Aspects of structural vibration passive control

In the last years “non conventional” seismic protection research strategies have reached remarkable improvements. Most of the proposed innovative approaches have the concept of “vibration control” in common, because their objectives consist in regulating the dynamic response, using special devices, to reduce vibrations induced by seismic activity or other environmental actions.
A control system consists of a set of parts having the capacity to influence a dynamic process. While the system analysis explains why systems respond the way they do, the body of knowledge called “Control Theory” deals with the modifications to the systems which will alter the response in a desirable manner.
In the case of Passive Control, the dynamic process is regulated without energy supply. The basic passive strategies are : Seismic Isolation, Supplementary Energy Dissipation and Mass Damping. Intensive research effort have been recently made on Active Control approach (see e.g. the review paper by Yang & Soong, 1988 ).

 

 

The relationships between cause (input) and effect (output) of any system may be represented by a block diagram. This is the graphic representation of functional I/O (input/output) of system elements providing a visual description of the interactions of the various elements according to its mathematical relationships.

 

 

The application of a control system requires knowledge of the system to be regulated. The control theory studies modifications to be applied to a system in order to achieve the desired behavior. System analysis studies the methods of behavior evaluation. The design of a control system requires identification of a regulation strategy to achieve the objectives of optimal behavior.
Regulation criteria, necessary to optimize performance and could be different for each design objective. These strategies should be identified and defined in relation to the problem’s nature under multiple restraints.
As well known, control systems can be classified into two distinct categories: systems with open-loop control laws and systems with closed-loop control laws. An open loop system is one in which the control action is independent from the output.

 

 

As a consequence, the controller ignores what is happening to the response of the structure. As shown in figure 4, the control law is a way of filtering the input signal of the primary system. In a closed-loop control system the control action somehow depends on the output which is therefore called feedback because it comes from a closed feedback sequence between cause and effect.

 

SUPPLEMENTARY ENERGY DISSIPATION

The supplementary energy dissipation strategy view the concentration of the energy dissipation in particular ad hoc devices thus preserving structural components.

 

 

The motion equation of the model, subject to base excitation ü_g (t)  can be written as:

 

This control strategy is equivalent to a closed loop regulation scheme.

 

BASE ISOLATION

The base isolation seismic control strategy introduced by J.M. Kelly, view the creation of a soft plane that acts as a filter, disconnecting the superstructure motion from the soil one. Therefore from a physical point of view, in a fixed base system the base excitation is directly applied to the structure while in a base isolated system the base excitation is filtered by the isolation level which acts as a controller regulating the excitation transmission to the superstructure.

 

 

The motion equations of the base isolated system are given by:

 

 

 

In the case of base isolated systems an “open loop control” is essentially implemented:

 

 

MASS DAMPING

The mass damping (TMD = Tuned Mass Damper), recently applied on civil constructions to control vibrations due to wind and moderate earthquake is a classic vibration reducing system of Mechanics whose mathematical formulation was introduced for the first time by Den Hartogh in 1940. The objective in adding the satellite system is to bring the main resonant peak of the amplitude down to its lowest possible value.
In this case the excitation of a controlled system activates the TMD, generally placed on roofs, capturing energy from the main system on which it applies a phase opposition inertial feedback.

 

 

The two-degrees-of-freedom linear model motion equation is given by:

 

This control strategy is equivalent to the following loop regulation scheme.

 

 

When this control system is applied to a multi-degrees-of-freedom system it allows a reduction of the amplification only in a narrow band of frequencies, generally centered on the fundamental frequency, as it is possible to see in the next figure

 

 

BASE ISOLATION + TMD

The passive-hybrid seismic protection system obtained through the combination of base isolation and tuned mass damping is proposed by Palazzo and Petti in 1994 with the scope to reduce the vulnerability of base isolated systems towards seismic events characterized by high energy content on low frequencies, which could produce large displacements at the isolation level with consequent collapse of the overall system.

The application scheme of this strategy is showed below:

 

 

Given wb e xb, wis e xis, wT e xT  the natural frequencies and the damping factors of the superstructure, isolation and TMD respectively, the motion equations of the model can be written as:

 

This control strategy is equivalent to the following loop regulation scheme.

 

 

The effect of TMD, reduction of amplification in a narrow band, favorably combines with Base Isolation because, as well known the fundamental mode is strongly dominant in isolated systems.  Consequently the combined system efficiently reduces seismic vibrations without affecting the superstructure well behavior.

 

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