Research Articles | Challenge Journal of Structural Mechanics

Determination of the exact mode frequencies of multi-storey structures by state-space method and a comparison with mode superposition method

Ahmad Yamin Rasa, Mehmet Hamit Özyazıcıoğlu


DOI: https://doi.org/10.20528/cjsmec.2021.01.001

Abstract


A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.


Keywords


structural dynamics; state-space method; mode superposition method; transient vibration; mode frequency

Full Text:

PDF

References


Avcar M (2104). Free vibration analysis of beams considering different geometric characteristics and boundary conditions. International Journal of Mechanics and Applications, 4(3), 94-100.

Borino G, Muscolin G (1986). Mode-Superposition methods in dynamic analysis of classically and non-classically damped linear systems. Earthquake Engineering and Structural Dynamics, 14, 705-717.

Caughey TK (1960). Classical normal modes in damped linear dynamic systems. Journal of Applied Mechanics, 27, 269-271.

Caughey TK, O'Kelly M (1965). Classical normal modes in damped linear dynamic system. Journal of Applied Me-chanics, 32(3), 583-588.

Civalek O, Avcar M (2020). Free vibration and buckling analyses of CNT reinforced laminated non‑rectangular plates by discrete singular convolution method. Engineering with Computers.

Felszeghy SF (1993). On uncoupling and solving the equations of motion of vibrating linear discrete systems. Transactions of the ASME, 60(2), 456-462.

Rasa AY (2017). Çok Katlı Yapıların Geçici Titreşimlerinin Durum-Uzayı Yaklaşımı ile İncelenmesi ve Modların Birleştirilmesi Yöntemiyle bir Karşılaştırma. M.Sc. thesis, Atatürk University, Erzurum, Turkey. (in Turkish)

Sinha R, Igusa T (1992). CQC and SRSS methods for non-classically damped structures. Earthquake Engineering and Structural Design, 24, 615-619.

Veletsos AS, Ventura CE (1986). Modal analysis of nonclassically damped linear systems. Earthquake Engineering and Structure Dynamics, 14, 217-243.

Villaverde R (2008). A complex modal superposition method for the seismic analysis of structures with supple-mental dampers. The 14th World Conference on Earthquake Engineering, 12-17, Beijing, China.

Wilson EL, Kiureghian A, Bayo EP (1981). A replacement for the SRSS method in seismic analysis. Earthquake Engineering and Structural Dynamics, 9, 187-192.

Wilson EL, Penzien J (1981). Evaluation of orthogonal damping matrices. International Journal for Numerical Methods in Engineering, 4, 5-10.

Zhou XY, Yu RF, Liang D (2004). The complex-complete-quadratic combination (CCQC) method for seismic re-sponses of non-classically damped linear MDOF system. 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada, paper No. 848.


Refbacks

  • There are currently no refbacks.