Calculating Free and Forced Vibrations of multi-story Shear Buildings by Modular method

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Calculating Free and Forced Vibrations of multi-story Shear Buildings by Modular method

Ashari EhsanEsna

Author Affiliations

¹YoungResearchers and elite Club, Qazvin Branch, Islamic Azad University, Qazvi,IRAN

Res. J. Recent Sci., Volume 3, Issue (1), Pages 83-90, January,2 (2014)

Abstract

The present study discretizes and calculates free and forced vibrations of a multi-story building by shear model. The present study shows that for free vibrations a dynamic system becomes a static system; as a result, static theories of linear structures can be used. Then, frequencies and modular forms are calculated. By contribution of Betti’s corresponding displacement theorem, orthogonal characteristic of modules is characterized. For forced vibrations, employment of module converts multi-degrees free engaged dynamic system to several independent single-degree free dynamic systems in each of which mass, spring stiffness and forced force for new system are linear combinations of mass, spring stiffness and forced force of engaged system. For example, frequencies, modular forms and forced displacement from transverse load to story such as hurricane force and acceleration imposed on building foundation, say earthquake, are manually calculated and compared by simulating with commercial-research software package, ANSYS. Results from ANSYS for forced vibrations are more accurate that results from approximate method of SAP 2000.

References

Paz M. and Leigh W., Structural Dynamics, Theory and Computations, Updated with SAP 2000, 5th Edition, Kluwer Academic Publishers, (2004)
Chopra A.K., Dynamics of Structures, Theory and Applications to Earthquake Engineering, 3rd Edition, Prentice Hall, (2000)
Chowdhury I.C. and Dasgupta S.P., Dynamics of Structure and Foundation, A Unified Approach, I. Fundamentals, CRC Press, (2009)
Chowdhury I.C. and Dasgupta S.P., Dynamics of Structure and Foundation, A Unified Approach, II. Applications, CRC Press, (2009)
Johnson E.A., Lam H.F., Katafygiotis L.S. and Beck J.L., A benchmark problem for structural health monitoring and damage detection, Structural control for civil and infrastructure engineering, 317-324 (2001)

[ref1] Paz M. and Leigh W., Structural Dynamics, Theory and Computations, Updated with SAP 2000, 5th Edition, Kluwer Academic Publishers, (2004)

[ref2] Chopra A.K., Dynamics of Structures, Theory and Applications to Earthquake Engineering, 3rd Edition, Prentice Hall, (2000)

[ref3] Chowdhury I.C. and Dasgupta S.P., Dynamics of Structure and Foundation, A Unified Approach, I. Fundamentals, CRC Press, (2009)

[ref4] Chowdhury I.C. and Dasgupta S.P., Dynamics of Structure and Foundation, A Unified Approach, II. Applications, CRC Press, (2009)

[ref5] Johnson E.A., Lam H.F., Katafygiotis L.S. and Beck J.L., A benchmark problem for structural health monitoring and damage detection, Structural control for civil and infrastructure engineering, 317-324 (2001)