Efficient method for dynamic condensation of nonclassically damped vibration systems

Qu, Zu-Qing; Selvam, R. P.

doi:10.2514/3.15070

Cited by 6 publications

(10 citation statements)

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“…sm mm mm mm mm sm t I T t (9) where I is the unit matrix of size m m and T is the transformation matrix between mm and sm in the whole system. Substituting Eq.…”

Section: Substructuring For Iirs Methodsmentioning

confidence: 99%

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Improvement of substructuring reduction technique for large eigenproblems using an efficient dynamic condensation method

2008

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An accelerated substructuring reduction procedure for the iterated improved reduced system (IIRS) method is proposed. The iterated IIRS method can be combined with a substructuring scheme to provide an efficient methodology for large-scale eigenvalue problems. Not only can it reduce eigenvalue analysis errors through successive iterations, but the accuracy of the eigenanalysis is not sensitive to the selected master degrees of freedom. In practical structural eigenproblems, reducing the number of iterations can save a great deal of computation cost. The present substructuring technique modifies the iterative form of the transformation matrices in each substructure to achieve faster convergence. Applications of the present method to two numerical examples demonstrate that the proposed method can obtain lower eigensolutions of structures more accurately and efficiently, as compared with those of the current substructuring technique.

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“…sm mm mm mm mm sm t I T t (9) where I is the unit matrix of size m m and T is the transformation matrix between mm and sm in the whole system. Substituting Eq.…”

Section: Substructuring For Iirs Methodsmentioning

confidence: 99%

“…Recently, an iterative method for nonclassically damped systems was proposed by Qu [8][9][10][11]. Qu presented various condensation methods for nonclassically damped systems defined in displacement space and state space.…”

Section: Introductionmentioning

confidence: 99%

Improvement of substructuring reduction technique for large eigenproblems using an efficient dynamic condensation method

2008

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“…Jenkinseta [21] used a finite element model to demonstrate the detailed dynamics of a typical raftisolation-receiver system using secondary force inputs in parallel with a passive isolation system. Qu and Selvam [22] developed dynamic condensation method to reduce the number of degrees of freedom of finite element models for a damped system. Xu [23] investigated the intensity of a rectangular plate with stiffeners using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

“…For complex structures, finite element analysis [21][22][23] (FEA) is often used to analyze the dynamic behavior with good accuracy in the low-frequency range. Jenkinseta [21] used a finite element model to demonstrate the detailed dynamics of a typical raftisolation-receiver system using secondary force inputs in parallel with a passive isolation system.…”

Section: Introductionmentioning

confidence: 99%

Research on transmission paths of a coupled beam-cylindrical shell system by power flow analysis

et al. 2009

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A power flow analysis based on a substructure approach is performed to exhibit vibration transmission in a complex coupled beam-cylindrical shell system. The system is divided into a shell substructure and a beam substructure, which are coupled by three spring-dampers. The theoretical receptance function of each substructure with a free-free interface condition is formulated by modal analysis to describe the dynamical behavior. On the basis of the receptance functions of the two substructures as well as synthesis through the geometrical compatibility and force balance conditions at the coupling interfaces, the dynamic characteristics of the coupled system are calculated. Both the input and transmitted powers within the system are estimated, and the influences of the excitation locations, the stiffness and loss factor of the spring-dampers on the vibration transmission are investigated as well.

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“…(2003) also conducted an eigenvalue analysis of a nonproportional damped beam, and an expansion in state form was generated in conjunction with a transfer matrix technique. Such analyses were also performed in (Qu and Selvam, 2002; Li et al., 2016; Lzaro, 2016), wherein the governing matrices were uniformly symmetric, although the effects of nonproportional damping were included. Through this specific literature review, the following conclusions are drawn at this stage.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solution and its validation by numerical inverse Laplace transformation and FEM for a damped Timoshenko beam subjected to impact and moving loads

Zhang

Liang

Zhao

2018

Journal of Vibration and Control

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This paper, taking the clamped boundary condition as an example, develops Su and Ma's fundamental solutions of the dynamic responses of a Timoshenko beam subjected to impact load. Based on that, a further extension regarding the general moving load case is also established. Kelvin–Voigt damping, whether proportionally or nonproportionally damped, is incorporated into the model, making it more comprehensive than the model of Su and Ma. Numerical inverse Laplace transformation is introduced to obtain the time-domain solution, where Durbin's formula and the corresponding convergence criteria are utilized in numerical experiments. Further, the real modal superposition method is applied at an analytical level to validate the numerical results by applying a proportionally damped condition. Total comparisons are made between the methods by sufficient case studies. The dynamic responses with and without damping effect are computed with wider slenderness to verify the correctness and effectiveness of the numerical results. Furthermore, parametric studies regarding the damping coefficients are performed to explore the nonproportional damping effect. The results show that the structural damping has significant influences on the dynamic behaviors and is especially stronger at small slender ratios. As the damping decreases the inherent frequencies and excites the low-frequency modal components more actively, a resonant phenomenon appears in high slenderness case when the beam experiences a low-speed moving load. Additionally, the computations in the moving load case indicate that the algorithm convergence is preferable when the number of grids exceeds 1000.

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Efficient method for dynamic condensation of nonclassically damped vibration systems

Cited by 6 publications

References 0 publications

Improvement of substructuring reduction technique for large eigenproblems using an efficient dynamic condensation method

Improvement of substructuring reduction technique for large eigenproblems using an efficient dynamic condensation method

Research on transmission paths of a coupled beam-cylindrical shell system by power flow analysis

Fundamental solution and its validation by numerical inverse Laplace transformation and FEM for a damped Timoshenko beam subjected to impact and moving loads

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