This investigation treats the large amplitude transverse vibration of a hinged beam with no axial restraints and which has arbitrary initial conditions of motion. Nonlinear elasticity terms arising from moderately large curvatures, and nonlinear inertia terms arising from longitudinal and rotary inertia of the beam are included in the nonlinear equation of motion. Using a Galerkin variational method and a modal expansion, the problem is reduced to a system of coupled nonlinear ordinary differential equations which are solved for arbitrary initial conditions, using the perturbation procedure of multiple-time scales. The general response and frequency-amplitude relations are derived theoretically. Comparison with previously published results is made.
Skip Nav Destination
Sign In or Register for Account
Article navigation
March 1973
Research Papers
Nonlinear Vibrations of a Hinged Beam Including Nonlinear Inertia Effects
S. Atluri
S. Atluri
Department of Aeronautics and Astronautics, University of Washington, Seattle, Wash.
Search for other works by this author on:
S. Atluri
Department of Aeronautics and Astronautics, University of Washington, Seattle, Wash.
J. Appl. Mech. Mar 1973, 40(1): 121-126 (6 pages)
Published Online: March 1, 1973
Article history
Received:
November 1, 1971
Revised:
March 1, 1972
Online:
July 12, 2010
Article
Article discussed|
View article
Connected Content
Citation
Atluri, S. (March 1, 1973). "Nonlinear Vibrations of a Hinged Beam Including Nonlinear Inertia Effects." ASME. J. Appl. Mech. March 1973; 40(1): 121–126. https://doi.org/10.1115/1.3422909
Download citation file:
Sign In
Get Email Alerts
Cited By
A Geometrically Inspired Model for Brittle Damage in Compressible Elastomers
J. Appl. Mech (August 2021)
Related Articles
On the Original Publication of the General Canonical Functional of Linear Elasticity
J. Appl. Mech (March,2000)
Extension and Simplification of Salukvadze’s Solution to the Deterministic Nonhomogeneous LQR Problem
J. Dyn. Sys., Meas., Control (March,2001)
Thermal Buckling of Initially Stressed Thick Plates
J. Mech. Des (July,1982)
Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation
J. Comput. Nonlinear Dynam (January,2010)
Related Proceedings Papers
Related Chapters
Some Laws to Affect the Results in Numerical Calculus
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
Static Deformations Budget
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume II: Stiffness and Metrology
Neural Network Approach for Estimating Mass Moments of Inertia and Center of Gravity in Military Vehicles
Intelligent Engineering Systems through Artificial Neural Networks, Volume 16