contributor author | A. H. Nayfeh | |
contributor author | S. A. Nayfeh | |
date accessioned | 2017-05-08T23:48:51Z | |
date available | 2017-05-08T23:48:51Z | |
date copyright | April, 1995 | |
date issued | 1995 | |
identifier issn | 1048-9002 | |
identifier other | JVACEK-28820#199_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/116276 | |
description abstract | We use two approaches to determine the nonlinear modes and natural frequencies of a simply supported Euler-Bernoulli beam resting on an elastic foundation with distributed quadratic and cubic nonlinearities. In the first approach, we use the method of multiple scales to treat the governing partial-differential equation and boundary conditions directly. In the second approach, we use a Galerkin procedure to discretize the system and then determine the normal modes from the discretized equations by using the method of multiple scales and the invariant manifold approach. Whereas one- and two-mode discretizations produce erroneous results for continuous systems with quadratic and cubic nonlinearities, all methods, in the present case, produce the same results because the discretization is carried out by using a complete set of basis functions that satisfy the boundary conditions. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Nonlinear Normal Modes of a Continuous System With Quadratic Nonlinearities | |
type | Journal Paper | |
journal volume | 117 | |
journal issue | 2 | |
journal title | Journal of Vibration and Acoustics | |
identifier doi | 10.1115/1.2873898 | |
journal fristpage | 199 | |
journal lastpage | 205 | |
identifier eissn | 1528-8927 | |
keywords | Boundary-value problems | |
keywords | Equations | |
keywords | Frequency | |
keywords | Functions AND Manifolds | |
tree | Journal of Vibration and Acoustics:;1995:;volume( 117 ):;issue: 002 | |
contenttype | Fulltext | |