A Modal Superposition Method for Non-Linear Structures

Kuran, Bayindir; Özgüven, H. Nevzat

doi:10.1006/jsvi.1996.0022

Cited by 51 publications

(34 citation statements)

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“…For each input scenario, the transmissibility curve of the isolator was first solved in the frequency domain with Newton-Raphaen iterations [25][26][27][28] and plotted as lines in the following figures. Then, direct time integration was also performed to validate the frequency domain results, where the time history responses of the nonlinear Zener model were obtained by integrating the original time domain equation (Eqs.…”

Section: Numerical Examples and Discussionmentioning

confidence: 99%

“…As the isolator subjected to harmonic excitation and considered with sufficient linear damping (e.g., with a linear modal damping of 0.1-0.3), the primary harmonic term can be assumed to dominate its steady-state response [25][26][27], i.e., r ≈ Im Re jϕ (3) where R denotes the complex response of the nonlinear secondary spring, ϕ denotes its generic angle and j is the imaginary unit.…”

Section: Description Of Nonlinear Zener Modelmentioning

confidence: 99%

“…(10) needs to be solved iteratively [8,[25][26][27][28][29][30] or inversely [31] to obtain the responses sincek eq f is dependent on the responses X 2 , although it can be written in a form of 'linear' transfer function. After solving Eq.…”

Section: Force Transmissibility Under Force Excitationsmentioning

confidence: 99%

“…(27). Thus, jump phenomenon can be avoided [8] if the response curve of the isolator under force excitations has just one or none point that satisfies Eq.…”

Section: Force Transmissibility Under Force Excitationsmentioning

confidence: 99%

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Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

2016

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In order to obtain an isolator with low resonance amplitude as well as good isolation performance at high frequencies, this paper explores the usage of nonlinear stiffness elements to improve the transmissibility efficiency of a sufficient linear damped vibration isolator featured with the Zener model. More specifically, we intend to improve its original poor highfrequency isolation performance and meanwhile maintain or even reduce its already low resonance amplitude by adding a nonlinear secondary spring into the isolator. Its isolation performances are evaluated under two input scenarios namely force transmissibility under force input and displacement transmissibility under base excitations, respectively. Thereafter, both analytical and numerical study is performed to compare the high-frequency transmissibility as well as resonance condition of the nonlinear isolator with its corresponding linear one. Results show that the introduction of nonlinear secondary spring in the Zener model can achieve an ideal improvement, i.e., reducing the transmissibility at high frequencies and meanwhile suppressing the resonance amplitude. It is also shown that both force and displacement transmissibility of the non-

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Section: Numerical Examples and Discussionmentioning

confidence: 99%

Section: Description Of Nonlinear Zener Modelmentioning

confidence: 99%

Section: Force Transmissibility Under Force Excitationsmentioning

confidence: 99%

“…(27). Thus, jump phenomenon can be avoided [8] if the response curve of the isolator under force excitations has just one or none point that satisfies Eq.…”

Section: Force Transmissibility Under Force Excitationsmentioning

confidence: 99%

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Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

2016

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“…The problem of orthogonality is not treated. Kuran et al [35] proposed a modal superposition method using iterative schemes and numerical integration of equations of motions. Parametric method was referred to and orthogonality problem has not been invoked.…”

Section: Eigenvectorsmentioning

confidence: 99%

Contribution to the Extension of Modal Analysis to Non-Linear Structure Using Volterra Functional Series

Tawfiq

Vinh

2003

Mechanical Systems and Signal Processing

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Displacement estimation of nonlinear structures using the force analogy method

2014

Structural Design Tall Build

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SUMMARY Significant effort has gone toward developing accurate and efficient displacement estimation procedures for the nonlinear multi‐degree‐of‐freedom (MDOF) system. Although the dynamic nonlinear analysis is capable of providing the high computational precision through the step‐by‐step time integration method, the simplified method is still expected and imperative for seismic design practices. The work presented in this paper focuses on the implementation of using the modal superposition method to estimate displacement responses of the nonlinear MDOF system based on the force analogy method (FAM). The current research demonstrated that the equation of motion for the nonlinear MDOF system can be decoupled, but other two governing equations in the FAM about the internal force, such as the moment and force of structural members, are not decomposable. Thus, the FAM is incorporated with the modal pushover analysis (MPA) method to determine the basic parameters of each mode such that the modal superposition method can be suitable for the solution of the nonlinear MDOF system. The procedure presented here is an approximately estimation method due to the application of MPA method. However, the value and potential for the maximum displacement estimation of the nonlinear MDOF system were demonstrated through the application in a framed structure. Copyright © 2014 John Wiley & Sons, Ltd.

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A Modal Superposition Method for Non-Linear Structures

Cited by 51 publications

References 0 publications

Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

Contribution to the Extension of Modal Analysis to Non-Linear Structure Using Volterra Functional Series

Displacement estimation of nonlinear structures using the force analogy method

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