Higher Approximate Solutions of the Duffing Equation : Odd Order Superharmonic Resonances in the Hard Spring System
スポンサーリンク
概要
- 論文の詳細を見る
In the previous paper, an algorithm was presented to obtain the periodic solutions and stability of nonlinear multi-degree-of-freedom systems with high speed and high accuracy, based on the harmonic balance method and the infinitesimal stability criterion. A revised algorithm is presented to give only odd order solutions which are composed of odd order harmonics only and so reduce the dimensions of the amplitude vector and Jacobian matrix to about one-half of the previous ones. The Duffing system with hard spring is analysed by this algorithm and the detailed frequency responses are computed for odd order superharmonic resonances (order 3, 5, 7, 9) which are odd order solutions. The results are shown for each resonance region in terms of (a) maximum amplitudes and norms, (b) superharmonic amplitudes, (c) fundamental amplitudes, and (d) fundamental and superharmonic phase angles. Some of these are confirmed by numerical simulation.
- 一般社団法人日本機械学会の論文
著者
-
Sueoka Atsuo
Faculty Of Engineering Kyushu University
-
TAMURA Hideyuki
Faculty of Engineering, Kyushu University
-
Tamura H
Department Of Intelligent Machinery And Systems Faculty Of Engineering Kyushu University
-
KONDOU Takahiro
Kyushu University.
-
Tamura Hideyuki
Faculty Of Engineering Kyoto University
関連論文
- Free Vibration Analysis of a Tree Structure by the Transfer Influence Coefficient Method : 2nd Report, Treatment of a Three-Dimensional Tree Structure and Numerical Computational Results
- Free Vibration Analysis of a Tree Structure by the Transfer Influence Coefficient Method : 1st Report, Formulation for a Two-dimensional Tree Structure
- Nonlinear Forced Vibration of Roller Chain
- Analysis of Coupled Vibration between Railway Vehicle Wheels and a Rail in Both Vertical and Horizontal Directions Using an Approximate Model with an Infinite Number of Vehicles
- Vibration Control of a Rotating Disk Subjected to a Periodic External Force by Dynamic Absorbers
- Nonlinear Response of Roller Chain to Combined Forcing and Parametric Excitations
- Vibrations of Nonlinear Systems with Discontinuities : The Case of a Preloaded Compliance System
- Nonlinear Free Vibration of Roller Chain Streched Vertically
- On the Static Running Accuracy of Cylindrical Roller Bearings
- Research on the Interaction between Power Source and Machinery : Part 3,Vibrating Lift Made by Utilizing the Principle of Self-Synchronization
- Nonlinear Harmonic and Parametric Resonances of a Roller Chain Stretched Horizontally
- Subharmonic Oscillation of Order 1/3 in Roller Chain : 1st Report, Theoretical Analysis of the System Having Multiple Degrees of Freedom
- Quenching of Frictional Vibration of a Rotating Circular Plate by Dynamic Absorbers
- Self-Excited vibrations of a Rotating Circular Plate : 2nd Report, The Case of a Circular Plate with Internal Resonance : Series C : Vibration Control Engineering Engineering for Industry
- Self-Excited Vibrations of a Rotating Circular Plate : The Case of a Circular Plate without Internal Resonances : Vibration, Control Engineering, Engineering for Industry
- Exact Solutions of Free Vibration in a Single-Degree-of-Freedom System Having an Arbitrary Cubic Spring Function (Asymmetrical Hard Spring)
- Exact Solutions of Free Vibration in a Single-Degree-of-Freedom System Having an Arbitrary Cubic Spring Function
- Chaotic Behaviour of a Nonlinear Vibrating System with a Retarded Argument
- Vibrations of a Forced Self-excited System with a Retarded Argument : Subharmonic Vibrations of Order 1/2
- On the Subharmonic Vibrations of Order 1/2 of a Nonlinear Vibrating System with a Duffing Type Restoring Characteristic : 2nd Report, Case of Soft Spring
- On the 1/2-th Subharmonic Vibrations of a Non-linear Vibrating System with a Hard Duffing Type Restoring Characteristic
- On the Stability of a Rotating Elastic Shaft Supported by Journal Bearings
- Vibrations of a Forced Self-excited System with Time Lag
- Transfer Stiffness Coefficient Method Combined with Concept of Substructure Synthesis Method : Linear Free and Forced Vibration Analyses of a Straight-Line Beam Structure
- An Approximate Model with an Infinite Number of Vehicles for Analysis of Coupled Vibrations Between Railway Vehicle Wheels and Rail in the Vertical Direction
- Coupled Vibrations Between Railway Vehicle Wheels and a Rail : Coupled Vibration Characteristics in the Horizontal Direction Taking Creep Forces into Account
