This paper provides an overview of building structure modeling and control under bidirectional seismic waves. It focuses on different types of bidirectional control devices, control strategies, and bidirectional sensors used in structural control systems. This paper also highlights the various issues like system identification techniques, the time-delay in the system, estimation of velocity and position from acceleration signals, and optimal placement of the sensors and control devices. The importance of control devices and its applications to minimize bidirectional vibrations has been illustrated. Finally, the applications of structural control systems in real buildings and their performance have been reviewed.
Historic studies expose the fact that several earthquakes have caused severe damage in civil structures all over the world including 1985 Mexico City, 1994 Northridge, 1995 Kobe, 1999 Kocaeli, 2001 Bhuj, 2008 Sichuan, 2008 Chile, and 2012 Emilia. The process of modification or controlling the building structures from severe damage has became a salient topic in structural engineering. The control of building structures from the hazardous earthquake waves is an area of great interest for the researchers that is growing rapidly [
The structural control methodology and its applications during earthquakes were first suggested by the researches more than a century ago. But major developments have been noticed during the last 25 years where the structures with preventive systems have been developed. Yao in 1972 [ the pattern in which the ground vibrates during earthquake, the design techniques of buildings to withstand earthquakes, innovative strategies for the response control of building structures.
Passive and active control systems play an important role in the response reduction of civil engineering structures subjected to strong seismic vibrations. Passive, active, and semiactive control systems are the most important class of structural engineering. The two techniques that can be utilized for the control of structural vibrations are implementation of smart materials in the construction of buildings [ the use of control devices like actuators, dampers, and isolators in the building structures [
A worldwide popularity and high demand of structural control and its application had given rise to various researches leading to the publication of many textbooks, for example, [ excitation criteria (e.g., unidirectional or bidirectional earthquake and winds), structural characteristics (e.g., natural frequency, degree-of-freedom, and nonlinearity in structures), design of the control system (e.g., devices types and quantity, device placements, system models, and control algorithm) [
Although the most of research has been vested on the seismic analysis considering unidirectional seismic waves, very less researches have been detected on bidirectional seismic waves. The fact cannot be denied that the earthquake has indeed an arbitrary direction, represented by a bidirectional ground movement [
The aim of this review is to address all aspects involved in bidirectional structure control, taking into consideration modeling and vibration control of building structures under bidirectional seismic inputs. This paper also addresses the application of all possible devices for bidirectional vibration control. The foundation on the methodology of state estimation, system identification, optimal device placement, and the effect of the time delay on the stability is discussed in this review. We compare different control strategies for the bidirectional vibrations, such as PID control,
Structural mechanics involves the study of vibrations incorporated in structures. In order to control a structure effectively, it is important to have the knowledge about its dynamics. The control of structures is associated with the safeguard of building structures from unidirectional or bidirectional seismic forces. One of the structural design objects is to model dynamic loadings and to produce innovative approach to curb vibration. The vibration control generates the required dynamics in the building structures within a stable range. This control design is decided by the structure of mathematical model [
All engineering structures are composed of intrinsic mass and elastic characteristics. The dynamic modeling has similar characteristics with the static analysis. However, the dynamic analysis is much complex than static analysis. For example, the mass modeling technique for the dynamic model requires an elastic model and a mass model minutely refined by discrete masses [
Recent earthquakes show that the bidirectional effect is the main damage source of the structural damage. The seismic analysis should consider the bidirectional excitation. The normal method of building structure design regards the seismic response arising from the ground motion that acts separately in the two orthogonal directions. Generally, the earthquake exhibits arbitrary direction which is represented as bidirectional ground movement, and it could reduce the participation of the traverse frames to the structure torsional and lateral stiffness. A noteworthy change in the elastic torsional behavior of the building is observed considering a nonlinear behavior in the transverse frames.
The effect of the magnitude of the axial forces acting in the corner columns in case of bidirectional ground motion subjected to structures is different from that in case of unidirectional ground motion [
The analysis of real buildings suggests that it is asymmetric in nature to some degree with a formal symmetric plan. The asymmetric nature of building will induce lateral as well as torsional vibrations simultaneously and is termed as torsion coupling (TC) considering the case of pure translational excitations. Soil-structure interaction (SSI) effects are considered and can be significant in case of the building structures constructed on soft medium. The effects of SSI can critically modify the dynamic characteristics of a structure such as natural frequencies, damping ratios, and mode shapes [
The knowledge of behavior and impact of the excitation forces plays a significant role in the formulation of the building structures dynamic model. The movement of the portion of the earth crust is termed as earthquake which is accompanied with the sudden release of stresses. Usually the epicenters for earthquake exist less than
Bidirectional ground forces that are exerted on the building structures.
