A set of reduced order differential equations of motion that are suited for analyzing the nonlinear dynamics of beams subjected to external excitations is developed using a variational formulation. The beam may have arbitrary property variations along its span, may carry any number of concentrated masses, and may have multiple supports. It may also be subjected to a base excitation in the form of a prescribed displacement imposed to the supports. The distributed and/or concentrated forces acting on the system may have a nonzero time average so that the equilibrium solution of the system does not necessarily coincide with its undeformed state. Because the first approximation to the elastic deformation of the beam is governed, in general, by partial differential equations with variable coefficients, the solution for the bending displacements at that level is obtained numerically. An analytical methodology is used to formulate, in a mathematically consistent manner, the reduced order nonlinear differential equations explicitly. Specific examples are then used in order to assess the combined effect of the nonlinear terms on the dynamic response of a beam subjected to both static and dynamic loads.
Skip Nav Destination
Close
Sign In or Register for Account
Article navigation
November 1997
Review Articles
General Reduced Order Analytical Model for Nonlinear Dynamic Analyses of Beams With or Without Lumped Masses
M. R. M. Crespo da Silva
M. R. M. Crespo da Silva
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy NY 12180-3590
Search for other works by this author on:
M. R. M. Crespo da Silva
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy NY 12180-3590
Appl. Mech. Rev. Nov 1997, 50(11S): S28-S35
Published Online: November 1, 1997
Article history
Online:
April 20, 2009
Citation
Crespo da Silva, M. R. M. (November 1, 1997). "General Reduced Order Analytical Model for Nonlinear Dynamic Analyses of Beams With or Without Lumped Masses." ASME. Appl. Mech. Rev. November 1997; 50(11S): S28–S35. https://doi.org/10.1115/1.3101844
Download citation file:
- Ris (Zotero)
- Reference Manager
- EasyBib
- Bookends
- Mendeley
- Papers
- EndNote
- RefWorks
- BibTex
- ProCite
- Medlars
Close
Sign In
17
Views
0
Citations
Get Email Alerts
Cited By
Performance and Manufacturing of Silicon-Based Vapor Chambers
Appl. Mech. Rev (January 2021)
Mixed Convection in Pipe and Duct Flows With Strong Magnetic Fields
Appl. Mech. Rev (January 2021)
Bio-Inspired Vibration Isolation: Methodology and Design
Appl. Mech. Rev (March 2021)
Shear Bands in Materials Processing: Understanding the Mechanics of Flow Localization From Zener's Time to the Present
Appl. Mech. Rev (November 2020)
Related Articles
Dynamic Analysis of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root
J. Appl. Mech (September,1999)
Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems
Appl. Mech. Rev (November,2001)
Systems of
Conservation Laws: Two-Dimensional Riemann Problems. Progress in Nonlinear Differential Equations
and Their Applications, Vol. 38
Appl. Mech. Rev (September,2002)
Nonlinear Free Vibration of a Symmetrically Conservative Two-Mass System With Cubic Nonlinearity
J. Comput. Nonlinear Dynam (January,2010)
Related Proceedings Papers
Related Chapters
Introduction to Analysis Tools
Dynamics of Particles and Rigid Bodies: A Self-Learning Approach
Cellular Automata: In-Depth Overview
Intelligent Engineering Systems through Artificial Neural Networks, Volume 20
Asymptotic Criterion for Solution of Nonlinear Differential Equation
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)