnetic field placement on the micro-vibration response.

• Wind and Structures
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• v.10 no.1
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• pp.45-60
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• 2007

Transmission tower is a vital component in electrical system. In order to accurately compute the dynamic response and reliability of transmission tower under the excitation of wind loading, a new method termed as probability density evolution method (PDEM) is introduced in the paper. The PDEM had been proved to be of high accuracy and efficiency in most kinds of stochastic structural analysis. Consequently, it is very hopeful for the above needs to apply the PDEM in dynamic response of wind-excited transmission towers. Meanwhile, this paper explores the wind stochastic field from stochastic Fourier spectrum. Based on this new viewpoint, the basic random parameters of the wind stochastic field, the roughness length $z_0$ and the mean wind velocity at 10 m heigh $U_{10}$, as well as their probability density functions, are investigated. A latticed steel transmission tower subject to wind loading is studied in detail. It is shown that not only the statistic quantities of the dynamic response, but also the instantaneous PDF of the response and the time varying reliability can be worked out by the proposed method. The results demonstrate that the PDEM is feasible and efficient in the dynamic response and reliability analysis of wind-excited transmission towers.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.311-325
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• 2020

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.771-784
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• 2018

This study aims to investigate the stochastic response of isolated and non-isolated highway bridges subjected to spatially varying earthquake ground motion model. This model includes wave passage, incoherence and site response effects. The wave passage effect is examined by using various wave velocities. The incoherency effect is investigated by considering the Harichandran and Vanmarcke coherency model. The site response effect is considered by selecting homogeneous firm, medium and soft soil types where the bridge supports are constructed. The ground motion is described by power spectral density function and applied to each support point. Triple concave friction pendulum (TCFP) bearing which is more effective than other seismic isolation systems is used for seismic isolation. To implement seismic isolation procedure, TCFP bearing devices are placed at each of the support points of the deck. In the analysis, the bridge selected is a five-span featuring cast-in-place concrete box girder superstructure supported on reinforced concrete columns. Foundation supported highway bridge is regarded as three regions and compared its different situation in the stochastic analysis. The stochastic analyses results show that spatially varying ground motion has important effects on the stochastic response of the isolated and non-isolated bridges as long span structures.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.179-191
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• 2009

A stochastic response spectrum method is proposed for simple evaluation of the structural response of an actively controlled aseismic structure. The response spectrum is constructed assuming a linear structure with an active mass damper (AMD) system, and an earthquake wave model given by the product of a non-stationary envelope function and a stationary Gaussian random process with Kanai-Tajimi power spectral density. The control design is executed using a linear quadratic Gaussian control strategy for an enlarged state space system, and the response amplification factor is given by the combination of the obtained statistical response values and extreme value theory. The response spectrum thus produced can be used for simple dynamical analyses. The response factors obtained by this method for a multi-degree-of-freedom structure are shown to be comparable with those determined by numerical simulations, demonstrating the validity and utility of the proposed technique as a simple design tool. This method is expected to be useful for engineers in the initial design stage for structures with active aseismic control.

• Structural Engineering and Mechanics
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• v.33 no.4
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• pp.407-428
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• 2009

The effects of the uniform and spatially varying ground motions on the stochastic response of fluid-structure interaction system during an earthquake are investigated by using the displacement based fluid finite elements in this paper. For this purpose, variable-number-nodes two-dimensional fluid finite elements based on the Lagrangian approach is programmed in FORTRAN language and incorporated into a general-purpose computer program SVEM, which is used for stochastic dynamic analysis of solid systems under spatially varying earthquake ground motion. The spatially varying earthquake ground motion model includes wave-passage, incoherence and site-response effects. The effect of the wave-passage is considered by using various wave velocities. The incoherence effect is examined by considering the Harichandran-Vanmarcke and Luco-Wong coherency models. Homogeneous medium and firm soil types are selected for considering the site-response effect where the foundation supports are constructed. A concrete gravity dam is selected for numerical example. The S16E component recorded at Pacoima dam during the San Fernando Earthquake in 1971 is used as a ground motion. Three different analysis cases are considered for spatially varying ground motion. Displacements, stresses and hydrodynamic pressures occurring on the upstream face of the dam are calculated for each case and compare with those of uniform ground motion. It is concluded that spatially varying earthquake ground motions have important effects on the stochastic response of fluid-structure interaction systems.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.703-715
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• 1996

In stochastic analysis, the randomness of the structural parameters is taken into consideration and the response variability is obtained in addition to the conventional (mean) response. In the present paper the structural response variability of plate structure is calculated using the weighted integral method and is compared with the results obtained by different methods. The stochastic field is assumed to be normally distributed and to have the homogeneity. The decomposition of strain-displacement matrix enabled us to extend the formulation to the stochastic analysis with the quadratic elements in the weighted integral method. A new auto-correlation function is derived considering the uncertainty of plate thickness. The results obtained in the numerical examples by two different methods, i.e., weighted integral method and Monte Carlo simulation, are in a close agreement. In the case of the variable plate thickness, the obtained results are in good agreement with those of Lawrence and Monte Carlo simulation.