An accurate method for first and second derivatives of dynamic responses

Q. Liu, J. Zhang, L. Gu, L. Yan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper has developed an accurate method for calculating the first and second derivatives of dynamic responses with respect to the design variables of structures subjected to dynamic loads. An efficient algorithm to calculate the dynamic responses, their first and second derivatives with respect to the design variables is formulated based on the Newmark-β method. The algorithm is achieved by direct differentiation and only a single dynamics analysis is required. An example is demonstrated with the new method proposed in this paper and the analytical method. The comparative numerical results show the new method is highly accurate compared to the analytical method.

Original languageEnglish (US)
Pages (from-to)389-398
Number of pages10
JournalJournal of Mechanics
Volume27
Issue number3
DOIs
StatePublished - Sep 1 2011

Fingerprint

Second derivative
dynamic response
Dynamic Response
Dynamic response
Derivatives
Analytical Methods
dynamic loads
Dynamic loads
Newmark Method
Dynamic analysis
Dynamic Load
Dynamic Analysis
Efficient Algorithms
Calculate
Numerical Results
Design

Keywords

  • First derivative of dynamic response
  • Hessian matrix
  • Second derivative of dynamic response
  • Sensitivity analysis

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

Cite this

An accurate method for first and second derivatives of dynamic responses. / Liu, Q.; Zhang, J.; Gu, L.; Yan, L.

In: Journal of Mechanics, Vol. 27, No. 3, 01.09.2011, p. 389-398.

Research output: Contribution to journalArticle

Liu, Q. ; Zhang, J. ; Gu, L. ; Yan, L. / An accurate method for first and second derivatives of dynamic responses. In: Journal of Mechanics. 2011 ; Vol. 27, No. 3. pp. 389-398.
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