Simple Harmonic Motion and Damped Resonance in Buildings - Essay Example

Damping occurs when the amplitude of the oscillations continuously decreases in size mainly due to the loss of energy from the system. The amplitude of these oscillations is time-dependent and is inversely proportional to the time. Higher damping means that the oscillations reduce in their size (Fang et al. 1999).
In physics’ terms, the tendency of a system to oscillate at an amplitude that is greater at certain frequencies as compared to others is called resonance. This situation occurs when the system has the capacity to stockpile and shift energy easily between more than two modes of storage. The losses that happen during the process of this cycle are called damping. With small damping, the resonance frequency tends to be the same as the natural frequency of the system. There are cases where systems have multiple resonance frequencies that are distinct (Kijewski-Correa and Pirnia, 2007).

Damping is hence the physical phenomenon of reducing motion through the dissipation of energy. In tall buildings, damping is important due to various reasons. The tall buildings are known to vibrate at natural frequencies that are low. This is a factor that makes the buildings to be very susceptible to dynamic resonance in cases of earthquake and wind. Wind energy is usually at its highest when the frequencies are low. Additionally, to the response to the wind gustiness, there is a common form of dynamic-wind response that is due to vortex shedding. The circumstances mentioned result in the creation of movements of the structure that is at right angles to the course of the storm (Terman, 1992).

Methods of controlling damping
Damping in tall buildings is mainly caused by intrinsic and supplementary sources. Intrinsic damping comes from connections, cladding, friction and seismic motion; in this case, this paper is interested in the seismic causes of the damping which is earthquakes. Supplementary damping is due to engineered devices such as friction devices, viscous and sloshes dampers and tuned mass dampers (Katsuhiko, 2005). There are broad methods that have been largely used to control damping;
a) Shaping or sculpting the building
When a building has an irregular shape, there is a great reduction of vortex shedding. Such a building can have additional tapering or some obstructions which have been built-in. These conditions have the gross effect of breaking vortices or preventing the whole building from being locked up simultaneously. The con with this technology is the reduction of the cost and space efficiency of the building (Willford, 2008).
b) Stiffening the building
This method is mostly traditional and is used to control the effect of wind. It is more appropriate for buildings that are short. In tall buildings, it can prove to be quite an expensive venture (Kijewski-Correa, 2005).
c) Addition of damping
This technique has been verified to be the most cost-effective in control of the dynamic response. In addition to adding the supplementary damping, there is the reduction of uncertainty about intrinsic damping (Brownjohn, 2005).
Damping in earthquakes and winds
The ratios for damping that are listed in the structure codes for earthquake cases are normally high, with the rates ranging from 2% for steel and 5% for concrete. The figures are basically higher for wind considering that there is higher energy absorption through the damage that is caused. This energy dissipation cannot be considered in wind loading due to the longer length of wind storms as compared to earthquakes. Wind also has a behavior that prolongs the windy inelastic behavior (Kijewski-Correa et al., 2006).
Technology: Types of dampers
Tuned mass dampers (TMD): These are in form of giant pendula located at the tops of the buildings. They oscillate out of phase with the movement of the building during wind or earthquake. This technology has been in constant use all over the world for quite some time now. Some of the drawbacks associated with them are the high expenses, complexity, and occupation of important parts of the building and little redundancy.
Tuned liquid dampers/ slosh dampers
They are applied in the same principle as the TMDs, though they use some liquid/slosh instead of the masses. They are bulkier as compared to TMDs but much cheaper.
Viscous dampers
They are giant dampers that dissipate energy through relative motion. They are used for the reduction of seismic effects in many places, especially in Japan.
Viscoelastic dampers
These dampers are sensitive to temperatures and so tend to dissipate some heat while in a storm. This makes them lose efficiency (Abe et al., 1998). Read More