Sub-combination Tones in a Nonlinear Vibratory System : Caused by Symmetrical Nonlinearity

スポンサーリンク

概要

• 論文の詳細を見る

• It has been shown that, in a nonlinear vibratory system subjected to several harmonic excitations of frequencies Ω_1,Ω_2,…, Ω_M, so-called combination tone can be induced with frequency Ω=│m_1Ω_1+m_2Ω_2+…+m_MΩ_M│ (m_1,m_2,…=±1,±2,…), When Ω is close to the natural frequency of the system. Also in this system a more general type of oscillation can be expected to occur with frequency Ω=(1/N)│m_1Ω_1Ω_2+…+m_MΩ_M│ (N=2,3,4,…; m_1,m_2,…=±1,±2,…) When Ω is close to the natural frequency. Such oscillations, if they occur, may be termed "sub-combination tone." The present paper concerns the occurrence of such oscillations in a typical case in which a system with nonlinear spring characteristics of a cubic function of the displacement is subjected to two periodic forces of frequencies Ω_1 and Ω_2. The theoretical analysis shows that the sub-combination tones of frequencies Ω=(1/2) │Ω_1±Ω_2│ can occur in the system. The theoretical analysis is checked by an analog-computer.

• 一般社団法人日本機械学会の論文

著者

• Yamamoto Toshio

  Faculty Of Engineering Nagoya University

• Yasuda Kimihiko

  Faculty Of Engineering Nagoya University

• NAKAMURA Takio

  Fujitsu Limited

• Nakamura Takio

  Fujitsu Limited.

• 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 Prestressed Circular Plate
• 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
• Single-Mode and Multimode Combination Tones in a Nonlinear Beam
• 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

もっと見る 閉じる

スポンサーリンク