Dynamics of Adjacent Structures During Horizontal Ground Motion (original) (raw)
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Earthquake response of adjacent structures with viscoelastic and friction dampers
Theoretical and Applied Mechanics, 2015
We study the seismic response of two adjacent structures connected with a dry friction damper. Each of them consists of a viscoelastic rod and a rigid block, which can slide without friction along the moving base. A simplified earthquake model is used for modeling the horizontal ground motion. Energy dissipation is taken by the presence of the friction damper, which is modeled by the set-valued Coulomb friction law. Deformation of viscoelastic rods during the relative motion of the blocks represents another way of energy dissipation. The constitutive equation of a viscoelastic body is described by the fractional Zener model, which includes fractional derivatives of stress and strain. The problem merges fractional derivatives as non-local operators and theory of set-valued functions as the non-smooth ones. Dynamical behaviour of the problem is governed by a pair of coupled multi-valued differential equations. The posed Cauchy problem is solved by use of the Gr?nwald-Letnikov numerica...
Dynamics of a Structure with Viscoelastic and Friction Dampers
2016
Miodrag Žigić 1 Dragan Spasić 2 Aleksandar Okuka 3 Nenad Grahovac UDK: 624.042.8 DOI:10.14415/konferencijaGFS 2016.025 Summary: Dynamics of a structure consisting of two rigid blocks positioned one on another with a viscoelastic and a friction damper is analyzed. Due to a horizontal ground excitation the viscoelastic plate is exposed to a shear loading. The fractional Zener model is used to describe properties of the viscoelastic body while the friction damper is modelled by the Coulomb friction law in a set-valued form. The horizontal ground motion is described by a simplified earthquake model by means of Ricker's waves.
Dinamika Susednih Konstrukcija Tokom Horizontalnog Kretanja Tla
Zbornik radova Građevinskog fakulteta, 2018
We analyzed two adjacent structures connected by a friction element to each other. Both structures consist of two blocks and a viscoelastic damper, which is modeled by the fractional Zener model. The friction force within the friction element is described by the Coulomb friction law in a set-valued form. Horizontal ground motion induces movement of both structures which can cause a destroying pounding effect. Energy brought to the system consisting of two structures connected by a friction damper dissipates by work done by viscoelastic and friction forces. Ground excitation is modeled by a simplified earthquake model by means of Ricker's waves.
Dynamic Response of a Structure to Earthquake Excitation
2017
Nenad Grahovac 1 Dragan Spasić 2 Miodrag Žigić 3 Aleksandar Okuka 4 UDK: 624.042.7:517.9 DOI:10.14415/konferencijaGFS2017.030 Summary: Behavior of a column like structure during earthquake excitation is studied. The structure consists of rigid blocks which move translatory during a horizontal ground motion. Fractional derivatives are used within a constitutive model of а viscoelastic damper. Dry friction damping during relative motion of the blocks is also considered. Governing equations of motion of the structure subjected to a single component horizontal ground acceleration are derived. The posed problem is solved by use of mathematical tools for dealing with non-smooth mechanical systems containing fractional derivatives.
A new formulation is proposed to model pounding between two adjacent structures, with natural periods T 1 and T 2 and damping ratios 1 and 2 under harmonic earthquake excitation, as non-linear Hertzian impact between two single-degree-of-freedom oscillators. For the case of rigid impacts, a special case of our analytical solution has been given by Davis ('Pounding of buildings modelled by an impact oscillator' Earthquake Engineering and Structural Dynamics, 1992; 21:253-274) for an oscillator pounding on a stationary barrier. Our analytical predictions for rigid impacts agree qualitatively with our numerical simulations for non-rigid impacts. When the di erence in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the stando distance. The maximum relative impact velocity of the coupled system can occur at an excitation period T * n which is either between those of the two oscillators or less than both of them, depending on the ratios T 1 =T 2 and 1 = 2 . Although the pounding force between two oscillators has been primarily modelled by the Hertz contact law, parametric studies show that the maximum relative impact velocity is not very sensitive to changes in the contact parameters.
