Determination of the steady-state response of viscoelastically supported cantilever beam under sinusoidal base excitation

2005 ◽  
Vol 281 (3-5) ◽  
pp. 1145-1156 ◽  
Author(s):  
Turgut Kocatürk
Keyword(s):  
Steady State ◽  
Cantilever Beam ◽  
Steady State Response ◽  
Base Excitation ◽  
State Response

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.

Predictions of the Periodic Response of a Single-Degree-of-Freedom Foam-Mass System by Using Incremental Harmonic Balance

2012 ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Driving Frequency ◽  
Steady State Response ◽  
Base Excitation ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Incremental Harmonic Balance

Vehicle occupants are exposed to low frequency vibration that can cause fatigue, lower back pain, spine injuries. Therefore, understanding the behavior of a seat-occupant system is important in order to minimize these undesirable vibrations. The properties of seating foam affect the response of the occupant, so there is a need for good models of seat-occupant systems through which the effects of foam properties on the dynamic response can be directly evaluated. In order to understand the role of flexible polyurethane foam in characterizing the complex seat-occupant system behavior better, the response of a single-degree-of-freedom foam-mass system, which is the simplest model representing a seat-occupant system, is studied. The incremental harmonic balance method is used to determine the steady-state behavior of the foam-mass system subjected to sinusoidal base excitation. This method is used to reduce the time required to generate the steady-state response at the driving frequency and at harmonics of the driving frequency from that required when using direct time-integration of the governing equations to determine the steady state response. Using this method, the effects of different viscoelastic models, riding masses, base excitation levels and damping coefficients on the response are investigated.

scholarly journals Analytical Solution of the Steady State Response of Suspension Bridge Tower-Pier Systems with Distributed Mass to Harmonic Base Excitation

2002 ◽  
Vol 21 (3) ◽  
pp. 157-168 ◽  
Author(s):  
C.J. Younis ◽  
D.E. Panayotounakos
Keyword(s):  
Steady State ◽  
Suspension Bridge ◽  
Equation Of Motion ◽  
Steady State Response ◽  
Viscoelastic Foundation ◽  
Base Excitation ◽  
State Response ◽  
The Galerkin Method ◽  
Bridge Tower ◽  
Lateral Deflections

A typical suspension bridge tower-pier system is considered, the tower mass of which is not negligible and assumes an arbitary distribution along the tower. The pier rests on a viscoelastic foundation and can follow rotational and horizontal motion. The surrounding soils perform a horizontal harmonic motion. The equation of motion of the pier as well as the partial differential equation of the lateral deflections of the tower with the accompanying boundary conditions, are derived. The solution of the above p.d.e. is taken as a sum of terms, each one corresponding to an eigenshape of vibration of the tower. Applying the Galerkin method a system of ordinary differential equations results. The system of all the o.d.e.′s of motion (the pier's and the tower's) is solved for the steady state response, and based upon the resulting deflections, the stresses along the tower are determined. A parametric study is carried out.

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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