Forced Nonlinear Oscillations of an Autoparametric System—Part 2: Chaotic Responses

1983 ◽  
Vol 50 (3) ◽  
pp. 663-668 ◽  
Author(s):  
H. Hatwal ◽  
A. K. Mallik ◽  
A. Ghosh
Keyword(s):  
Statistical Analysis ◽  
Nonlinear Oscillations ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Forced Oscillations ◽  
Mean Square ◽  
Chaotic Oscillations ◽  
System Part ◽  
The Mean ◽  
Two Degree Of Freedom

Chaotic oscillations arising in forced oscillations of a two degree-of-freedom autoparametric system are studied. Statistical analysis of the numerically integrated nonperiodic responses is shown to be a meaningful description of the mean square values and the frequency contents of the responses. Some qualitative experimental results are presented to substantiate the necessity of performing the statistical analysis of the responses even though the system and the input are deterministic.

Forced Nonlinear Oscillations of an Autoparametric System—Part 1: Periodic Responses

1983 ◽  
Vol 50 (3) ◽  
pp. 657-662 ◽  
Author(s):  
H. Hatwal ◽  
A. K. Mallik ◽  
A. Ghosh
Keyword(s):  
Numerical Integration ◽  
Harmonic Balance ◽  
Nonlinear Oscillations ◽  
Parametric Instability ◽  
Forced Oscillations ◽  
Instability Zone ◽  
Method Of Harmonic Balance ◽  
Numerical Integrations ◽  
System Part ◽  
Two Degree Of Freedom

Forced oscillations of a two degree-of-freedom autoparametric system are studied with moderately high excitations. The approximate results obtained by the method of harmonic balance are found to be satisfactory by comparing with those obtained by numerical integration. In the primary parametric instability zone, separate regions of stable and unstable harmonic solutions are obtained. In the regions of unstable harmonic solutions, depending on the forcing amplitude and frequency, the solutions may be amplitude modulated or completely nonperiodic. In the latter case the numerical integrations do not converge.

Forced Oscillations of Non-Linear Two-Degree-of-Freedom Systems

1966 ◽  
Vol 8 (3) ◽  
pp. 252-258 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Numerical Integration ◽  
Transient Response ◽  
Internal Resonance ◽  
Perturbation Technique ◽  
Degree Of Freedom ◽  
Forced Oscillations ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom ◽  
Good Agreement

This paper shows how the Lighthill-Poincaré perturbation technique may be used to determine the transient response of ‘lightly coupled’ non-linear multi-degree-of-freedom oscillatory systems subject to arbitrary forcing functions. The results in general are complex but simplify in many important cases. A comparison is made between the analytical results and results obtained by a numerical integration of the equations on a computer. Good agreement is noted. The method fails under conditions of ‘internal resonance’ of the system.

scholarly journals THE CORRELATION BETWEEN VOCABULARY MASTERY AND READING COMPREHENSION AT THE SECOND YEAR STUDENTS OF SMPN 3 GUNUNGSARI

2020 ◽  
Vol 4 (2) ◽  
pp. 122
Author(s):  
Sudirman Sudirman
Keyword(s):  
Reading Comprehension ◽  
Statistical Analysis ◽  
Quantitative Method ◽  
T Test ◽  
Degree Of Freedom ◽  
Final Score ◽  
The Mean ◽  
Second Year

The research entitled The Correlation Between Vocabulary Mastery and Reading Comprehension  aims at finding out there is whether any correlation between vocabulary mastery and reading comprehension at the second year students of SMPN 3 Gunungsari. This research was designed by using descriptive quantitative method. The research took 30 students as sample of this study. To analyses the data this research used statistic computation by product moment correlation, to get the final score. The data found that the mean score of reading comprehension was 54.4 and vocabulary was 53,6. After computing by the statistical analysis of Product Moment, the value shows 1.631 while the t-table was 1.671 and 2.390. This result of this investigation indicated that there is no significant between vocabulary and reading comprehension. The value of t-test was 1.631 is lower than 1.671 and 2.390 in 0.05 and 0.01 significant level. While the degree of freedom (df) = 60. It can be concluded that there is no correlation between vocabulary mastery and reading comprehension.

Parametric Stability of a Two-Degree-of-Freedom Machine System: Part I—Equations of Motion and Stability

1987 ◽  
Vol 109 (2) ◽  
pp. 210-215 ◽  
Author(s):  
R. I. Zadoks ◽  
A. Midha
Keyword(s):  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Degree Of Freedom ◽  
Computationally Efficient ◽  
Machine System ◽  
Stable Operating ◽  
System Part ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Two Degree Of Freedom

An important question facing a designer is whether a certain machine system will have a stable operating condition. To date, the investigations which deal with this question have been scarce. This study treats an elastic two-degree-of-freedom system with position-dependent inertia and external forcing. In Part I, the nonlinear equations of motion are derived and linearized about the system’s steady-state rigid-body response. The stability of the linearized equations is examined using Floquet theory, and a computationally efficient method for approximating the monodromy matrix is presented. A specific example is proposed and the results are presented in Part II of this paper.

Response of Two-Degree-of-Freedom Rotating Machinery System With Quadratic Nonlinearity

1990 ◽  
Vol 112 (2) ◽  
pp. 103-113 ◽  
Author(s):  
A. Ertas ◽  
G. Anlas
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Center Of Mass ◽  
Degree Of Freedom ◽  
Saturation Phenomenon ◽  
Nonlinear Springs ◽  
Rotating Machine ◽  
Two Degree Of Freedom ◽  
Machinery System

A two-degree-of-freedom model of a rotating machine with nonlinear springs of quadratic type is studied. The multiple scales method is used to investigate the nonlinear oscillations of the forced system where the forcing is due to the eccentricity e of the rotor about its center of mass. The behavior of the system for the primary resonances Ω = ω1, Ω = ω2, and internal resonance ω2 = 2ω1 is analyzed. Other features, such as amplitude jump and saturation phenomenon, have been observed. The amplitudes versus detuning parameters for both cases are plotted. The critical values of mass ratios and spring ratios for the presence of an internal resonance are studied and interpreted for this particular application.

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