Forced Vibrations of Single-Degree-of-Freedom Systems with Nonperiodically Time-Varying Parameters

2002 ◽  
Vol 128 (12) ◽  
pp. 1267-1275 ◽  
Author(s):  
Q. S. Li
Keyword(s):  
Forced Vibrations ◽  
Degree Of Freedom ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Varying Parameters ◽  
Single Degree ◽  
Time Varying Parameters

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

Resonance Classification in a Cubic System

1971 ◽  
Vol 38 (3) ◽  
pp. 585-590 ◽  
Author(s):  
D. J. Ness
Keyword(s):  
Stability Analysis ◽  
Parametric Excitation ◽  
Degree Of Freedom ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Resonance Phenomena ◽  
Cubic System

A weakly nonlinear, single-degree-of-freedom cubic system subject simultaneously to a time-varying force and parametric excitation is considered. The various types of resonance phenomena exhibited by the system are classified and a detailed stability analysis is presented for one case of particular interest.

A New Exact Approach for Analyzing Free Vibration of SDOF Systems with Nonperiodically Time Varying Parameters

1999 ◽  
Vol 122 (2) ◽  
pp. 175-179 ◽  
Author(s):  
Q. S. Li
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Functional Relation ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Varying Parameters ◽  
Exact Approach ◽  
Time Varying Parameters ◽  
Constant Coefficients ◽  
Good Agreement

A new exact approach for analyzing free vibration of single degree of freedom (SDOF) systems with nonperiodically time varying parameters is presented in this paper. The function for describing the variation of mass of a SDOF system with time is an arbitrary continuous real-valued function, and the variation of stiffness with time is expressed as a functional relation with the variation of mass and vice versa. Using appropriate functional transformation, the governing differential equations for free vibration of SDOF systems with nonperiodically time varying parameters are reduced to Bessel’s equations or ordinary differential equations with constant coefficients for several cases, and the corresponding exact analytical solutions are thus obtained. A numerical example shows that the results obtained by the derived exact approach are in good agreement with those calculated by numerical methods, illustrating that the proposed approach is an efficient and exact method. [S0739-3717(00)00902-8]

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