scholarly journals Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hashem S. Alkhaldi ◽  
Ibrahim M. Abu-Alshaikh ◽  
Anas N. Al-Rabadi
Keyword(s):  
Dynamic Response ◽  
Fractional Derivatives ◽  
Single Degree Of Freedom ◽  
Moving Vehicle ◽  
Single Degree ◽  
Damping Characteristics ◽  
The Laplace Transform ◽  
Fractional Differential ◽  
Damped Systems ◽  
Special Case

This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam. The beam is attached to multi single-degree-of-freedom (SDOF) fractionally-damped systems, and it is subjected to a vehicle moving with a constant velocity. The damping characteristics of the beam and SDOF systems are described in terms of fractional derivatives. Three coupled second-order fractional differential equations are produced and then they are solved by combining the Laplace transform with the decomposition method. The obtained numerical results show that the dynamic response decreases as (a) the number of absorbers attached to the beam increases and (b) the damping-ratios of used absorbers and beam increase. However, there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. Furthermore, the obtained results show very good agreements with special case studies that were published in the literature.

Vibration of a Beam-Oscillator System Subjected to a Moving Vehicle: Fractional Derivative Approach

2012 ◽  
Author(s):  
Hashem S. Alkhaldi ◽  
Ibrahim Abu-Alshaikh ◽  
Anas N. Al-Rabadi
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Moving Load ◽  
Moving Vehicle ◽  
Beam Dynamic ◽  
Damping Characteristics ◽  
Born Series ◽  
The Laplace Transform ◽  
Derivatives Of

The dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam is investigated. The beam is appended at its mid-span by a single-degree-of-freedom (SDOF) fractionally-damped oscillator. The beam is further subjected to a vehicle modeled as a spring-dashpot system moves with a constant velocity over the beam. Hence, the damping characteristics of the beam and SDOF attached-oscillator are formally described in terms of fractional derivatives of arbitrary orders. In the analysis, the beam, SDOF oscillator, and the vehicle are assumed to be initially at rest. A system of three coupled differential equations is produced. These equations are handled by combining the Laplace transform with the Born series. Thereafter, curves are plotted to show the effect of the moving vehicle and the fractional derivatives behavior on the dynamic response of the beam. The numerical results show that the dynamic response decreases as the damping-ratios of the used absorber and beam increase. However, there are some optimal values of fractional derivative orders which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivative model. A comparison between the moving load and moving vehicle shows a significant reduction in the beam dynamic response in the case when vehicle is compared with the running load.

scholarly journals Response of Fractionally Damped Beams with General Boundary Conditions Subjected to Moving Loads

2012 ◽  
Vol 19 (3) ◽  
pp. 333-347 ◽  
Author(s):  
R. Abu-Mallouh ◽  
I. Abu-Alshaikh ◽  
H.S. Zibdeh ◽  
Khaled Ramadan
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Damping Characteristics ◽  
The Laplace Transform ◽  
The Right

This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams with general boundary conditions. The beams are assumed to be subjected to a load moving at a uniform velocity. The damping characteristics of the beams are described in terms of fractional derivatives of arbitrary orders. In the analysis where initial conditions are assumed to be homogeneous, the Laplace transform cooperates with the decomposition method to obtain the analytical solution of the investigated problems. Subsequently, curves are plotted to show the dynamic response of different beams under different sets of parameters including different orders of fractional derivatives. The curves reveal that the dynamic response increases as the order of fractional derivative increases. Furthermore, as the order of the fractional derivative increases the peak of the dynamic deflection shifts to the right, this yields that the smaller the order of the fractional derivative, the more oscillations the beam suffers. The results obtained in this paper closely match the results of papers in the literature review.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

Modal analysis and dynamic response of two adjacent single-degree-of-freedom systems linked by spring-dashpot-inerter elements

2018 ◽  
Vol 174 ◽  
pp. 736-752 ◽  
Author(s):  
Michela Basili ◽  
Maurizio De Angelis ◽  
Daniele Pietrosanti
Keyword(s):  
Dynamic Response ◽  
Modal Analysis ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree

