"Summed and Differential Harmonic"Oscillation in Non-Linear Vibratory Systems : Systems with Unsymmetrical Nonlinearity

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概要

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• The author has studied "summed and differential harmonic" oscillations occurring in rotating shaft systems, i.e., vibratory systems with gyroscopic terms. In the present paper, the author treats "summed and differential harmonic" oscillations appearing in rectilinear vibratory systems, the nature of which is quite different from that of systems with gyroscopic terms. By analytical discussion, it is concluded that summed types only can take place in rectilinear vibratory systems while both summed and differential type can occur in rotating shaft systems. Further, experimental results for two experimental apparatus having different construction from each other verify that "summed and differential harmonic" oscillations actually appear in rectilinear vibratory systems, and summed type only can take place.

• 一般社団法人日本機械学会の論文

著者

• Yamamoto Toshio

  Faculty Of Engineering Nagoya University

関連論文

• On the Internal Resonance in a Nonlinear Two-Degree-of-Freedom System : Forced Vibrations near the Higher Resonance Point When the Natural Frequencies Are in the Ratio 1:2
• Ultra-Subharmonic Oscillations in a Nonlinear Vibratory System
• On "Summed and Differential Harmonic" Oscillations in Nonlinear Vibratory Systems with Multiple-Degrees-of-Freedom
• Internal Resonance in a Rotating Shaft System : The Coincidence of Two Critical Speeds for Subharmonic Oscillation of the Order l/2 and Synchronous Backward Precession
• Effects of Nonlinear Spring Characteristics on the Dynamic Unstable Region of an Unsymmetrical Rotor
• Effects of Quartic Nonlinear Restoring Forces on 1/2-0rder Subharmonic and Summed-and-Differential Harmonic Oscillations of a Rotating Shaft : Variations of Resonance Curves and Occurrence of Unstable Vibrations
• Super-Summed-and-Differential Harmonic Oscillations in a Symmetrical Rotating Shaft System
• Vibrations of a Rotating Shaft with Rotating Nonlinear Restoring Forces at the Major Critical Speed
• Combination Tones in a Rotating Shaft System
• Unstable Vibrations of an Unsymmetrical Shaft at the Secondary Critical Speed due to Ball Bearings
• Nonlinear Forced Oscillations of a Rotating Shaft Carrying an Unsymmetrical Rotor at the Major Critical Speed
• Super-Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Shaft and an Unsymmetrical Rotor
• Subharmonic and Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Rotor
• Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Shaft
• Combination Tones of Summed Type in Nonlinear Vibratory Systems
• On the Internal Resonance in a Nonlinear Two-degree-of-freedom System : When the Natural Frequencies Are in the Ratio 2 : 3
• The Particular Vibration Phenomena Due to Ball Bearings at the Mayor Critical Speed : 2nd report, On the Effects of Symmetrical Nonlinear Spring Characteristics
• Oscillations of a Rotating Shaft with Symmetrical Nonlinear Spring Characteristics
• Super-Division Harmonic Oscillations Caused by Nonlinearity of the Fourth Order
• Super-Division Harmonic Oscillations in a Nonlinear Multidegree-of-Freedom System
• Internal Resonance in a Nonlinear Multi-degree-of-freedom Vibratory System When Its Natural Frequencies Satisfy the Condition p_1+p_2=p_3 or 2p_1+p_2=p_3
• Summed and Differential Harmonic Oscillations in a Slender Beam
• Sub-combination Tones in a Nonlinear Vibratory System : Caused by Symmetrical Nonlinearity
• Combination Oscillations in a Non-Linear Vibratory System with One Degree of Freedom
• Unstable Vibrations of an Unsymmetrical Rotor Supported by Flexible Bearing Pedestals
• On the Internal Resonance in a Nonlinear Two-Degree-of-Freedom System : Forced Vibrations Near the Lower Resonance Point When the Natural Frequencies are in the Ratio 1 : 2
• Subharmonic Oscillations of a Slender Beam
• Internal Resonance in a Parametrically Excited Three-Degree-of-Freedom System with Nonlinear Spring Characteristics : 1st Report, the Case that the Relation lp_i + mp_j = np_ Holds among the Natural Frequencies : Series C : Vibration Control Engineeri
• The Particular Vibration Phenomena Due to Ball Bearings at the Major Critical Speed
• On the Subharmonic Oscillations of Unsymmetrical Shafts
• On Vibrations of a Rotor with Variable Rotating Speed
• The Effect of a Flat Shaft on the Unstable Vibrations of the Shaft Carrying an Unsymmetrical Rotor
• On the Response Curves and the Stability of "Summed and Differential Harmonic"Oscillations
• On the Oscillations of "Summed and Differential Types"under Parametric Excitation : Vibratory Systems with Damping
• On the Vibrations of the Shaft Carrying an Asymmetrical Rotating Body
• Combination Tones of Differential Type in Nonlinear Vibratory Systems
• Unstable Vibrations of the Shaft Carrying an Unsymmetrical Rotating Body : Vibrations Induced by Flexibility of Bearing Pedestals
• On Sub-Harmonic and"Summed and Differential Harmonic"Oscillations of Rotating Shaft
• Forced Vibrations of a Rotor with Rotating Inequality
• On the Forced Vibrations of the Shaft Carrying an Unsymmetrical Rotor : Forced Vibrations Having the Circular Frequencies Differing from the Rotating Angular Velocity of the Shaft
• "Summed and Differential Harmonic"Oscillation in Non-Linear Vibratory Systems : Systems with Unsymmetrical Nonlinearity
• On the Forced Vibrations of the Shaft Carrying an Unsymmetrical Rotating Body : Response Curves of the Shaft at the Major Critical Speeds
• On the Oscillations of "Summed and Differential Types of Higher Order" under Parametric Excitation

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