Literature Review : LARGE AMPLITUDE FORCED VIBRATIONS OF SIMPLY-SUPPORTED THIN CYLINDRI CAL SHELLS Ginsberg, J. H. J. Appl. Mech., Trans. ASME 40 (2), 471-477 (June 1973) 17 refs Refer to Abstract No. 73-1229

1974 ◽  
Vol 6 (4) ◽  
pp. 74-75
Author(s):  
W.D. Iwan
Keyword(s):  
Literature Review ◽  
Large Amplitude ◽  
Forced Vibrations ◽  
Simply Supported ◽  
Trans Asme

Transition Mechanisms Attendant to Large Amplitude Parametric Vibrations of Rectangular Plates

1967 ◽  
Vol 89 (4) ◽  
pp. 619-625 ◽  
Author(s):  
J. H. Somerset
Keyword(s):  
Rectangular Plate ◽  
Large Amplitude ◽  
Strong Influence ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Parametric Vibrations ◽  
Periodic Load ◽  
Simply Supported ◽  
Stochastic Loading ◽  
Parametric Oscillations

Experiments have been conducted to investigate the transition mechanisms attendant to the parametric vibrations of a simply supported rectangular plate subjected to a periodic load of the form P = P0 + P1 cos γt. It is found that the transition mechanisms, such as “jumps” within the zone and “dropout” from the zone, are influenced by the initial curvature of the plate and by interactions with the source of energy. Due to the possibility of transitions between the parametric oscillations and forced vibrations of the plate, “splitting” of the zone may occur. Preliminary experiments indicate that the transition mechanisms have a strong influence on the response of the plate to stochastic loading.

Large amplitude flexural vibration of simply supported skew plates.

AIAA Journal ◽  
1973 ◽  
Vol 11 (9) ◽  
pp. 1279-1282 ◽  
Author(s):  
M. SATHYAMOORTHY ◽  
K. A. V. PANDALAI
Keyword(s):  
Large Amplitude ◽  
Flexural Vibration ◽  
Simply Supported

Free Vibration of a Large-Amplitude Deflected Plate—Reexamination by the Dynamical Systems Theory

1986 ◽  
Vol 53 (3) ◽  
pp. 633-640 ◽  
Author(s):  
J. Lee
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Invariant Tori ◽  
Plate Thickness ◽  
Standard Technique ◽  
Simply Supported ◽  
Nonlinear Plate ◽  
Power Spectral ◽  
Mode Truncation ◽  
Energy Components

For a simply supported large-amplitude deflected plate, Fourier expansion of displacement reduces the nonlinear plate equation to a system of infinitely coupled modal equations. To close off this system, we have suppressed all but the four lowest-order symmetric modes. In the absence of damping and forcing, the four-mode truncation can be recasted into a Hamiltonian of 4 DOF. Hence, the free vibration of nonlinear plate can be investigated by the standard technique of Hamiltonian systems. It has been found that subsystems of 2 DOF are practically stable in that the invariant tori remain on a smooth surface up to total energy of 1000, at which modal displacements can be 40 times the plate thickness. On the other hand, the trajectory of 4 DOF system develops chaos at a much lower energy value of 76, corresponding to modal displacements twice the plate thickness. This has been evidenced by many spikes in the power spectral density of displacement time-series and an erratic pattern that modal energy components cut through an energy sphere.

A Nonlinear Analysis of the Wahl–Fischer Torsional Instability

2020 ◽  
Vol 88 (2) ◽  
Author(s):  
E. F. Infante ◽  
S. Doughty
Keyword(s):  
Large Amplitude ◽  
Linear Analysis ◽  
Mathematical Explanation ◽  
Nonlinear Methods ◽  
Strongly Nonlinear ◽  
Instability Problem ◽  
Torsional Instability ◽  
Mechanical Devices ◽  
Trans Asme ◽  
Nonlinear Nature

Abstract This is an extension to a previous study of the Wahl–Fischer torsional instability problem (Infante and Doughty, “An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem”, J. Appl. Mech. Trans. ASME, 2020, 87(10), p. 101004). There, we provided a mathematical explanation of the reasons for the existence of torsional oscillations observed in numerical simulations and in actual mechanical devices such as the exhaust fan system studied by Wahl and Fischer. That explanation was mostly based on linear analysis. This paper presents an additional mathematical explanation of the nature and form of the large self-excited oscillations, due to the strongly nonlinear nature of the system and the large amplitude of these oscillations. Because the oscillations are large, their study requires the use of nonlinear methods.

The physiological value of different vibrations and rhythms (literature review)

2015 ◽  
Vol 9 (1) ◽  
pp. 0-0 ◽  
Author(s):  
Паньшина ◽  
M. Panshina ◽  
Беляева ◽  
Elena Belyaeva ◽  
Хадарцева ◽  
...  
Keyword(s):  
Literature Review ◽  
Complex Systems ◽  
Human Body ◽  
Golden Section ◽  
Forced Vibrations ◽  
Self Organization ◽  
Schumann Resonance ◽  
Physiological Processes ◽  
Oscillating Systems ◽  
Physiological Value

The review highlights the issues of functioning of self-oscillating systems in the human body, the importance of resonance in the life, the conformity physiological parameters to the principles of fractals, the Golden section and Fibonacci dependencies. The authors described natural and forced vibrations. Conjugation biosphere Schumann resonance with the functioning of organs and body systems, in particular, the normalization of melatonin-serotonin balance is demonstrated in this work. The authors have identified the value of the vibra-tions and rhythms in physiological processes of locomotor and cardiovascular systems. The parameters of life were evaluated from the viewpoint of the theory of chaos and self-organization of complex systems.

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