The Dynamic Response of a System With Preloaded Compliance

1988 ◽  
Vol 110 (3) ◽  
pp. 278-283 ◽  
Author(s):  
S. W. Shaw ◽  
P. C. Tung
Keyword(s):  
Dynamic Response ◽  
Piecewise Linear ◽  
Harmonic Excitation ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Linear Features ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Periodic ◽  
Model Equations

We consider the dynamic response of a single degree of freedom system with preloaded, or “setup,” springs. This is a simple model for systems where preload is used to suppress vibrations. The springs are taken to be linear and harmonic excitation is applied; damping is assumed to be of linear viscous type. Using the piecewise linear features of the model equations we determine the amplitude and stability of the periodic responses and carry out a bifurcation analysis for these motions. Some parameter regions which contain no simple stable periodic motions are shown to possess chaotic motions.

An Efficient Method for Compensating Truncated Higher Modes in Structural Dynamics Modification

1986 ◽  
Vol 200 (1) ◽  
pp. 41-48 ◽  
Author(s):  
K R Chung ◽  
C W Lee
Keyword(s):  
Structural Dynamics ◽  
Efficient Method ◽  
Curve Fitting ◽  
Modal Parameters ◽  
Frequency Range ◽  
Single Degree Of Freedom ◽  
Higher Modes ◽  
Numerical Example ◽  
Single Degree ◽  
Damped Systems

An efficient method for compensating the effects of the truncated higher modes in structural dynamics modification (SDM) is developed to predict the accurate modal parameters of locally modified structures. The effects of the truncated higher modes are represented by a fictitious, effective mode residing beyond the frequency range of interest. The modal parameters are then easily obtained by the iterative single degree-of-freedom curve-fitting technique developed for lightly damped systems. A numerical example demonstrates the effectiveness of the improved SDM technique.

scholarly journals Dynamic Response of RC Cantilever Beam by Equivalent Single Degree of Freedom Method on Elastic Analysis – A Review on Transformation Factors and Dynamic Magnification Factors

2018 ◽  
Vol 159 ◽  
pp. 01005
Author(s):  
Sri Tudjono ◽  
Patria Kusumaningrum
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Cantilever Beam ◽  
Mode Shape ◽  
Degree Of Freedom ◽  
Elastic Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Magnification Factors ◽  
Method Analysis

The response of multi-degree-of-freedom (MDOF) structure can be correlated to the response of an equivalent single-degree-of-freedom (SDOF) system, implying that the response is controlled by a single, unchanged mode shape. This equivalent SDOF method is eminent as an approximate method of dynamic analysis. In this study, equivalent SDOF method analysis is carried out on RC cantilever beam subjected to dynamic blast loading to review the transformation factors (TFs) provided by TM5-1300 code.

scholarly journals Dynamic Response of Breasting Dolphin Moored with 40,000 DWT Ship due to Parallel Passing Ship Phenomenon

2018 ◽  
Vol 147 ◽  
pp. 05003
Author(s):  
Heri Setiawan ◽  
Muslim Muin
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dynamic Response ◽  
Computer Program ◽  
Lateral Force ◽  
Degree Of Freedom ◽  
Hydrodynamic Interactions ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

When a ship is moving through another ship moored nearby, hydrodynamic interactions between these ships result in movements of the moored vessel. The movement may occur as surge, sway, and/or yaw. When a ship is passing a moored vessel parallelly, this effect will give a dominant lateral force on the moored ship and response from this phenomenon will appear in a certain time. Only dynamic response due to sway force is considered in this study, the sway force shall be absorb by the breasting dolphin. 40,000 DWT shall be moored to the breasting dolphin. Three passing ships size are considered, the breasting dolphin shall be modeled as a single degree of freedom model. This model will be subjected to a force caused by parallel passing ship. The model is assumed to be in a state of quiet water, this assumption is taken so that the fluid does not provide additional force on the model. The SDOF system shall be analyzed using a computer program designed to solve an ordinary differential equation.

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