Steady-State Transverse Response in Coupled Planar Vibration of Axially Moving Viscoelastic Beams

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
Hu Ding
Keyword(s):  
Steady State ◽  
Transverse Vibration ◽  
Nonlinear Models ◽  
Numerical Results ◽  
State Response ◽  
Planar Vibration ◽  
Transverse Loads ◽  
Steady State Responses ◽  
Axially Moving ◽  
Transverse Response

Steady-state periodical response is investigated for planar vibration of axially moving viscoelastic beams subjected external transverse loads. A model of the coupled planar vibration is established by introducing a coordinate transform. The model can reduce to two nonlinear models of transverse vibration. The finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies. The effect of material parameters and excitation parameters on the amplitude of the steady-state responses are examined. Numerical results also indicate that the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters, and the two models of transverse vibration yield satisfactory results.

scholarly journals Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams

2011 ◽  
Vol 18 (1-2) ◽  
pp. 281-287 ◽  
Author(s):  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Transverse Vibration ◽  
Nonlinear Models ◽  
Transverse Motion ◽  
Steady State Response ◽  
Partial Differential ◽  
State Response ◽  
Axially Moving

Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steady-state periodical response are numerically investigated. An integro-partial-differential equation and a partial-differential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steady-state response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steady-state response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the integro-partial-differential equation gives results more closely to the coupled planar vibration.

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.

Trigonometric Collocation for Computation of Steady State Responses of Cracked Structures

2012 ◽  
Author(s):  
Bakeer Bakeer ◽  
Oleg Shiryayev ◽  
Ammaar Tahir
Keyword(s):  
Steady State ◽  
Fatigue Cracks ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Vibration Period ◽  
State Response ◽  
Trigonometric Collocation ◽  
Steady State Responses ◽  
Cracked Structures ◽  
State Responses

Development of vibration-based structural health monitoring techniques requires the use of various computational methods to predict dynamic responses of damaged structures. The method described in this work can be used for prediction of steady state harmonic responses for structures with fatigue cracks and may have several advantages over alternative techniques. The method appears to be relatively easy to implement and computationally inexpensive. The steady state response of the system at a given number of time points distributed over one vibration period is represented in terms of Fourier series containing higher frequency harmonics. Equations of motion are formulated in the form that allows for easy computation of Fourier coefficients for all terms in the series. Iterative procedure is used for determining the time of stiffness change in order to capture bilinear dynamic behavior. We present results of initial investigation by applying the method to a model of a cantilever beam with a crack.

Moving Load on a Fluid-Solid Interface: Subsonic and Intersonic Regimes

1973 ◽  
Vol 40 (4) ◽  
pp. 885-890 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Point Load ◽  
Numerical Results ◽  
Plane Interface ◽  
Steady State Response ◽  
State Response ◽  
Solid Interface

The steady-state response of a semi-infinite solid, with an overlying semi-infinite fluid, subjected at the plane interface to a moving point load is determined for subsonic and intersonic load velocities. Some numerical results for the displacements at the interface are presented and compared to the results obtained in the absence of the fluid.

Analysis of a Hydrodynamic Bearing Under Transverse Vibration of an Axially Moving Band

1990 ◽  
Vol 112 (3) ◽  
pp. 514-523 ◽  
Author(s):  
C. A. Tan ◽  
C. D. Mote
Keyword(s):  
Transverse Vibration ◽  
High Frequency ◽  
Low Frequency ◽  
Fluid Inertia ◽  
Hydrodynamic Bearing ◽  
Steady State Responses ◽  
Axially Moving ◽  
Moving Band ◽  
Unsteady Fluid ◽  
Impedance Functions

This paper presents a mathematical model of the flow and pressure developed in a hydrodynamic guide bearing film under transverse vibration of a translating band. The guide bearing is commonly used in band and circular sawing systems. The perturbed pressure is derived in the frequency domain based on a linearized, incompressible fluid film model. Unsteady fluid inertia, caused by the high frequency vibration modes of the flexible band, is included in the model. The perturbed pressure is generated by two mechanisms, one caused by the band convection, and the other by the band transverse vibration. Moreover, the pressure generations are governed by fluid impedance functions, which characterize the viscous diffusion across the film. Results for both the transient and steady state responses of the film are presented and discussed. It is shown that the pressure component caused by the band convection, which has not been considered in the literature, is important at low frequency. The pressure component caused by the band transverse vibration is dominant at high frequency.

scholarly journals Limitations of Bifurcation Diagrams in Boost Converter Steady-State Response Identification

2017 ◽  
Vol 8 (2) ◽  
pp. 59-65
Author(s):  
Željko Stojanović ◽  
Denis Pelin
Keyword(s):  
Steady State ◽  
Initial Period ◽  
Boost Converter ◽  
Steady State Response ◽  
Bifurcation Diagrams ◽  
State Response ◽  
Mode Of Operation ◽  
Steady State Responses ◽  
State Responses ◽  
Conduction Mode

Steady-state responses of the boost converter operating in discontinuous conduction mode of operation are identified by using bifurcation diagrams as a typical simulation tool for identification of steady-state responses. The structure of simulated bifurcation diagrams is dependent on the initial period of sampling and the initial instant of sampling. The influence of these parameters on calculation of bifurcation diagrams was studied. Some possible issues, pitfalls and misinterpretations are commented as well as some recommendations about steady-state response identification are given

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