Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

• Published in: Acta mechanica Sinica Vol. 25; no. 6; pp. 871 - 882
• Main Authors: Ozkaya, E, Sarigiil, M, Boyaci, H
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-12-2009
• Subjects: Bernoulli; Classical and Continuum Physics; Computational Intelligence; Curvature; Engineering; Engineering Fluid Dynamics; Equations of motion; Foundations; Mathematical analysis; Method of multiple scales; Nonlinearity; Research Paper; Resonant frequency; Theoretical and Applied Mechanics; Vibration; 横向振动; 积分微分方程; 立方非线性; 运动方程; 频率计算; Slightly curved beam; Nonlinear elastic foundation; Concentrated mass; Nonlinear vibrations
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-009-0275-1

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.