Stochastic Analysis of a Fractionally Damped Beam

2001 ◽  
Author(s):  
Om P. Agrawal
Keyword(s):  
Stochastic Analysis ◽  
Normal Modes ◽  
Continuous Beam ◽  
Analytical Technique ◽  
System A ◽  
Laplace Transform Technique ◽  
Mass Damper ◽  
Duhamel Integral ◽  
Fractional Green’S Function ◽  
Response Expression

Abstract This paper presents a general analytical technique for stochastic analysis of a continuous beam whose damping characteristic is described using a fractional derivative model. In this formulation, the normal-mode approach is used to reduce the differential equation of a fractionally damped continuous beam into a set of infinite equations each of which describes the dynamics of a fractionally damped spring-mass-damper system. A Laplace transform technique is used to obtain the fractional Green’s function and a Duhamel integral type expression for the system’s response. The response expression contains two parts, namely zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for White noise. The approach can be extended to all those systems for which the existence of normal modes is guaranteed.

Analytical Solution for Stochastic Response of a Fractionally Damped Beam

2004 ◽  
Vol 126 (4) ◽  
pp. 561-566 ◽  
Author(s):  
Om P. Agrawal
Keyword(s):  
Stochastic Analysis ◽  
Normal Modes ◽  
Continuous Beam ◽  
Stochastic Response ◽  
Analytical Technique ◽  
System A ◽  
Laplace Transform Technique ◽  
Duhamel Integral ◽  
Fractional Green’S Function ◽  
Response Expression

This paper presents a general analytical technique for stochastic analysis of a continuous beam whose damping characteristic is described using a fractional derivative model. In this formulation, the normal-mode approach is used to reduce the differential equation of a fractionally damped continuous beam into a set of infinite equations, each of which describes the dynamics of a fractionally damped spring-mass-damper system. A Laplace transform technique is used to obtain the fractional Green’s function and a Duhamel integral-type expression for the system’s response. The response expression contains two parts, namely, zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed-form stochastic response expressions are obtained for white noise for two cases, and numerical results are presented for one of the cases. The approach can be extended to all those systems for which the existence of normal modes is guaranteed.

Stochastic Analysis of a 1-D System With Fractional Damping of Order 1/2

2002 ◽  
Vol 124 (3) ◽  
pp. 454-460 ◽  
Author(s):  
Om P. Agrawal
Keyword(s):  
White Noise ◽  
Stochastic Analysis ◽  
Damping Ratio ◽  
Expansion Method ◽  
Stochastic Dynamic ◽  
Stochastic Response ◽  
Analytical Technique ◽  
Damped System ◽  
Duhamel Integral ◽  
General Response

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duhamel integral type expressions for the response of the system. The general response contains two parts, namely zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics, namely the variance and covariance responses of the system. Closed form stochastic response expressions are obtained for white noise. Numerical results are presented to show the stochastic response of a fractionally damped system subjected to white noise. Results show that stochastic response of the fractionally damped system oscillates even when the damping ratio is greater than its critical value.

An Analytical Scheme for Stochastic Dynamic Systems Containing Fractional Derivatives

1999 ◽  
Author(s):  
Om P. Agrawal
Keyword(s):  
White Noise ◽  
Expansion Method ◽  
Stochastic Dynamic ◽  
Stochastic Response ◽  
Analytical Technique ◽  
Analytical Scheme ◽  
Damped System ◽  
Duhamel Integral ◽  
General Response ◽  
Stochastic Dynamic Systems

Abstract This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duhamel integral type expressions. The general response contains two parts, namely zero state and zero input. For a stochastic analysis the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for white noise. Numerical results are presented to show the stochastic response of a fractionally damped system subjected to white noise.

