Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method

Khan, Muhammad Sabeel; Kaneez, Hajra

doi:10.1590/1679-78253327

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…The interaction between the pressure field of an internal fluid-filled channel network and the deformation field of the supporting elastic structure is formulated. In order to derive accurate modeling, the following assumptions are made (Sabeel Khan and Kaneez, 2017; Zhang et al, 2016a): (i) the fluid is incompressible with a constant plug-flow velocity profile; (ii) rotary inertia and shear deformation are neglected; (iii) even though deflections are large, the strain in the system is assumed to be small with the moderate rotation; (iv) plane cross sections remain perpendicular to the beam axis after deformation; and (v) a 2D soft robotic arm model with planar motions are considered.…”

Section: System Description and Problem Formulationmentioning

confidence: 99%

Steady-state dynamic analysis of a nonlinear fluidic soft actuator

Haji

Bamdad

2022

Journal of Vibration and Control

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The internal channel networks embedded within a soft structure can be a fruitful mechanism to create and activate actuators in the research fields of soft robotics. The deformation of the supporting elastic structure from the pressurized viscous fluid into the channels needs an accurate investigation. In this paper, accurate modeling and dynamic analysis of this nonlinear soft actuator is our goal. In this modeling, the soft actuator is considered the Euler–Bernoulli beam with large deflection and nonlinear strain. After implementing Hamilton’s principle, the assumed mode method is used to achieve the mathematical model in terms of the multi-mode system that is more similar to the flexible nature of the actuation system. Steady-state dynamics is investigated by a combination of the complex averaging method with arc-length continuation. The accuracy of the proposed modeling is validated by comparing simulation results to those obtained with a nonlinear finite element method and numerical method. It shows that only one-third of the degree-of-freedoms used for the finite element method are sufficient to obtain equivalent converged solutions with the proposed model. The effect of nonlinear strain and multi-mode consideration in the analysis of the proposed modeling is investigated. It is advantageous to analyze the system performance by looking into the geometrical parameters and fluid properties.

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Section: System Description and Problem Formulationmentioning

confidence: 99%

Steady-state dynamic analysis of a nonlinear fluidic soft actuator

Haji

Bamdad

2022

Journal of Vibration and Control

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Nonlinear extensional-flexural vibrations in variable cross section beams with eccentric intermediate mass

Aghaei

Moeenfard

Moavenian

2021

International Journal of Mechanical Sciences

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A novel method for characterizing temperature-dependent elastic modulus and glass transition temperature by processing the images of bending cantilever slender beams at different temperatures

et al. 2018

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We propose a novel method for estimating the elastic modulus of several materials by processing the bending image of cantilever material sheets. The calculated results (tested for five samples) were consistent with data obtained by direct measurement using a tensile strength device. By placing the cantilever sheets in an environment inside of which the temperature could be controlled, we were able to obtain the temperature dependence of elastic modulus. We identified a drastic drop of elastic modulus at a certain temperature and assumed this temperature corresponds to glass transition temperature. We also introduced an equation for describing the elastic modulus around that critical temperature and were able to estimate the glass transition temperature for all tested polymer materials. Surprisingly, the estimated glass transition temperatures conform to data obtained by direct measurement using a DTA device. Since the elastic modulus changes suddenly around the glass transition temperature, the proposed method might be more accurate than measurement using a DTA device where the glass transition temperature corresponds to the location of a weak peak at the DTA curve. This is the first attempt for estimating the glass transition temperature of polymer based on bending of cantilever slender beam, and seems to be the simplest method. The method is very potential for developing new equipment for determining the glass transition temperature of polymeric materials.

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Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method

Cited by 4 publications

References 18 publications

Steady-state dynamic analysis of a nonlinear fluidic soft actuator

Steady-state dynamic analysis of a nonlinear fluidic soft actuator

Nonlinear extensional-flexural vibrations in variable cross section beams with eccentric intermediate mass

A novel method for characterizing temperature-dependent elastic modulus and glass transition temperature by processing the images of bending cantilever slender beams at different temperatures

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