There is a single mass system at base of which a base isolated system is attached. So this whole system is a two degree of freedom system which is subjected to rotational component of earthquake ground motion. Due to rotational motion this system is subjected to two type of motions, one rocking response (translational motion due to rotation) and other torsional motion. Base isolation part is deflected in non-linear range, while super-structure above it is deflected in linear range. So I want to write equation of motion for rocking response. In it problem is that, I can not multiply the rotation with the height directly for base-isolation part, as it is in non-linear range, while for superstructure rotation can be multiplied by height directly.
Dear Ketan kumar Sengar
Please follow these links:
Article Seismic behavior of rocking base-isolated structures
https://www.researchgate.net/publication/309174699_AN_ANALYTICAL_MODEL_FOR_THE_DYNAMIC_RESPONSE_OF_AN_ELASTIC_SDOF_SYSTEM_FIXED_ON_TOP_OF_A_ROCKING_SINGLE-_STORY_FRAME_STRUCTURE_EXPERIMENTAL_VALIDATION
https://www.researchgate.net/publication/307560595_THE_ROCKING_RESPONSE_OF_SEISMICALLY_ISOLATED_FREE-_STANDING_RIGID_BLOCKS
https://www.researchgate.net/publication/277404947_Dynamics_of_the_Vertically_Restrained_Rocking_Column
https://benthamopen.com/FULLTEXT/TOBCTJ-11-217
http://www.eaee.org/Media/Default/2ECCES/2ecces_eaee/1573.pdf
https://www.frontiersin.org/articles/10.3389/fbuil.2018.00034/full
https://www.researchgate.net/publication/317234938_Dynamics_of_rocking_podium_structures
https://www.researchgate.net/publication/306415734_A_finite_element_model_for_seismic_response_analysis_of_deformable_rocking_frames
https://www.researchgate.net/publication/280913114_An_analytical_model_of_a_deformable_cantilever_structure_rocking_on_a_rigid_surface_Development_and_verification
https://www.researchgate.net/publication/277404666_The_Dynamics_of_the_Rocking_Frame
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