Transients in Simple Undamped Oscillators Under Inertial Disturbances

1959 ◽  
Vol 26 (2) ◽  
pp. 217-223
Author(s):  
Antongiulio Dornig
Keyword(s):  
Exact Solution ◽  
Maximum Amplitude ◽  
Degree Of Freedom ◽  
Inertial Forces ◽  
Constant Acceleration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Approximate Formulas

Abstract Single-degree-of-freedom systems acted upon inertial forces are often found in technical applications. In this paper we shall study the transients in the vibrations of the system due to a change in speed in the machine in which the inertial forces are generated. We shall state the problem in the most general case, and then study the starting and the stopping with constant acceleration. After giving the exact solution of the problem we shall derive very simple approximate formulas for the determination of the maximum amplitude reached in these transients.

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

2019 ◽  
Vol 24 (12) ◽  
pp. 3843-3861 ◽  
Author(s):  
Mario Lázaro
Keyword(s):  
Past History ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Critical Curves ◽  
History Of ◽  
Definition Of ◽  
Analytical Expressions ◽  
Critical Damping

In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.

A New Approach to Nonlinear Oscillations

2001 ◽  
Vol 68 (6) ◽  
pp. 951-952 ◽  
Author(s):  
B. Wu ◽  
P. Li
Keyword(s):  
Governing Equation ◽  
Nonlinear Oscillation ◽  
Harmonic Balance ◽  
Nonlinear Oscillations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
New Approach ◽  
Single Degree ◽  
Method Of Harmonic Balance ◽  
Approximate Formulas

This paper deals with nonlinear oscillation of a general single-degree-of-freedom system. By combining the linearization of the governing equation with the method of harmonic balance, we establish two analytical approximate formulas for the period. These two formulas are valid for small as well as large amplitudes of oscillation.

Forced Vibrations of a Single-Degree-of-Freedom System With Coulomb Bearing Friction

1969 ◽  
Vol 36 (4) ◽  
pp. 871-873 ◽  
Author(s):  
E. V. Wilms
Keyword(s):  
Coulomb Friction ◽  
Degree Of Freedom ◽  
Half Cycle ◽  
Piecewise Linearization ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Forcing Function ◽  
Bearing Friction

The equation of motion of a single-degree-of-freedom mechanical system with Coulomb friction acting at two bearings is derived. The equation is nonlinear, but may be solved by piecewise linearization. For the case of transient oscillations, the amplitude decreases by a constant ratio every half cycle and, in this respect, the behavior resembles that of viscous damping rather than the type of Coulomb damping which has previously been investigated. The steady-state response with a forcing function is determined for the case of small damping. In addition to the amplitude and phase angle of the motion, a solution requires the determination of a second angle which defines the linearized regions.

Analysis and Determination of Associated Linkage, Redundant Constraint, and Degree of Freedom of Closed Mechanisms With Redundant Constraints and/or Passive Degree of Freedom

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Yi Lu ◽  
Nijia Ye ◽  
Yang Lu ◽  
Bingyi Mao ◽  
Xu Zhai ◽  
...  
Keyword(s):  
Degree Of Freedom ◽  
Type Synthesis ◽  
Single Degree Of Freedom ◽  
Redundant Constraints ◽  
Single Degree ◽  
Redundant Constraint ◽  
In Series ◽  
Associated Linkage

The relations among the associated linkages (ALs), the redundant constraints, the passive degree of freedom (DoF), and the degree of freedom are studied systematically for the type synthesis of the closed mechanisms in this paper. First, the kinematic pairs with multidegree of freedoms are formed by combination of the basic joints with single degree of freedom in series, and the formulae are derived for the calculation of the degree of freedoms of the associated linkages, the number of the basic joints, and the valid numbers of the basic links in the associated linkages. Second, many different associated linkages and the number of basic links are derived, and the relations among the associated linkages, the redundant constraints, the passive degree of freedom, and the degree of freedoms of the closed mechanisms are analyzed. Third, some topology graphs are derived and the relative closed mechanisms with the redundant constraints and the passive degree of freedom are synthesized. Finally, the redundant constraints and the degree of freedoms of the closed mechanisms are determined.

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