Forced Vibration of Systems With Nonlinear, Nonsymmetrical Characteristics

1957 ◽  
Vol 24 (3) ◽  
pp. 435-439
Author(s):  
S. Mahalingam
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Nonlinear Vibration ◽  
Forced Vibration ◽  
Free Vibrations ◽  
Frequency Function ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Vibration Absorber ◽  
Single Degree

Abstract A one-term approximate solution is given for the amplitudes of steady forced vibration of a single-degree-of-freedom system with a nonlinear (nonsymmetrical) spring characteristic. The method is similar to that of Martienssen (1), but the construction uses a modified curve (or “frequency function”) in place of the actual spring characteristic, the curve being so chosen that it gives the correct frequency for free vibrations. The method is extended to deal with a nonlinear vibration absorber fitted to a linear system.

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

Impact of a Mass on a Damped Elastically Supported Beam

1948 ◽  
Vol 15 (2) ◽  
pp. 125-136
Author(s):  
W. H. Hoppmann
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Numerical Solutions ◽  
Coefficient Of Restitution ◽  
Tabular Form ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
Single Degree ◽  
Elastically Supported

Abstract In this paper a study is made of the problem of the central impact of a mass on a simply supported beam on an elastic foundation with considerations of internal and external damping. The differential equation for the forced vibration of the beam is developed. It is solved for the case in which the force is a function of time and is concentrated at the center of the beam. Formulas are obtained for the deflections. An expression is developed for the coefficient of restitution which is essential in determining the deflections and the strains. Criteria are devised for determining the cases in which the beam may be considered as a single-degree-of-freedom system when damping and an elastic foundation are considered. The importance of these criteria is discussed. A numerical example illustrating the theory developed in the paper is worked out in detail. Results of computations for several numerical solutions are given in tabular form.

Broadening the frequency bandwidth of a finite extensibility nonlinear vibration absorber by exploiting its internal resonances

2020 ◽  
Vol 102 (3) ◽  
pp. 1239-1270
Author(s):  
Alex Elías-Zúñiga ◽  
Luis Manuel Palacios-Pineda ◽  
Daniel Olvera-Trejo ◽  
Oscar Martínez-Romero
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Absorber ◽  
Frequency Bandwidth ◽  
Internal Resonances ◽  
Nonlinear Vibration Absorber ◽  
Finite Extensibility

Linearization Equations for Vibration Induced by Oscillatory Flow

1979 ◽  
Vol 46 (4) ◽  
pp. 946-948 ◽  
Author(s):  
P-T. D. Spanos ◽  
T. W. Chen
Keyword(s):  
Linear System ◽  
Oscillatory Flow ◽  
Degree Of Freedom ◽  
Approximate Determination ◽  
Equivalent Linearization ◽  
Mean Velocity ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonzero Mean

Equations are presented for the approximate determination through equivalent linearization of the response of a single-degree-of-freedom linear system to excitation induced by oscillatory flow with nonzero mean velocity. The reliability of the proposed methodology is examined.

Three-Element Vibration Absorber–Inerter for Passive Control of Single-Degree-of-Freedom Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Abdollah Javidialesaadi ◽  
Nicholas E. Wierschem
Keyword(s):  
Passive Control ◽  
Translational Motion ◽  
Tuned Mass Damper ◽  
Degree Of Freedom ◽  
Superior Performance ◽  
Underlying Structure ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Mass Damper

In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

Integration of a Nonlinear Vibration Absorber and Levitation Magnetoelectric Energy Harvester for Whole-Spacecraft Systems

2019 ◽  
Vol 32 (3) ◽  
pp. 298-309 ◽  
Author(s):  
Ye-Wei Zhang ◽  
Shi-Lei Wang ◽  
Zhi-Yu Ni ◽  
Zhi-Wei Fang ◽  
Jian Zang ◽  
...  
Keyword(s):  
Nonlinear Vibration ◽  
Energy Harvester ◽  
Vibration Absorber ◽  
Nonlinear Vibration Absorber
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