On the Dynamics of Fractional Visco-Elastic Beams

2012 ◽  
Author(s):  
Salvatore Di Lorenzo ◽  
Francesco P. Pinnola ◽  
Antonina Pirrotta
Keyword(s):  
Elastic Beam ◽  
Constitutive Law ◽  
Dynamic Loads ◽  
Elastic Behavior ◽  
Advanced Manufacturing ◽  
Suitable Model ◽  
Bernoulli Beam ◽  
Static Behavior ◽  
Creep Tests ◽  
Euler Bernoulli Beam

With increasing advanced manufacturing process, visco-elastic materials are very attractive for mitigation of vibrations, provided that you may have advanced studies for capturing the realistic behavior of such materials. Experimental verification of the visco-elastic behavior is limited to some well-known low order models as the Maxwell or Kelvin models. However, both models are not sufficient to model the visco-elastic behavior of real materials, since only the Maxwell type can capture the relaxation tests and the Kelvin the creep tests, respectively. Very recently, it has been stressed that the most suitable model for capturing the visco-elastic behavior is the spring-pot, characterized by a fractional constitutive law. Based on this assumption, the quasi-static behavior has been investigated very recently, however for noise control there is a need of exploiting the dynamic behavior of such a fractional visco-elastic beam. The present paper introduces the dynamic response of fractional visco-elastic Euler-Bernoulli beam under dynamic loads.

The elastochrone: the descent time of a sphere on a flexible beam

2009 ◽  
Vol 465 (2107) ◽  
pp. 2293-2311 ◽  
Author(s):  
Jeffrey M. Aristoff ◽  
Christophe Clanet ◽  
John W.M. Bush
Keyword(s):  
Gravitational Field ◽  
Theoretical Model ◽  
Elastic Beam ◽  
Beam Theory ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Horizontal Beam ◽  
Theoretical Predictions ◽  
Static Regime ◽  
Euler Bernoulli Beam

We present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler–Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the load trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favourably with our experimental observations in this quasi-static regime. The time taken for descent along an elastic beam, the elastochrone, is shown to exceed the classical brachistochrone, the shortest time between two points in a gravitational field.

DYNAMIC STABILITY OF A BEAM ON AN ELASTIC FOUNDATION INCLUDING STRESS WAVE EFFECTS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250017 ◽  
Author(s):  
YING LIU ◽  
G. LU
Keyword(s):  
Dynamic Stability ◽  
Elastic Foundation ◽  
Stress Wave ◽  
Axial Load ◽  
Elastic Beam ◽  
Beam Theory ◽  
Stress Wave Propagation ◽  
Bernoulli Beam ◽  
Wave Effects ◽  
Euler Bernoulli Beam

This paper examines the dynamic stability of an elastic beam on the elastic foundation, in which the stress wave effect is taken into account. Based on Euler–Bernoulli beam theory, the dynamic response of the elastic beam on the elastic foundation to a small transverse perturbation is analyzed. By considering the stress wave propagation in the beam and the constraint of the elastic foundation, the critical bifurcation condition of elastic beam is derived, and the critical axial load of the elastic beam is predicted. Furthermore, the effects of the elastic foundation and the beam length on buckling condition are discussed by using numeric examples. Finally, an approximate solution of critical axial load for elastic beam on the elastic foundation is provided, which may be used to investigate elastic beam buckling problem.

scholarly journals Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Pengfei Liu ◽  
Hongjun Liu ◽  
Qing Wu
Keyword(s):  
Transfer Matrix ◽  
Timoshenko Beam ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Elastic Beam ◽  
Vibration Characteristics ◽  
Bernoulli Beam ◽  
Flexible Wheelset ◽  
Euler Bernoulli Beam

The elastic vibration of the wheelset is a potential factor inducing wheel-rail defects. It is important to understand the natural vibration characteristics of the flexible wheelset for slowing down the defect growth. To estimate the elastic free vibration of the railway wheelset with the multidiameter axle, the transfer matrix method (TMM) is applied. The transfer matrices of four types of elastic beam models are derived including the Euler–Bernoulli beam, Timoshenko beam, elastic beam without mass and shearing stiffness, and massless elastic beam with shearing stiffness. For each type, the simplified model and detailed models of the flexible wheelset are developed. Both bending and torsional modes are compared with that of the finite element (FE) model. For the wheelset bending modes, if the wheel axle is modelled as the Euler–Bernoulli beam and Timoshenko beam, the natural frequencies can be reflected accurately, especially for the latter one. Due to the lower solving accuracy, the massless beam models are not applicable for the analysis of natural characteristics of the wheelset. The increase of the dividing segment number of the flexible axle is helpful to improve the modal solving accuracy, while the computation effort is almost kept in the same level. For the torsional vibration mode, it mainly depends on the axle torsional stiffness and wheel inertia rather than axle torsional inertia.