- Coupled Vibrations Between Railway Vehicle Wheels and a Rail : 4th Report, Analysis of Coupled Vertical Vibrations between Wheels and a Rail
- A Method of Vibrational Analysis Using a Personal Computer (Suggested Transfer Influence Coefficient Method) : Series C : Vibration, Control Engineering, Engineering for Industry
- A Method of Vibrational Analysis Using a Personal Computer (2nd Report, Application of the Transfer Influence Coefficient Method to a Distributed Flexural Vibrational System) : Series C : Vibration, Control Engineering, Engineering for Industry
- Coupled Vibrations between Railway Vehicle Wheels and a Rail : 2nd Report, Axial Steady-state Vibration of a Rotating Wheel
- Coupled Vibrations between Railway Vehicle Wheels and the Rail : 3rd Report, Analysis of Vertical Steady-state Vibrations
- On the Static Running Accuracy of Ball Bearings
- A Method of High Speed Structural Analysis Using a Personal Computer : Comparison with the Transfer Matrix Method
- On the Radial Vibration of Ball Bearings : Computer Simulation
- Coupled Lateral Vibrations between Rail and Railway Vehicle's Wheels Part 1,Equations of Motion of Rail and Its Characteristics
- Free Vibration Analysis of a Multiple Straight-Line Structure Regarded as a Distributed Mass System by the Transfer Influence Coeflicient Method
- Free Vibration Analysis of a Multiple Straight Line Structure Regarded as a Discrete System by the Transfer Influence Coefficient Method
- Exact Solutions of the Autonomous Duffing Equation and Their Computation : Expression of Solutions and Trial Calculation of a Characteristic Parameter) : Vibration, Control Engineering, Engineering for Industry
- Higher Approximate Solutions of the Duffing Equation : Primary Resonance in the Soft Spring System
- Analyses of the Chaotic Vibration of a Magnetically Levitated Body.
- Vibrations of a Forced Self-Excited System with a Retarded Argument : Influence of Initial Conditions
- Nonlinear Response of a Roller Chain to Combined Forcing and Parametric Excitations (4 th Report, Experiment of 1/3-Harmonic and Parametric Combination Resonance -No.2) : Series C : Vibration, Control Engineering, Engineering for Industry
- 1/3-Harmonic and Parametric Combination Resonance of a Roller Chain : Vibration, Control Engineering, Engineering for Industry
- Higher Approximate Solutions of the Duffing Equation : Odd Order Superharmonic Resonances in the Hard Spring System
- On a Method of Higher Approximation and Determination of Stability Criterion for Steady Oscillations in Nonlinear Systems
- Polygonal Wear of Work Rolls in a Hot Leveler of Steel Making Machine
- On the Spring Characteristics of a Ball Bearing : Fluctuation due to ball revolution
- Vibration of Rotor due to Ball Bearing : 3rd Report, Spring Property of Bearing Containing a Large Number of Balls
- Vibration of Rotor Based on Ball Bearing : 1st Report, Static Stiffness of Ball Bearing
- Numerical Scheme and Program for the Solution and Stability Analysis of a Steady Periodic Vibration Problem
- Vibration of Rotor Based on Ball Bearing : 2nd Report, Static Stiffness of Ball Bearing Containing a Small Number of Balls
- On the Spring Characteristics of a Ball Bearing : Extreme Characteristics with Many Balls
- Self-excited Vibration of a Circular Plate Subjected to Frictional Forces Exerted in Two Regions on Its Outer Circumference : Part 2, The Case of a Circular Plate with a Effect of Internal Resonances
- Self-excited Vibration of a Circular Plate Subjected to Frictional Forces Exerted in Two Regions on Its Outer Circumference : Part 1, The Case of a Circular Plate without Effect of Internal Resonances
- Self-excited Vibration of a Circular Plate Subjected to Frictional Forces Exerted in Two Regions on Its Outer Circumference : The Case of a Circular Plate Subjected to Distributed Frictional Forces without the Effect of Internal Resonances
- Pattern Formation Generated in a Winder System of Textile Machine(Special Issue on Nonlinear Dynamics)
- On the Static Running Accuracy of Ball Bearings : 2nd Report, Results and Discussion
- Optimum Design of Rotating Machine with Overhung Weight : Part 2, Numerical and Experimental Results
- Optimum Design of Rotating Machines with Overhung Weight : Part 1, Formulation of Optimum Problems
- Higher Approximation of Steady Oscillations in Nonlinear Systems with Single Degree of Freedom : Suggested Multi-Harmonic Balance Method