Non-Linear Vibration Problems Treated by the Averaging Method of W. Ritz. Part 2. Single Degree of Freedom Systems Single Term Approximations

1951 ◽  
Author(s):  
Karl Klotter
Keyword(s):  
Averaging Method ◽  
Degree Of Freedom ◽  
Linear Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Single Term ◽  
Non Linear ◽  
Vibration Problems

scholarly journals Non-Linear Vibration Isolators with Unknown Excitation and Unmodelled Dynamics: Sliding Mode Active Control

2019 ◽  
Vol 9 (17) ◽  
pp. 3567 ◽  
Author(s):  
Zhang ◽  
Hu ◽  
Liu ◽  
Ouyang ◽  
Zhang
Keyword(s):  
Sliding Mode ◽  
Control Methods ◽  
Practical Application ◽  
Linear Vibration ◽  
Single Degree Of Freedom ◽  
Vibration Isolators ◽  
Single Degree ◽  
Non Linear ◽  
The One ◽  
Twisting Algorithm

For a class of single-degree-of-freedom non-linear passive vibration isolators with unknown excitation and unmodelled dynamics, two sliding mode control methods—a conventional one and the other using a super-twisting algorithm—were proposed to complement and improve the performances and the robustness of the passive isolators. The proposed control methods only require the estimation of the loading and measured velocities of the isolators. Numerical simulations for a non-linear isolator with quasi-zero stiffness demonstrated that both methods were effective and easy to implement, and the one using a super-twisting algorithm was more promising from the perspective of practical application.

A Mechanical Analyzer for the Solution of Vibration Problems of a Single Degree of Freedom

1948 ◽  
Vol 15 (2) ◽  
pp. 146-150
Author(s):  
E. E. Weibel ◽  
N. M. Cokyucel ◽  
R. E. Blau
Keyword(s):  
Generalized Solution ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Simple Construction ◽  
Dimensionless Form ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Constant Magnitude ◽  
Linear Damping ◽  
Vibration Problems

Abstract A mechanical-analogy-type analyzer is described which is of relatively simple construction being limited to single-degree-of-freedom problems. Whithin this limitation solutions may be obtained for systems which include various types of nonlinear elasticity and of nonlinear damping. Included is a generalized solution obtained on the analyzer giving in dimensionless form the maximum displacements and forces in a system having nonlinear (linear plus cubic) elasticity and linear damping caused by a force pulse of constant magnitude and finite duration. The bearing of the results on the starting torques in nonlinear systems is indicated.

Ultraharmonic Resonance of a System with an Asymmetrical Restoring Force Characteristic

1969 ◽  
Vol 11 (6) ◽  
pp. 592-597 ◽  
Author(s):  
W. Carnegie ◽  
Z. F. Reif
Keyword(s):  
Theoretical Analysis ◽  
Averaging Method ◽  
Degree Of Freedom ◽  
Force Characteristic ◽  
Analogue Computer ◽  
Static Deflection ◽  
Restoring Force ◽  
Disturbing Force ◽  
Single Degree Of Freedom ◽  
Single Degree

The ultraharmonic resonance of order 2, excited by a centrifugal type disturbing force, is investigated for a single-degree-of-freedom system with a Duffing restoring force characteristic. The effect of gravity is taken into account. The resulting asymmetry of the restoring force is expressed in terms of the static deflection parameter. The Ritz averaging method is used for the theoretical analysis and the results are verified by means of an analogue computer.

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