The forces acting on the
The main factors of the seismic movement for the building are the amplitude (displacement, velocity, and acceleration) and the frequency of the ground motion. The ground motion is complex, and the vibration frequency is time-varying. The ground motion and the building vibration affect each other, depending on the distance between the natural frequency of the building structure and seismic motion frequency. When the seismic wave frequency is close to the natural frequency of the building, the damage becomes bigger. Structure analysis shows that the shorter the building, the higher the natural frequency. One of the prime concerns is controlling the structure vibrating with respect to low frequency, because the major part of the structure elastic energy is stored in low frequency zone [
A controllable building structure can be regarded as a planar structure on a fixed base. The asymmetric characteristic of the building induces simultaneous lateral and torsional vibrations, known as torsion coupling (TC) [
The torsion coupled force.
The seismic forces result in building oscillation.
The simplest structure is one-story under lateral translational motion at the roof level. It is a single degree-of-freedom system. The motion model is [
A single degree-of-freedom system for one-story building.
Similarly, the equation of motion of a linear structure with
The technique of modeling the stiffness parameter
When both ground translation and rotation are considered, the motion equation is [
The mathematical analysis of the TC structure yields the following mass matrix, damping matrix, and stiffness matrix:
For a simple case, the mass of each floor is concentrated at the floor plate (
Three-dimensional building structures with parameters of each floor.
If we only consider
The torsion effect on the building is in
Vibration suppression in appropriate quantity can prevent the structures from fracture or collapse. Some devices play this suppression role to prevent the structure from damage. The control devices, such as actuators, isolators, and dampers, are installed to suppress the external vibrations. These structural control devices are getting more popularity and attention along with their applications in building structures. The structural control devices for the seismic hazards can be categorized as passive, active, hybrid, and semiactive [
A passive control device is incorporated to a structure. It modifies the stiffness or the damping of the structure in an suitable way. The passive control system does not require an external power source for its operation. It generates control force opposite to the motion of controlled structured system [
There are many passive control devices, for example, viscoelastic dampers, tuned mass dampers, frictional dampers, tuned liquid dampers, and base-isolation systems [
The forces of the passive control devices solely depend on the structural motion. They can be expressed as [
We use the following sections to describe some famous dampers for the bidirectional control.
The tuned mass damper (TMD) is considered to be an energy dissipation system, although the primitive concept of this system is not to dissipate energy. It transfers the energy from the building structure to the tuned mass dampers (absorbers). The basic principle of TMD is to obtain optimal damping parameters, in order to control the displacement of an undamped system subjected to a harmonic force [
The coupled lateral-torsional motions under seismic excitations are exhibited by the building structures with intended eccentricities between their mass and stiffness centers. Reference [
The multiple tuned mass damper (MTMD).
Tuned liquid column damper (TLCD) has uniform cross-section with U shaped tube attached. The schematic view has been shown in Figure
The tuned liquid column damper.
Reference [
The circular tuned liquid column damper (CTLCD) is shown in Figure
The circular tuned mass damper (CTLCD).
Reference [
The tuned liquid mass damper.
The stiffness of TMD and the liquid high are determined as
Tuned liquid column dampers (TLCDs) are a special type of TLDs that depends on the motion of a column of liquid in a U-tube-like container to neutralize the forces acting on the structure. The introduction of the damping factor is done in the oscillating liquid column through an orifice in the liquid passage. The damping, however, unlike TMDs, is amplitude dependent, and thus the TLCD dynamics are associated with nonlinearity. On the other hand, circular tuned liquid column dampers (CTLCDs) are very much active when exposed to torsional response. As the earthquake is practically multidimensional, the torsionally coupled vibration factor cannot be ignored and so CTLCD is much favored in this case. Reference [
The main drawback of the passive control devices is that they cannot adapt the change of the natural frequency caused by the structural nonlinearities and huge seismic excitations, especially for multiple floor buildings [
Since 1970s, remarkable progress has been made in the field of active control of civil engineering structures subjected to natural forces such as winds and earthquakes [ Motion control can be achieved with greater effectiveness. In account of ground motions, it is relatively insensitive. It can be applied to the multihazard remission circumstances. Control objectives can be selected flexibly.
In order to control actively, the external excitations and inner structural responses are needed. Measured information is sent to the control algorithm to generate desired control forces. So the active devices usually use displacement sensors.
The active tuned mass damper (ATMD) uses control strategy to improve the tuned mass damper (TMD). It improves the effectiveness in minimizing the structural response [
The active controller should be able to absorb the translation-torsion coupled vibrations. Besides the translational vibrations, the torsional vibrations under the seismic waves also affect the performance of ATMD. An asymmetric structure under the coupled lateral-torsional responses is discussed in [
The active tuned mass damper for a 2-DoF structure.
Semiactive control devices are regarded as controllable passive devices. The main objective of these devices is saving control resources. The actuators of the semiactive control do not add mechanical energy to the structure directly. The power break down semiactive control system offers some degrees of protection with the help of embedded passive components.
