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.

Dynamic Response of a Beam With Absorber Exposed to a Running Force: Fractional Calculus Approach

2012 ◽  
Author(s):  
Ibrahim Abu-Alshaikh ◽  
Anas N. Al-Rabadi ◽  
Hashem S. Alkhaldi
Keyword(s):  
Fractional Calculus ◽  
Dynamic Response ◽  
Fractional Derivative ◽  
Initial Conditions ◽  
Damping Ratio ◽  
Experimental Models ◽  
Damping Characteristics ◽  
Damping Behavior ◽  
The Laplace Transform ◽  
Vibration Parameters

This paper analyzes the transverse vibration of Bernoulli-Euler homogeneous isotropic simply-supported beam. The beam is assumed to be fractionally-damped and attached to a single-degree-of-freedom (SDOF) absorber with fractionally-damping behavior at the mid-span of the beam. The beam is also exposed to a running force with constant velocity. The fractional calculus is introduced to model the damping characteristics of both the beam and absorber. The Laplace transform accompanied by the used decomposition method is applied to solve the handled problem with homogenous initial conditions. Subsequently, curves are depicted to measure the dynamic response of the utilized beam under different set of vibration parameters and different values of fractional derivative orders for both of the beam and absorber. The results obtained show that the dynamic response decreases as both the damping-ratio of the absorber and beam increase. The results reveal that there are critical values of fractional derivative orders which are different from unity. At these optimal values, the beam behaves with less dynamic response than that obtained for the full-order derivatives model of unity order. Therefore, the fractional derivative approach provides better damping models for fractionally-damped structures and materials which may allow researchers to choose suitable mathematical models that precisely fit the corresponding experimental models for many engineering applications.

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.

Active Wave Cancellation of the Axially Moving String

2001 ◽  
Author(s):  
Chin An Tan ◽  
Shenger Ying
Keyword(s):  
Boundary Conditions ◽  
Initial Conditions ◽  
General Boundary ◽  
Closed Form Expression ◽  
Control Law ◽  
General Boundary Conditions ◽  
Axially Moving String ◽  
Axially Moving ◽  
Active Wave ◽  
Control Forces

Abstract The active wave control of the linear, axially moving string with general boundary conditions is presented in this paper. Considerations of general boundary conditions are important from both practical and experimental viewpoints. The active control law is established by employing the idea of wave cancellation. An exact, closed-form expression for the transverse response of the controlled system, consisting of the flexible structure, the wave controller, and the sensing and actuation devices, is derived in the frequency domain. Two actuation forces, one upstream and one downstream of an excitation force, are applied. The proposed control law shows that all modes of the string are controlled and the vibration in the regions upstream and downstream of the control forces can be cancelled. However, these results are based on ideal conditions and the assumption of zero initial conditions at the non-fixed boundaries. Effects of non-zero boundary motions at the instant of application of the control forces are examined and the control is shown to be effective under these conditions. The stability and robustness of the control forces are improved by the introduction of a stabilization coefficient in the control law. The effectiveness, robustness and stability of the control forces are demonstrated by simulations and verified by experiments on axially moving belt drive and chain drive systems.

Dynamic Response of a Spinning Timoshenko Beam With General Boundary Conditions and Subjected to a Moving Load

1994 ◽  
Vol 61 (1) ◽  
pp. 152-160 ◽  
Author(s):  
J. W.-Z. Zu ◽  
R. P. S. Han
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Original System ◽  
Adjoint System ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Adjoint Systems ◽  
Analysis Technique

The dynamic response of a spinning Timoshenko beam with general boundary conditions and subjected to a moving load is solved analytically for the first time. Solution of the problem is achieved by formulating the spinning Timoshenko beams as a non-self-adjoint system. To compute the system dynamic response using the modal analysis technique, it is necessary to determine the eigenquantities of both the original and adjoint systems. In order to fix the adjoint eigenvectors relative to the eigenvectors of the original system, the biorthonormality conditions are invoked. Responses for the four classical boundary conditions which do not involve rigidbody motions are illustrated. To ensure the validity of the method, these results are compared with those from Euler-Bernoulli and Rayieigh beam theories. Numerical simulations are performed to study the influence of the four boundary conditions on selected system parameters.

scholarly journals Dynamic and Sound Radiation Characteristics of Rectangular Thin Plates with General Boundary Conditions

2019 ◽  
Vol 6 (1) ◽  
pp. 117-131
Author(s):  
Yuan Du ◽  
Haichao Li ◽  
Qingtao Gong ◽  
Fuzhen Pang ◽  
Liping Sun
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Sound Radiation ◽  
Current Method ◽  
Thin Plates ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Radiation Characteristics ◽  
Aspect Ratios

AbstractBased on the classical Kirchhoff hypothesis, the dynamic response and sound radiation of rectangular thin plates with general boundary conditions are studied. The transverse displacements of plate are represented by a double Fourier cosine series and three supplementary functions. The potential discontinuity associated with the original governing equation can be transferred to auxiliary series functions. All kinds of boundary conditions can be easily achieved by varying stiffness value of springs on each edge. The natural frequencies and vibration response of the plates are obtained by means of the Rayleigh–Ritz method. Sound radiation characteristics of the plate are derived using Rayleigh integral formula. Current method works well when handling dynamic response and sound radiation of plates with general boundary conditions. The accuracy and reliability of current method are confirmed by comparing with related literature and FEM. The non-dimensional frequency parameters of the rectangular plates with different boundary conditions and aspect ratios are presented in the paper, which may be useful for future researchers.Meanwhile, some interesting points are foundwhen analyzing acoustic radiation characteristics of plates.

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.

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