Nonlinear response of beams with viscoelastic elements by an iterative linearization method

• Published in: International journal of non-linear mechanics Vol. 146; p. 104132
• Main Authors: Jiao, Yiyu, Xu, Wei, Song, Yi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2022
• Subjects: Fractional derivative; Nonlinear beam; Random vibration; Statistical linearization; Nonlinear beam; Statistical linearization; Random vibration; Fractional derivative
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2022.104132

An iterative successive linearization approach based on energy optimization is presented to estimate the response statistics of a moderately largely vibrating beam endowed with a fractional derivative, subject to combined harmonic and random excitations. The presented method is developed by constructing two sets of optimized linear systems, so that the responses of the new system are equivalent to those of the original system in the sense of average and statistical characteristics. Specifically, the iterative deterministic and statistical linearization methods are utilized successively, based on optimizations of the average and mean square difference between the potential energies associated with the original systems and their linear counterparts. Numerical examples are given with Monte Carlo data to demonstrate the reliability and accuracy of the presented method. •An iterative linearization approach, where the deterministic and statistical linearization method based on potential energies are implemented successively, has been developed as an approximate method for nonlinear response of beams with viscoelastic elements.•Improvement of accuracy in approximate response statistics compared with the classical linearization method is achieved by the presented method.•Deflections of a moderately largely vibrating beam under combined excitations is investigated to show the accuracy of the presented method, compared with Monte Carlo simulation and classical linearization data.•The influence of the fractional order on deflections, which renders the viscoelastic property, is well captured by the presented method.