Wave Propagation in Buildings as Periodic Structures: Timoshenko Beam with Rigid Floor Slabs Model

Özmutlu, Aydin; Ebrahimian, Mahdi; Todorovska, Maria I.

doi:10.1061/(asce)em.1943-7889.0001436

Cited by 15 publications

(6 citation statements)

References 37 publications

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“…In the continuous system calculation model, depending on the structural bearing system and the importance of axial displacements, the structures can be idealized as an equivalent flexural-shear beam, shear beam, Timoshenko beam, flexural beam, and sandwich beam. Studies on the modelling of buildings as equivalent Timoshenko beams have been conducted in the literature [20][21][22][23][24][25][26][27][28][29][30]. In these studies, it was concluded that the Timoshenko beam model is suitable for the analysis and identification of regular buildings.…”

Section: Mathematical Model Of the Spsw Systemmentioning

confidence: 99%

An approach for dynamic analysis of steel plate shear wall systems

Gungor¹,

Bozdoğan²

2022

JCE

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In this paper, the Timoshenko beam model (continuous system model) is originally adapted for dynamic analysis of steel plate shear wall (SPSW) systems. Dynamic characteristics for the first three modes are found by solving differential equation of the equivalent Timoshenko beam model using the differential transformation method. Dynamic characteristics are tabulated for quick and practical calculation. With the help of the dynamic characteristics, the response spectrum analysis of such buildings is performed. The continuous system calculation model has been used in the literature for free vibration analysis of such systems. Using the approach developed in this study, it is possible to calculate not only natural periods, but also the base shear force, maximum storey displacement, and maximum storey drift ratio. The differential transformation method is used in this study for solving the differential equation written according to the continuous system calculation model. To investigate the suitability of the method presented in the study, an example taken from the literature is solved and the results are evaluated. The results show that the method presented can be used in the preliminary design stage.

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Section: Mathematical Model Of the Spsw Systemmentioning

confidence: 99%

An approach for dynamic analysis of steel plate shear wall systems

Gungor¹,

Bozdoğan²

2022

JCE

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“…Periyodik yapılar üzerine çalışmalar sınıflandırıldığında iki kategoride; geometrik ve malzeme periyodikliği üzerine bunların toplandığı ortaya çıkmaktadır. Mikro ölçekteki kirişlerden [6], köprüler [7], geniş açıklıklı yapılar [8] ve binalar [9] gibi makroskobik yapılara kadar çeşitli mühendislik alanlarında karşılaşılabilecek periyodik yapılarda eğilme dalga yayılımı ve titreşimleri ortaya çıkar. Mekanik dalgaların veya titreşimlerin kontrol edilmesinde en önemli yapılar yerel rezonatörler [10] veya fononik kristallerdir [11].…”

Section: Introductionunclassified

Propagation of flexural waves in beams with periodic lumped mass

Özmutlu

2022

NÖHÜ Müh. Bilim. Derg.

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In this study, dispersion analysis is carried out in the Euler-Bernoulli beam with periodic lumped mass, and periodicity effects are investigated. First, the dispersion relation is derived using the propagator matrix method for an infinitely long periodic beam with lumped mass. The banded frequency spectrum is given depending on the mass ratio. Then, in the case of a finite number of periodic lumped masses, the effect on wave propagation was investigated and the transmission function was obtained. Finally, the displacement mode shapes of the barrier consisting of these lumped masses were obtained for the pass and stop band frequency values. The results show that it is possible to use designs made with periodic lumped masses as wave barriers.

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“…Examples of simple models are shear and Timoshenko beams, which can model 1D vertically propagating waves, the latter considering the effect of dispersion caused by bending deformation, beams with slabs, which consider dispersion due to periodicity of the floors, and shear plates, which can also model the wave passage effects. 1,9,[20][21][22][23]34,45 In contrast to these simple models, which assume that plane sections remain plane, the more complex models, such as frames and generalized beams derived by homogenization of frames, take into account internal deformations in the structure. [51][52][53][54][55] These generic models studied typically are prismatic, with uniform or piecewise uniform cross-sections.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in a doubly tapered shear beam: Model and application to a pyramid‐shaped skyscraper

Todorovska

Girmay²,

Wang³

et al. 2021

Earthq Engng Struct Dyn

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One dimensional wave propagation is studied in a cantilever conical structure deforming in shear. The structure has rectangular cross-section both dimensions of which decrease linearly along the polar axis (hence, doubly tapered). The equation motion is derived and solved in terms of spherical Bessel functions, which can be expressed exactly as finite algebraic expressions in terms of powers and sine and cosine functions of the polar coordinate. The transfer-matrix for a truncated pyramid element is then derived and generalized to a chain of elements. The model is used to represent a 48-story pyramid-shaped steel-frame skyscraper, the Transamerica Tower in San Francisco, California, in which the Loma Prieta, 1989 earthquake (𝑀 w = 6.9, epicentral distance, 𝑅 ≈ 90 km) was recorded by an array of accelerometers. The building is modeled by homogeneous and layered truncated pyramids. Wave propagation through the building is studied by analysis of impulse response functions computed from the observed earthquake accelerations. In addition, its equivalent homogeneous beam shearwave velocity is identified solely from its geometry and observed fundamental frequency of vibration. Further, the variation of wave velocity along is height is identified by least squares fit of a layered pyramid model in the observed impulse response functions. The results reveal equivalent homogeneous pyramid wave velocity of about 150-160 m/s in both directions, which is similar to other steelframe structures. The identified wave velocity profiles are consistent with the structural design. The identified parameters can be used as reference in future structural health monitoring of this structure.

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Wave Propagation in Buildings as Periodic Structures: Timoshenko Beam with Rigid Floor Slabs Model

Cited by 15 publications

References 37 publications

An approach for dynamic analysis of steel plate shear wall systems

An approach for dynamic analysis of steel plate shear wall systems

Propagation of flexural waves in beams with periodic lumped mass

Wave propagation in a doubly tapered shear beam: Model and application to a pyramid‐shaped skyscraper

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