Non-linear vibration of a moderately thick shallow clamped arch

Singh, Pradeep; Ali, S. M. J.

doi:10.1016/s0022-460x(75)80174-x

Cited by 6 publications

(2 citation statements)

References 11 publications

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“…Rehfield (1974) derived the equations of motion of a shallow arch with an arbitrary rise function and studied the free vibrations. By adding the effects of transverse shear and rotary inertia, Singh and Ali (1975) studied a moderately thick clamped beam with a sinusoidal rise function. Tien et al(1994) studied the dynamics of a shallow arch subjected to harmonic excitation.…”

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confidence: 99%

Elasti̇k Mesnetleri̇n Hafi̇fçe Eğri̇ Bi̇r Ki̇ri̇şi̇n Nonli̇neer Ti̇treşi̇mleri̇ne Etki̇leri̇

Sarıgül¹

2018

Uludağ University Journal of the Faculty of Engineering

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In this study, nonlinear vibrations of a slightly curved beam having arbitrary rising function are handled. The beam is restricted in longitudinal direction using elastic supports on both ends. Sag-to-span ratio of the beam, which is assumed to have sinusoidal curvature function at the beginning, is taken as 1/10. Beam being of Euler-Bernoulli type rests on Winkler elastic foundation and carries an arbitrarily placed concentrated mass. Equations of motion are obtained by using Hamilton Principle. Cubic and quadratic nonlinear terms have been aroused at the mathematical model because of the foundation and the beam's elongation. The Method of Multiple Scales (MMS), a perturbation technique, is used to solve the equations of motion analytically. The primary resonance case is taken into account during steady-state vibrations. The natural frequencies are obtained exactly for different control parameters such as supports' types, locations of the masses and linear coefficient of foundation. Frequency-amplitude and frequencyresponse graphs are drawn by using amplitude-phase modulation equations.

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confidence: 99%

Elasti̇k Mesnetleri̇n Hafi̇fçe Eğri̇ Bi̇r Ki̇ri̇şi̇n Nonli̇neer Ti̇treşi̇mleri̇ne Etki̇leri̇

Sarıgül¹

2018

Uludağ University Journal of the Faculty of Engineering

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“…Singh and Ali [13] studied a moderately thick clamped beam with a sinusoidal rise function by adding the effects of transverse shear and rotary inertia. Yamaki and Mori [14] analyzed a clamped buckled beam by considering the first three symmetric modes.…”

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confidence: 99%

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

2009

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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 nonlinear 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 multiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequencies 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.

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References

1995

Nonlinear Oscillations

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(1974). The inverse scattering transform Fourier analysis for nonlinear problems. Stud Appl. Math.. 53,249-315.588 Adams, 0. E. and R. M. Evan-Iwanowski (1973 Agrawal, B. N. (1975). Nonstationary and nonlinear vibration analysis and its application.Agrawal, B. J., and R. M. Evan-lwanowski (1973). Resonances in nonstationary, nonlinear, Ahmad, J., and H. C. Lee (1975). Nonlinear acoustic response of a cylindrical shell. J.Ahuja, R., and R. C. Duffield (1975). Parametric instability of variable crosssection beams Aks, S., and R. Carhart (1970). Renormalized perturbation theory for the weakly nonlinear

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Non-linear vibration of a moderately thick shallow clamped arch

Cited by 6 publications

References 11 publications

Elasti̇k Mesnetleri̇n Hafi̇fçe Eğri̇ Bi̇r Ki̇ri̇şi̇n Nonli̇neer Ti̇treşi̇mleri̇ne Etki̇leri̇

Elasti̇k Mesnetleri̇n Hafi̇fçe Eğri̇ Bi̇r Ki̇ri̇şi̇n Nonli̇neer Ti̇treşi̇mleri̇ne Etki̇leri̇

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

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