Response of frictional base isolation systems to horizontal-vertical random earthquake excitations
Probabilistic Engineering Mechanics, 1988
Responses of a rigid structure with a frictional base isolation system subjected to random horizontal-vertical earthquake excitations are studied. The ground accelerations are modelled by segments of stationary and nonstationary Gaussian white noise and filtered white noise processes. The technique of nonstationary equivalent linearization is used for the response analysis. The differential equation governing the covariance matrix is solved and for a range of values of parameters, the root-mean-square displacement and velocity responses of the structure are calculated. The results are compared with those obtained by a series of Monte-Carlo digital simulations and reasonable agreement is observed. For several values of parameters, responses of the structure to the accelerograms of the North-South and vertical components of El Centro 1940 earthquake are studied. Particular attentions are given to the effects of vertical excitation and the elastic stiffness of the isolation system. It is observed that vertical excitation amplifies the horizontal slip of the structure to an extent. The amount of amplification under various conditions are evaluated and discussed. It is also shown that the slip displacement decreases sharply as the elastic restoring force of the isolator increases.
On the Seismic Response of Collided Structures
This study examines the inelastic behavior of adjacent planar reinforced concrete (R.C.) frames subjected to strong ground motions. The investigation focuses on the effects of vertical ground motion on the seismic pounding. The examined structures are modeled and analyzed by RUAUMOKO dynamic nonlinear analysis program using reliable hysteretic models for both structural members and contact elements. It is found that the vertical ground motion mildly affects the seismic response of adjacent buildings subjected to structural pounding and, for this reason, it can be ignored from the displacement and interstorey drifts assessment. However, the structural damage is moderately affected by the vertical component of earthquakes.
Seismic Response of Adjacent Structures Connected with Semi-Active Variable Friction Dampers
The International Journal of Acoustics and Vibration, 2010
In this paper, the responses of two adjacent structures connected with semi-active variable friction dampers (SAVFD) under various earthquake excitations are investigated. By controlling the clamping force, SAVFD is able to adjust its slip force and remain in slip state during an earthquake of arbitrary intensity. The objective of this study is to evaluate the optimum value of the gain multiplier and its importance in the structural-response reduction of coupled structures. The optimum gain multiplier, defined as the ratio of damper force to critical damper control force, is investigated for the SAVFD connected, adjacent structures subjected to four different types of earthquake ground motions. A numerical study is carried out for two adjacent, multi-degree-of-freedoms (MDOF) structures connected with SAVFD. The investigation is also carried out to determine the effectiveness of dampers in terms of the reduction of structural responses-namely, displacement, acceleration, and shear forces of adjacent, connected structures. In addition, to minimize the cost of the dampers, the study is conducted with only 50 percent of total dampers at optimal locations, rather than placing the dampers at all floor levels. The predictive control with direct-output feedback concept is considered, and the results are compared with uncontrolled and passive-control cases. Results show that by using SAVFD to connect the adjacent structures of different fundamental frequencies, earthquake-induced responses of either structure can be effectively reduced. Further, it is observed that two adjacent MDOF structures connected with 50 percent of the total dampers at proper locations reduces earthquakeinduced responses as much as when they are connected at all floor levels; thus, the cost of the dampers can be significantly reduced.
Earthquake Interaction Between AdjacentBuildings Under Friction Effects
WIT Transactions on the Built Environment, 1970
A numerical approach is presented for an inequality problem arising in the earthquake analysis of adjacent buildings. This problem concerns the unilateral contact-impact between neighboring buildings, when friction and P-delta effects are taken into account. The proposed numerical approach is based on a double discretization, in space and time, and on optimization methods. First, the Finite Element Method is applied in space. A piecewise linearization for the nonconvex contact laws and for the Coulomb frictional behaviour is used. Next, with the aid of Laplace transform, the linear equality problem conditions are transformed to convolutional ones, involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then, by using a time marching scheme, in each time step a nonconvex linear complementarity problem is solved. Finally, the proposed method is illustrated by means of a numerical example and some conclusions useful for the civil engineering praxis are discussed.