Adaptive h-version eigenfrequency analysis

Wiberg, Nils‐Erik; Baušys, Romualdas; Hager, Patrik

doi:10.1016/s0045-7949(98)00235-1

Cited by 26 publications

(22 citation statements)

References 27 publications

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“…Therefore they are very different from the usual linear eigenvalue problems, because they possess an infinite number of eigensolutions even though the order of the dynamic stiffness matrix is finite. Hence the higher natural frequencies are obtainable from the transcendental eigenproblem, unlike the linear eigenproblem in which higher natural frequencies can be modelled with reasonable accuracy only by accepting the large computational cost of making the size of elements small enough Wiberg et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

An accurate method for transcendental eigenproblems with a new criterion for eigenfrequencies

Kennedy

Williams

2004

International Journal of Solids and Structures

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Section: Introductionmentioning

confidence: 99%

An accurate method for transcendental eigenproblems with a new criterion for eigenfrequencies

Kennedy

Williams

2004

International Journal of Solids and Structures

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“…This type of post-process is used in other contexts, for instance, in assessing the error L 2 -norm in static problems [60,61] or, in building enhanced vibration modes and eigenfrequencies [62]. In the following, the post-process strategy introduced in [62] is presented.…”

Section: Assessing Space Discretization Errorsmentioning

confidence: 99%

Error Assessment in Structural Transient Dynamics

Verdugo

Mariné

Dı́ez

2014

Arch Computat Methods Eng

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This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates.

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“…This method has been employed to control a p-adaptive strategy [21]. However, this procedure seemed unpractical [22].…”

Section: State Of Knowledgementioning

confidence: 99%

“…At the end of the 1990s Wiberg and coworkers published a series of papers on adaptive methods for natural vibrations [22][23][24][25]. They developed Superconvergent Patch Recovery based method for eigenfrequency error evaluation.…”

Section: State Of Knowledgementioning

confidence: 99%