Frame with and without viscous damper under earthquake loading (energy balance equation , kinetic energy , internal energy,…)
In this example, we intend to simulate the frame with viscous damper and without viscous damper in the abaqus software
The frame is composed of 7 stories and 3 spans and height between each one of the stories is 3 meters
In this question, the Kobe earthquake is applied to the bottom of the frame and following the base shear and displacement diagrams will be drawn
In this picture, you can observe the diagram of horizontal displacement for frame with viscous damper and frame without viscous damper
As you observe, when use viscous damper, the quantity of displacement will be decreased
In this picture , the base shear diagram for the frame with viscous damper and frame without viscous damper has been drawn
As it can observed , when viscous damper is used, the quantity of base shear is decreased
In this picture , the diagrams of various type of energy for the frame with viscous damper have been drawn
In this question , external work is the same earthquake energy
As it can be observed, when using viscous damper, a large part of the earthquake energy will be absorbed by viscous damper. in other words, a lot of earthquake energy would be wasted when exposing to viscous damper
In this picture , we have drawn all sorts of energy for frame without viscous damper
As you observe , when viscous damper is not used , a large part of the earthquake energy will be converted to plastic strain. in other words , a lot of earthquake energy has been spent to deformation of structure
In this picture , energy balance equation and various type of energy being used in civil engineering can be observed
Types of energy
Frictional dissipation (energy dissipated by friction) >>>> ALLFD
Kinetic energy >>>> ALLKE
Plastic dissipation (energy dissipated by plastic strain) >>>> ALLPD
Strain energy (elastic strain energy) >>>> ALLSE
Viscous dissipation (energy dissipated by viscous damper OR energy absorbed by damper >>>> ALLVD
External work >>>> ALLWK
The adding result of kinetic energy , strain energy, plastic dissipation , viscous dissipation , frictional dissipation and total energy is equal to external work
In this picture , you can see the formula of internal energy
The adding result of strain energy and plastic dissipation is equal to internal energy
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