✦ LIBER ✦

ASYMPTOTIC APPROACH FOR NON-LINEAR PERIODICAL VIBRATIONS OF CONTINUOUS STRUCTURES

✍ Scribed by I.V. ANDRIANOV; V.V. DANISHEVS'KYY

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 324 KB
Volume: 249
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.2001.3878

No coin nor oath required. For personal study only.

✦ Synopsis

An asymptotic approach for determining periodic solutions of non-linear vibration problems of continuous structures (such as rods, beams, plates, etc.) is proposed. Starting with the well-known perturbation technique, the independent displacement and frequency is expanded in a power series of a natural small parameter. It leads to in"nite systems of interconnected non-linear algebraic equations governing the relationships between modes, amplitudes and frequencies. A non-trivial asymptotic technique, based on the introduction of an arti"cial small parameter is used to solve the equations. An advantage of the procedure is the possibility to take into account a number of vibration modes. As examples, free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non-linear restoring force are considered. Resonance interactions between di!erent modes are investigated and asymptotic formulae for corresponding backbone curves are derived.

2002 Academic Press

📜 SIMILAR VOLUMES

HIGHER ORDER ANALYSIS FOR NON-LINEAR VIB

HIGHER ORDER ANALYSIS FOR NON-LINEAR VIBRATIONS OF CONTINUOUS SYSTEMS

✍ A. MACCARI 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 141 KB

Periodic Solutions for Non-linear Equati

Periodic Solutions for Non-linear Equations of Structured Populations

✍ Stefano Bertoni 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 216 KB

We show the existence of non-trivial periodic solutions for a class of non-linear equations, model of age-structured populations. To this aim we use the theory of Centre Manifold for a class of abstract differential equations introduced by Desch and Schappacher, and show that a Hopf Bifurcation Theo

A combined approach for the identificati

A combined approach for the identification of continuous non-linear systems

✍ H. U. Voss; H. Rust; W. Horbelt; J. Timmer 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 893 KB

Non-linear finite element modal approach

Non-linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates

✍ Y. Y. Lee; H. Y. Sun; J. N. Reddy 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 1 views

A theoretical analysis is presented for the large amplitude vibration of symmetric and unsymmetric composite plates using the non-linear finite element modal reduction method. The problem is first reduced to a set of Duffing-type modal equations using the finite element modal reduction method. The m

A SEMI-ANALYTICAL APPROACH TO THE NON-LI

A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

✍ L. AZRAR; R. BENAMAR; R.G. WHITE 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 466 KB

The semi-analytical approach to the non-linear dynamic response of beams based on multimode analysis has been presented in Part I of this series of papers (Azrar et al., 1999 Journal of Sound and <ibration 224, 183}207 [1]). The mathematical formulation of the problem and single mode analysis have b

Discussion of paper ‘Revisiting Eurocode

Discussion of paper ‘Revisiting Eurocode 8 formulae for periods of vibration and their employment in linear seismic analysis’ by Helen Crowley and Rui Pinho, Earthquake Engineering and Structural Dynamics 2010; 39(2):223–235

✍ S. Bahadir Yuksel 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 38 KB 👁 1 views