Nonlinear Vibration of Carbon Nanotube Resonators Considering Higher Modes

2015 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Multiple Scales ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Objective System ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

Nonlinear forced vibration of the carbon nanotubes based on the Euler-Bernoulli beam theory is studied. The Euler-Bernoulli beam theory is implemented to find the governing equation of the vibrations of the carbon nanotube. The Pasternak and Nonlinear Winkler foundation is assumed for the objective system. It is supposed that the system is supported by hinged-hinged boundary conditions. The Galerkin procedure is employed in order to find the nonlinear ordinary differential equation of the vibration of the objective system considering two modes of vibrations. The primary and secondary resonant cases are developed for the objective system employing the multiple scales method. Influence of different factors such as length, thickness, position of applied force, Pasternak and Winkler foundation are fully shown on the primary and secondary resonance of the system.

scholarly journals Rail Joint Model Based on the Euler-Bernoulli Beam Theory

2019 ◽  
Vol 8 (2) ◽  
pp. 16-29
Author(s):  
Traian Mazilu ◽  
Ionuţ Radu Răcănel ◽  
Cristian Lucian Ghindea ◽  
Radu Iuliu Cruciat ◽  
Mihai-Cornel Leu
Keyword(s):  
Beam Theory ◽  
Joint Model ◽  
Experimental Results ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Model Based ◽  
Bernoulli Beam Theory ◽  
Proposed Model ◽  
Joint Gap ◽  
Euler Bernoulli Beam

Abstract In this paper, a rail joint model consisting of three Euler-Bernoulli beams connected via a Winkler foundation is proposed in order to point out the influence of the joint gap length upon the stiffness of the rail joint. Starting from the experimental results aiming the stiffness of the rail joint, the Winkler foundation stiffness of the model has been calculated. Using the proposed model, it is shown that the stiffness of the rail joint of the 49 rail can decreases up to 10 % when the joint gap length increases from 0 to 20 mm.

Dynamic Behavior of Sandwich Beams with Different Cores

2012 ◽  
Vol 468-471 ◽  
pp. 1344-1348
Author(s):  
Ying Wu ◽  
Han Bin Jia ◽  
Dong Xu Zhang ◽  
Lei Tian ◽  
Yan Jun Lü
Keyword(s):  
Dynamic Behaviour ◽  
Metal Foam ◽  
Lattice Structure ◽  
Beam Theory ◽  
Porous Metal ◽  
Nonlinear Ordinary Differential Equation ◽  
Sandwich Beams ◽  
Bernoulli Beam ◽  
Metal Fiber ◽  
Euler Bernoulli Beam

The nonlinear dynamic behaviour of sandwich beams with different cores under transverse cycling loads is investigated in this paper. Based on Euler-Bernoulli beam theory, the second-order nonlinear ordinary differential equation of the sandwich beams with different cores is established by applying Hamilton’s principle and Galerkin method. The effects of the cores of metal foam and lightweight wood and porous metal fiber as well as pyramid lattice structure on the dynamic behaviour are studied through numerical simulations. It is shown that the dynamic behaviour of sandwich beams is not solely determined by and

Nonlinear Vibration of Nanobeam With Quadratic Rational Bezier Arc Curvature

2014 ◽  
Author(s):  
Hassan Askari ◽  
Zia Saadatnia ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Governing Equation ◽  
Oscillation Amplitude ◽  
Beam Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Linear Frequency ◽  
Euler Bernoulli Beam

Nonlinear vibration of nanobeam with the quadratic rational Bezier arc curvature is investigated. The governing equation of motion of the nanobeam based on the Euler-Bernoulli beam theory is developed. Accordingly, the non-uniform rational B-spline (NURBS) is implemented in order to write the implicit form of the governing equation of the structure. The simply-supported boundary conditions are assumed and the Galerkin procedure is utilized to find the nonlinear ordinary differential equation of the system. The nonlinear natural frequency of the system is found and the effects of different parameters, namely, the waviness amplitude, oscillation amplitude, aspect ratio, curvature shape and the Pasternak foundation coefficient are fully investigated. The hardening and softening responses of the natural frequency of structure are detected for variations of the shape and amplitude of the curvature waviness. It is revealed that the ratio of nonlinear to linear frequency increases with an increase in the oscillation amplitudes. It is found that by increasing the Pasternak foundation coefficient, the ratio of nonlinear to linear frequency decreases.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

2012 ◽  
Vol 24 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Harvesters ◽  
Bernoulli Beam Theory ◽  
Spectral Finite Element ◽  
Euler Bernoulli Beam ◽  
Element Method

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).

Case Study of the Effect of Combined Axial and Lateral Loadings on the Critical Buckling Capacity of Piping Supports

2020 ◽  
Author(s):  
Phillip Wiseman ◽  
Alex Mayes ◽  
Shreeya Karnik
Keyword(s):  
Large Deformation ◽  
Axial Loading ◽  
Beam Theory ◽  
Second Order ◽  
Lateral Acceleration ◽  
Bernoulli Beam ◽  
Deformation Method ◽  
Closed Form Solutions ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

Abstract Snubbers are used in industry to restrain piping in dynamic events which can see significant axial loading as well as lateral acceleration. Snubbers are often employed with an extension when required to bridge gaps between the piping and building structure. As a result, they are susceptible to buckling instability issues. The pipe support and restraint design by analysis buckling criteria for supports given within the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 1, Subsection NF is investigated to determine the behavior of snubber assemblies under combined axial and lateral loadings. Four types of analyses are performed on the assemblies under the action of axial loading to demonstrate finite element and closed form solutions. These include the following: linear Eigen buckling, nonlinear second order large deformation method, energy method and Euler Bernoulli beam theory. In addition, a variety of snubber assembly sizes are subjected to combined axial and lateral loading in the form of multiple magnitudes of lateral acceleration. The behavior was analyzed by the Euler Bernoulli beam theory and nonlinear second order large deformation method. The techniques of each method are compared providing explanations of the assumptions taken, relevant limitations and recommended applications.

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