The semiactive devices take the advantages of the passive and the active control. It requires less power than the active control devices. They can even be operated by the battery in the case of power failure during the seismic event [
The magnetorheological (MR) damper is the most popular semiactive damping device. It works on the magnetorheological fluid and is controlled by a magnetic field. Generally, the magnetic field is produced by electromagnet. It requires minimal power for its operation. The suspended minute iron particles in a base fluid are termed as MR fluids. This type of liquids has the capability of changing from free flowing linear viscous state to semisolid state with controllable yield strength under a magnetic field.
The result of uncovering the liquid to a magnetic field is the particles use the form of chains. These chains obstruct the flow and solidify the fluid in a span of milliseconds. The stress is directly proportional to the magnitude of the applied magnetic field [
The application of MR damper to control the torsional and torsionally coupled responses subjected to bidirectional seismic waves is investigated in [
Simple mechanical model of MR.
The governing force
Hybrid base isolation (HBI) had been a matter of interest for a number of researchers due to its effectiveness and consists of a passive base isolation system combined with a control actuator to generate the effects of the base isolation system. Several research on base isolation system has been carried out and installed in several structural engineering projects due to its positive attributes like simplicity, reliability, and effectiveness. Reference [
HMD system installed in
The equation of motion for HMD system installed in
Comparison of control devices.
The appropriate design of a controller is utterly necessary so that it can send essential control signal to the control devices in order to reduce the structural responses. The main strategy involved within the control scheme to prevent the collapse of building structures under bidirectional seismic waves is to control the coupled translation-torsion response of the building structures [
Time delay from the measurement to the actuator is a limit for vibration control. The control loop includes vibration data measurement, data filtration, control algorithm, data transmission, and actuation. The control loop has also phase shift by time delay [
The motion equation of
The proper placement of sensing and control devices is an important research field of structural control. It gives the measurement and control operation effectively. It also affects the controllability and observability of the controlled system [
The working principle of PID controller is based on the feedback error
The most important optimal controllers are the linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) control. The equation of motion can be exhibited in the form mentioned below:
The increase in elements of
Reference [
The result of the entire analysis was in the favour of the algorithm not only being an effective measure to control the bidirectional horizontal response of earthquake but also reducing the isolation layer movement by large extent. Reference [
The controller was installed and then the vibration tests are performed. These test results suggested that the control action generated was effective and as per the design. Reference [
Then using the above criteria, the state space equation can be written as
The sliding mode control (SMC) is designed for uncertain nonlinear systems [
The control force of sliding mode control is
In [
A neural network (NN) is characterized by
The combination of NN with the classical control theory yields better control results [
Linguistic criteria are an effective feature of fuzzy control rules that can be easily modified and understood clearly [
In their study, bell shaped membership functions have been used and are represented by
The minimization of structural torsion responses using semiactive dampers has been presented by [
Holland, 1975, was the first to propose the general scheme of genetic algorithm (GA) and uses natural genetic theory to build an optimal search algorithm [ Code and decode the variables into the strings form. Fit each solution string. Evaluate strings of the next generation by applying genetic operators.
The aim of the optimization problem is to evaluate the minimum of the performance index:
The applications of the GA method to structural control are published by various researchers. Reference [
In the investigation mentioned, a nonuniform mutation operator is applied as the genetic operator to evaluate better solution for the new generation. It is expressed by
The study results suggest that the new control technique efficiently reduces the response of two irregular 3D building structures under seismic inputs including structures with plan and irregular elevation. The study results suggest that the new control technique efficiently reduces the response of two irregular 3D building structures under seismic inputs including structures with plan and irregular elevation. Reference [
The concept of absorber system with multiobjective optimal design for torsionally coupled earthquake excited structures is presented by [
In this review, the modeling and structural control techniques of building structures subjected to bidirectional earthquake are considered. The main difference with normal structure controllers is the lateral-torsional coupled response. We discuss recent new techniques, methodology, and concepts in this areas. We focus all important results in last two decades in the field of structural engineering with respect to the bidirectional earthquakes.
From the analysis of the above paper, we have the following important observations: Most of existing reviews only consider the structure control under unidirectional seismic wave. This review explores the effects of bidirectional seismic waves, which are normal for the real earthquake. Real buildings are generally asymmetric in nature to some extent. These criteria induce lateral and torsional vibrations in combination. The reduction of translational and torsional response of structures often involves the usage of multiple dampers [ Hybrid control devices are more popular due to their abilities for the seismic vibration along 3-DoF. The authors [ Few papers use sliding mode control to reduce translation-torsion coupled vibration with bidirectional seismic inputs. Finding placement of control devices is a challenging task especially for coupled lateral and torsional responses. In case of building structures subjected to multiple excitations, the use of online identification technique is better. The intelligent control is favored for the structural control, because it does not require system information.
The authors declare that there is no conflict of interests regarding the publication of this paper.