Why are horizontal degrees of freedom (DOF) mainly considered in the dynamic equation of motion rather than other DOFs such as vertical and rotational for control of structures?
Measuring rotational acceleration can be obtained with measurements from linear sensors, but result in considerable measurement errors.
Nowadays rotational accelerometers have been developed for direct measurement of angular acceleration and rotations have to be extracted from it.
Dear Keyvan Aghabalaei,
All the horizontal, vertical, and rotational degrees of freedom are important.
However, the horizontal (translational) degrees of freedom are primarily considered in the vibration control of most structures, such as buildings, because: a) the horizontal degrees of freedom are indicative of most of the structural performance parameters, and b) the vertical and the rotational (torsional) degrees of freedom are sometimes neglected.
The horizontal translational degrees of freedom and the torsional (rotation about the vertical) axis become more important for the vibration response control of most structures under excitations, such as earthquake and wind.
The vertical degrees of freedom are sometimes neglected when the vertical effect of the excitations is considered to be negligible (as compared to the horizontal excitation and the gravity load). However, the vertical degrees of freedom are also very important for some structures, such as bridges, cantilevers, and other long span structures.
The rotational/torsional degrees of freedom are also sometimes neglected for symmetrical structures, where the torsional effect of the excitation is estimated to be zero.
With best regards,
Daniel H. Zelleke.
Dear Daniel Habtamu Zelleke ,
Thank you for your reply. I wonder if the horizontal component of an earthquake can also excite the vertical DOFs in a structural system?
Regards.
Dear Keyvan Aghabalaei Baghaei,
In some situations, the horizontal components of earthquake ground motions can excite the vertical degrees of freedom (cause vibration vertical deformation/vibration). This may happen depending on the structural configuration.
For example, consider a fictitious structure, which looks like the letter “F” with fixed support. In this fictitious example, there are two cantilever beams supported on a column.
If this structure is subjected to only the horizontal component of an earthquake, the column deforms and vibrates as a simple vertical cantilever. This initiates the vertical deformation and vibration of the cantilever beams.
With best regards,
Daniel.
Dear Daniel Habtamu Zelleke ,
Thank you for your reply.
Regards,
Dear Keyvan;
The state of the art of structural control field shows that most of the researchers simplify the structural behavior to unidirectional, hence studying only horizontal translation. this may be due to many reasons but many because the focus is on the control strategy itself rather than the structure behavior, however recently more research papers are interested in bidirectional movements and irregular structures including rotations.
Another reason for using only horizontal degree of freedom is the complexity of the model specially if using a lumped mass representation, FE method also can be very complicated.
Hope this will clarify your ideas.
Warm regards.
Dear Mahdi Abdeddaim & Mohsen Azimi ,
Thank you for your comments. I wonder if there are any relevant references on the state space formulation of dynamic motion equations for buildings with complex DOFs, including rotational and vertical.
Regards,
Keyvan
Nowadays, depends on the reviewer what type will be asked. If yoh consider full degree of freedom then the reviewer says must not use and will reject and if you use uni again will say this is not correct. The main reason is that nowadays researchers need to be lucky that the goes to unbiased reviewer. Otherwise what ever new idea goes in front of biased reviewer will get rejection. Rest at each analysis some of the DOFs will be important not all at the same time.
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