Localized and Non-Localized Normal Modes in a Strongly Nonlinear Discrete System

1991 ◽  
Author(s):  
Alexander F. Vakakis
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Linear Vibration ◽  
Mode Localization ◽  
Linear Mode ◽  
Strongly Nonlinear ◽  
System A ◽  
Coupling Stiffness ◽  
Nonlinear Normal ◽  
Nonlinear Discrete System

Abstract The free oscillations of a strongly nonlinear, discrete oscillator are examined by computing its “nonsimilar nonlinear normal modes.” These are motions represented by curves in the configuration space of the system, and they are not encountered in classical, linear vibration theory or in existing nonlinear perturbation techniques. For an oscillator with weak coupling stiffness and “mistiming,” both localized and nonlocalized modes are detected, occurring in small neighborhoods of “degenerate” and “global” similar modes of the “tuned” system. When strong coupling is considered, only nonlocalized modes are found to exist. An interesting result of this work is the detection of mode localization in the “tuned” periodic system, a result with no counterpart in existing theories on linear mode localization.

Development of V-Shaped Hybrid Mass Damper and its Application to High-Rise Buildings

1995 ◽  
Author(s):  
Masanori Imazeki ◽  
Koji Tanida ◽  
Masao Mutaguchi ◽  
Yuji Koike ◽  
Tamotsu Murata ◽  
...  
Keyword(s):  
First Year ◽  
Building Structures ◽  
Large Space ◽  
Natural Period ◽  
High Rise ◽  
High Rise Building ◽  
System A ◽  
Mass Damper ◽  
Story Building ◽  
Auxiliary Mass

Abstract A hybrid mass damper system has been developed with a view to counteracting wind- and earthquake-excited vibrations of large high-rise building structures. In order to eliminate the large space needed to accommodate a pendulum-type mass damper adapted to the long period of high-rise building, mechanism has been devised for suspending the auxiliary mass on a V-shaped rail sliding on rollers. The base angle of the V-shaped rail is varied for adjusting the natural period of the mass damper system. A suboptimal algorithm based on the minimum norm method has been adopted for designing the auxiliary mass driving system. Three units of this damper system, each equipped with auxiliary mass weighing 110 tons, have been installed on a 52-story building. Satisfactory performance conforming in all practical aspects with design has been verified from vibration test on actual building after installation. As sequel, the functioning of the system during the first year of service is also reported.

Partial Stochastic Linearization of a Spherical Pendulum With Coriolis Damping Produced by Radial Spring and Damper

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
L. D. Viet
Keyword(s):  
Numerical Simulation ◽  
Stochastic Analysis ◽  
Radial Direction ◽  
Spherical Pendulum ◽  
Analysis And Design ◽  
Partial Linearization ◽  
System A ◽  
Stochastic Linearization ◽  
Linearized System ◽  
Sway Motion

This study considers the stochastic analysis of a spherical pendulum, whose bidirectional vibration is reduced by spring and damper installed in the radial direction between the point mass and the cable. Under sway motion, the centrifugal force results in the radial motion, which in its turn produces the Coriolis force to reduce sway motion. In stochastic analysis and design, the problem is that the Monte Carlo simulation is time-consuming, while the full stochastic linearization totally fails to describe the effectiveness of the spring and damper. We propose the partial linearization applied to the Coriolis damping to overcome the disadvantages of two mentioned methods. Moreover, the proposed technique can give the analytical solution of partial linearized system. A numerical simulation is performed to verify the proposed approach.

scholarly journals A Stochastic Analysis of Hard Disk Drives

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Field Cady ◽  
Yi Zhuang ◽  
Mor Harchol-Balter
Keyword(s):  
Stochastic Analysis ◽  
Hard Disk Drives ◽  
Closed Form Solution ◽  
Hard Disk ◽  
Form Solution ◽  
Access Time ◽  
Analytical Technique ◽  
Wide Range ◽  
Average Access Time ◽  
Memory Request

We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.

Dynamic Performance of Vehicle-Turnout-Bridge Coupling System in High-Speed Railway

2011 ◽  
Vol 50-51 ◽  
pp. 654-658
Author(s):  
Rong Chen ◽  
Wang Ping ◽  
Shun Xi Quan
Keyword(s):  
Relative Position ◽  
High Speed ◽  
Dynamic Performance ◽  
Dynamic Responses ◽  
Continuous Beam ◽  
Analysis Model ◽  
Wheel Load ◽  
System A ◽  
Coupling System ◽  
Contact Relation

