Determination of the periodic steady-state response of systems of implicit state equations using Newton's method

1972 ◽  
Vol 60 (7) ◽  
pp. 902-903
Author(s):  
T.J. Aprille
Keyword(s):  
Steady State ◽  
Newton’S Method ◽  
Newton's Method ◽  
Steady State Response ◽  
State Equations ◽  
State Response ◽  
Periodic Steady State

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.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

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