scholarly journals An Evaluation of the Fixed Point Method of Vibration Analysis for a Particular System With Initial Damping

1963 ◽  
Vol 85 (3) ◽  
pp. 233-236 ◽  
Author(s):  
D. B. Bogy ◽  
P. R. Paslay
Keyword(s):  
Steady State ◽  
Approximate Method ◽  
Fixed Point Method ◽  
Steady State Response ◽  
Vibratory System ◽  
State Response ◽  
System Use ◽  
Two Degree Of Freedom ◽  
Maximum Steady State

The maximum steady-state response of a particular linear damped two-degree-of-freedom vibratory system is minimized by determining the optimum damping constant for a single damper. This is accomplished by both a well-known approximate method and by an exact numerical method. Since the approximate method does not take into account the damping which is initially in the system, attention in this analysis is directed to determining the influence of the initial damping on the optimum value for the single damper. In order to make direct comparison of the methods, a system was chosen in which an exact numerical determination of the optimum damping was possible. The results of the investigation show for the particular case considered that, although the value of the damping constant for the optimum damper increases considerably as initial damping is included in the system, use of the value obtained for the initially undamped case would give values of the maximum steady-state response within 10 percent of the optimized value for the range of initial damping commonly encountered.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

scholarly journals Steady state response of a nonlinear system

1980 ◽  
Vol 3 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Sudhangshu B. Karmakar
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear System ◽  
Linear Model ◽  
Series Solution ◽  
Steady State Response ◽  
State Response ◽  
Equivalent Linear Model

This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multidimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.

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