In order to study dynamic behavior of vehicle-turnout-bridge coupling system, a vehicle-turnout-bridge dynamic analysis model is established by employing the dynamic finite element method (FEM). When No.18 crossover turnouts(with a speed of 350km/h) are laid symmetrically on the 6×32m continuous beam, influences of turnout/bridge relative position and wheel/rail contact relation in turnout zone on the system dynamic responses are analyzed. The result shows that: wheel/rail contact of turnout zone (especially the frog) has great effect on dynamic responses of turnout on bridge, thus the nose rail height of frog should be optimized to mitigate the wheel load transition and its longitudinal gradient. In terms of the 32m-span continuous beam, the best relative position is frog part of turnout arranged in the range of 1/8 and 1/4 of span.

Seismic analysis of the rail-counterweight system in elevators considering the stiffness of rail brackets

2020 ◽  
pp. 136943322097477
Author(s):  
Xiaoyan Wang ◽  
Selim Günay ◽  
Wensheng Lu
Keyword(s):  
Maximum Stress ◽  
Seismic Analysis ◽  
Stiffness Ratio ◽  
Continuous Beam ◽  
Seismic Responses ◽  
Maximum Displacement ◽  
Maximum Deformation ◽  
Simply Supported ◽  
System A ◽  
Earthquake Characteristics

The rail in the rail-counterweight system in elevators is vertically supported along the building height by the rail brackets. In the numerical model of the rail-counterweight system, the rail-bracket assembly is modelled as a continuous beam supported by linear springs representing the rail brackets and the stiffness of the bracket is contributed to the overall stiffness of the rail-bracket assembly. To investigate the effect of the rail brackets on the seismic responses of the rail-counterweight system, a parameter named “stiffness ratio” is proposed in a rail-bracket assembly, defined as the ratio of the stiffness of the bracket to that of the simply supported continuous beam representing the rail at mid-span of an intermediate span. The stiffness of the brackets is varied by changing the stiffness ratio of the rail-bracket assembly, and the corresponding seismic responses of the rail-counterweight system are analyzed, including the maximum stress in the rail, the maximum deformation of the brackets, and the maximum displacement of the roller guide off the rail. A comprehensive analysis is conducted by considering four rail spans and three earthquake motions. The variations of the responses with the increasing stiffness ratio are dependent on the earthquake characteristics and the rail spans. The less the rail span is, the less important the effects of the stiffness ratio are. Nevertheless, the seismic responses of the rail-counterweight system generally have little change when the stiffness ratio is up to 4 and more. It is indicated that increasing of the stiffness ratio are not necessarily capable of improving the seismic performance of the counterweight system, especially when the stiffness ratio or the stiffness coefficient of the brackets is large, varying the stiffness ratio is unhelpful to change the rail-counterweight responses.

Numerical Comparison of Damping Amplification Effects Obtained in Neighbourhood of a Mechanism's Singular Position - Viscous and Electromagnetic Cases

2013 ◽  
Vol 597 ◽  
pp. 145-150
Author(s):  
Krzysztof Lipiński
Keyword(s):  
Numerical Model ◽  
Finite Elements ◽  
Multibody System ◽  
Complete System ◽  
Numerical Comparison ◽  
Continuous Beam ◽  
Numerical Investigations ◽  
Constraint Equations ◽  
System A ◽  
Amplification Mechanism

In the paper, effects of numerical investigations are presented. Vibrations of mechanical and electromechanical systems are considered and compared. In the system, a continuous beam is considered as the main vibrating element. Two energy dissipations methods are compared: viscous dampers and DC generators. To increase the damping effectiveness, velocity amplification is proposed, i.e., a mechanism is introduced between the beam and the damping element, and the mechanism configuration is set as closed to the singular position of it. According to some observed fundamental differences in the guiding physical properties of some blocks present in the considered system, two structurally different sub-models are introduced in the numerical model of the complete system. The first sub-model corresponds to the amplification mechanism (considered as composed of rigid elements). The mechanism is modelled as a multibody system. The second sub-model corresponds to the continuous beam. The beam is modelled with used of the finite elements technique. To joint the sub-models, constraint equations are proposed. They express a revolute joint that is present between the mechanisms second rod and the beam enforced to vibrate.

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