A Multi-Scale Approach to the Analysis of Ultra Deepwater Unbonded Flexible Risers

2009 ◽  
Author(s):  
Ali Bahtui ◽  
Giulio Alfano ◽  
Hamid Bahai
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Large Scale ◽  
Element Model ◽  
Constitutive Law ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Multi Scale ◽  
Non Linear ◽  
Euler Bernoulli Beam

The results of a detailed, non-linear finite-element analysis of a small-scale (i.e. 1.7m long) six-layer unbonded flexible riser, accounting for interlayer contact and frictional slip, are used to calibrate a novel, simplified constitutive model for a 3D, non-linear Euler-Bernoulli beam model suitable for large scale analyses (hundreds of meters in length where water depth is more than 1000m). The detailed finite element model contains all the layers, each modeled separately with contact interfaces between them. The finite element model includes the main features of the riser geometry with very little simplifying assumptions made. The detailed finite element model is formulated in the framework of a novel, multi-scale approach potentially suitable for ultra deepwater applications. A simple, three-dimensional Euler-Bernoulli beam element, suitable for large scale analyses, is developed based on a non-linear constitutive law for the beam cross-section relating bending curvatures to the conjugate stress resultants.

Tuning Stiffness Nonlinearity: Theory and Applications

2020 ◽  
Author(s):  
Mohamed Zanaty ◽  
Ilan Vardi ◽  
Simon Henein
Keyword(s):  
Compliant Mechanisms ◽  
Real Life ◽  
Beam Theory ◽  
Elastic Behavior ◽  
Bernoulli Beam ◽  
Stiffness Constant ◽  
Real Life Situation ◽  
Tuning Methods ◽  
Nonlinear Elastic ◽  
Euler Bernoulli Beam

Abstract Perfect elasticity is not achievable in real-life situation, so spring stiffness is not perfectly constant. In this paper, we study the effect of modifying non-linear stiffness terms while keeping the nominal stiffness constant. We introduce three methods to design and tune linear and nonlinear elastic behavior in the context of compliant mechanisms and we present mechanical realizations. These designs are modeled using Euler-Bernoulli beam theory. Numerical simulation and experimental measurement show a good match with the theoretical model. We then present applications of our stiffness tuning methods to mechanical meta-materials, mechanical resonators, and mechanical computation.

Output variance constrained bending control of rotating Euler–Bernoulli beam

2016 ◽  
Vol 231 (2) ◽  
pp. 202-211 ◽  
Author(s):  
Tugrul Oktay
Keyword(s):  
Closed Loop ◽  
Vibration Suppression ◽  
Rotation Angle ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Bernoulli Beam ◽  
Constrained Bending ◽  
Euler Bernoulli Beam ◽  
Output Variance ◽  
Beam Rotation

In this article bending control of rotating Euler–Bernoulli beam is considered. It is assumed that the fixed-free elastic beam is attached to a servomotor using a variance constrained controller, specifically output variance constrained controller for vibration suppression. Equations of motion of the system obtained via Hamilton's principle and Galerkin method are used. The resulting linearized state-space models obtained considering just one or three modes are used for control system design. Output variance constrained controllers are designed in order to control bending at the beam tip and beam rotation angle with different variance constraint magnitudes. Closed-loop responses are analyzed when they experience white noise perturbations. Comparisons between system having tighter variance constraint and weaker variance constraint are also performed. Finally, robustness of Output variance constrained controllers with respect to the modeling uncertainty (i.e. variation of number of modes) is examined.

scholarly journals Dynamic response of the tower of a NREL5MW wind turbine generator

2018 ◽  
Vol 234 ◽  
pp. 04008
Author(s):  
Ivo Angelov
Keyword(s):  
Wind Turbine ◽  
Forced Vibrations ◽  
Dynamic Loads ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Turbine Generator ◽  
Wind Turbine Generator ◽  
Forced Motion ◽  
Aerodynamic Interaction ◽  
Euler Bernoulli Beam

Considering the complexity of the aerodynamic interaction between a non-homogeneous, nonstationary wind field and a wind turbine, one can easily establish that the constructive elements of the turbine will be exposed to dynamic loads, which will eventually lead to forced motion and particularly to forced vibrations. One of the most significant elements of every wind turbine is the tower of the generator. The tower is subjected to forced vibrations and transmits all dynamic loads that appear in the wind turbine. That is why a dynamic analysis of the tower is worth executing. In this research such an analysis is made considering the tower of the generator as Euler-Bernoulli beam structure and considering it as a Love-Kirchhoff shell structure.

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