Optimal seismic analysis of degrading planar frames using a weighted energy method to associate inelastic mode shapes: Part II application

Structural engineers routinely use rational dynamic analysis methods for the seismic analysis of buildings. In linear analysis based on modal superposition or response spectrum approaches, the overall response of a structure (for instance, base shear or inter-storey drift) is obtained by combining the responses in several vibration modes. These modal responses depend on the input load, but also on the dynamic characteristics of the building, such as its natural periods, mode shapes, and damping. At the design stage, engineers can only predict the natural periods using eigenvalue analysis of structural models or empirical equations provided in building codes. However, once a building is constructed, it is possible to measure more precisely its dynamic properties using a variety of in situ dynamic tests. In this paper, we use ambient motions recorded in 27 reinforced concrete shear wall (RCSW) buildings in Montréal to examine how various empirical models to predict the natural periods of RCSW buildings compare to the periods measured in actual buildings under ambient loading conditions. We show that a model in which the fundamental period of RCSW buildings varies linearly with building height would be a significant improvement over the period equation proposed in the 2010 National Building Code of Canada. Models to predict the natural periods of the first two torsion modes and second sway modes are also presented, along with their uncertainty.

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Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping

Advances in Mathematical Physics ◽

10.1155/2020/3060867 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Ran Duan ◽

Mina Jiang ◽

Yinghui Zhang

Keyword(s):

Asymptotic Behavior ◽

Dirichlet Boundary ◽

Boundary Effect ◽

Initial Perturbation ◽

Time Dependent ◽

Asymptotic Behavior Of Solutions ◽

P System ◽

Weighted Energy Method ◽

Weighted Energy ◽

Constant State

In this paper, we consider the asymptotic behavior of solutions to the p-system with time-dependent damping on the half-line R+=0,+∞, vt−ux=0,ut+pvx=−α/1+tλu with the Dirichlet boundary condition ux=0=0, in particular, including the constant and nonconstant coefficient damping. The initial data v0,u0x have the constant state v+,u+ at x=+∞. We prove that the solutions time-asymptotically converge to v+,0 as t tends to infinity. Compared with previous results about the p-system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to H3R+×H2R+. Our proof is based on the time-weighted energy method.

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Modal Test of Scaled-Down Reactor Internals in SMART Considering the Fluid-Structure Interaction

ASME 2011 Small Modular Reactors Symposium ◽

10.1115/smr2011-6574 ◽

2011 ◽

Author(s):

Seungho Lim ◽

Kyungrok Ha ◽

Kyoung-Su Park ◽

No-Cheol Park ◽

Young-Pil Park ◽

...

Keyword(s):

Dynamic Characteristics ◽

Seismic Analysis ◽

Fluid Structure Interaction ◽

Mass Effect ◽

Mode Shapes ◽

Structural Dynamic ◽

Fluid Structure ◽

Structure Interaction ◽

Standard Design ◽

Reactor Internals

The System-integrated Modular Advanced ReacTor (SMART) is a small modular integral-type reactor for the seawater desalination and small-scaled power generation under development in Korea. Although the SMART is innovative reactor with a sensible mixture of the proven technology and advanced design features aimed at enhanced safety, there is no valid prototype which can specify the structural dynamic characteristics of reactor internals. Thus, extensive research for the technology verification and standard design approval are in progress. One of them is to perform the dynamic characteristics identification of reactor internals. Especially, it is focused on the added mass effect caused by the fluid-structure interaction because the reactor internals is submerged in the reactor coolant. The extracted dynamic characteristics such as the natural frequencies and the vibratory mode shapes can be used as the basis on further dynamic analysis, for example, seismic analysis and a postulated pipe break analysis.

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Free Vibration of Rectangular Membranes With Linearly Varying Tension and Light Flexural Rigidity

14th Biennial Conference on Mechanical Vibration and Noise: Vibrations of Mechanical Systems and the History of Mechanical Design ◽

10.1115/detc1993-0259 ◽

1993 ◽

Author(s):

D. J. Gorman

Keyword(s):

Free Vibration ◽

Energy Method ◽

Flexural Rigidity ◽

Mode Shapes ◽

Classical Solutions ◽

Linear Variation ◽

Simple Task ◽

Gravitational Forces ◽

Analytical Results

Abstract The proposal to utilize tensioned rectangular membranes as antennae in interspace communication has resulted in the focus of considerable attention on the free vibration of membranes with complicated in-plane loadings. In this paper the problem of analizing the vibration of a rectangular membrane with linear variation in tension in one direction is examined. This tension variation occurs due to gravitational forces when the membranes are tested experimentally in vibration laboratories. The Rayleigh-Ritz energy method is employed to obtain analytical results. Convergence is found to be rapid. Mode shapes are compared with those of known classical solutions when no tension variation is permitted. Generation of the eigenvalue matrix is demonstrated to be a very simple task.

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