Nonlinear Forced Vibration of a Beam-Type Resonator With Attached Eccentric Mass

2014 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Forced Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Nonlinear Resonance ◽  
Beam Theory ◽  
Attached Mass ◽  
Beam Type ◽  
Nonlinear Forced Vibration ◽  
Euler Bernoulli Beam

In this paper, the nonlinear model of an asymmetric micro-bridge resonator with an attached eccentric mass is investigated. The resonator is treated using the Euler-Bernoulli beam theory. The attached mass represents the electrostatic comb-drive actuator in micro-electromechanical applications. The center of mass of the actuator is assumed to be off the neutral axis of the beam. The governing equations of motion are derived assuming that a concentrated harmonic force is applied to the attached mass. The nonlinear forced vibration of the system is studied using the method of multiple scales. It has been demonstrated that the eccentricity of the mass may lead to different types of nonlinear resonance, e.g., superharmonic and internal resonance. The end application of the structure under investigation is in resonant sensing and energy harvesting applications.

Nonlinear Free Vibration of a Beam With Off-Axis Attached Mass

2013 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Free Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Beam Theory ◽  
Governing Equations ◽  
Attached Mass ◽  
Lumped Mass ◽  
Nonlinear Free Vibration ◽  
Euler Bernoulli Beam

A model of a clamped-clamped beam with an attached lumped mass is presented in this paper. The system is modeled using the Euler-Bernoulli beam theory. In the models presented in literature, it is assumed that the center of mass of the attached mass is located on the neutral axis of the beam. In this paper, this assumption is relaxed. The governing equations of motion are derived. It has been shown that the off-axis center of mass of the attached mass generates an amplitude-dependent transverse force in the beam, which introduces a quadratic nonlinearity. The nonlinear governing equations of motion are solved using the Multiple Scales method. The nonlinear free vibration frequencies are determined.

Dynamic Analysis of a Beam-Type Resonator With Off-Axis Attached Mass

2012 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Kamran Behdinan
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Beam Theory ◽  
Numerical Approach ◽  
Governing Equations ◽  
Bernoulli Beam ◽  
Comb Drive ◽  
Comb Drives ◽  
Beam Type ◽  
Euler Bernoulli Beam

In this paper, the model of a micro-machined beam-type resonator is presented. The resonator is a micro-bridge which is modeled using Euler-Bernoulli beam theory. A comb-drive electrostatic actuator is attached to the micro-bridge for the excitation/detection of vibrations. In the models presented in the literature, it is assumed that the center of mass of the comb-drive is located on the neutral axis of the beam. In this paper, it is demonstrated that this assumption can not be applied for asymmetric-shaped comb-drives. Furthermore, the governing equations of motion are derived by relaxing the above assumption. It has been shown that the off-axis center of mass of the comb-drive generates an amplitude-dependent transverse force in the beam, which is essentially a nonlinear effect. The governing equations of motion are solved using a hybrid analytical-numerical approach. The end application of the structure under investigation is in resonant sensing and energy harvesting applications.

Nonlinear Forced Vibration of Curved Carbon Nanotube Resonators

2016 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Carbon Nanotube ◽  
Forced Vibration ◽  
Primary Resonance ◽  
Beam Theory ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Forced Vibration ◽  
Resonator System ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

Nonlinear forced vibration of the nonlocal curved carbon nanotubes is investigated. The governing equation of vibration of a nonlocal curved carbon nanotube is developed. The nonlinear Winkler and Pasternak type foundations are chosen for the nanotube resonator system. Furthermore, the shape of the carbon nanotube system is assumed to be of a sinusoidal curvature form and different types of the boundary conditions are postulated for the targeted system. The Euler-Bernoulli beam theory in conjunction with the Eringen theory are implemented to obtain the partial differential equation of the system. The Galerkin method is applied to obtain the nonlinear ordinary differential equations of the system. For the sake of obtaining the primary resonance of the considered system the multiple time scales method is utilized. The influences of different parameters, namely, the position of the applied force, different forms of boundary condition, amplitude of curvature, and the coefficient of the Pasternak foundation, on the frequency response of the system were fully investigated.

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.

Flow-Induced Nonlinear Vibration of Non-Uniform Nanotubes

2017 ◽  
Author(s):  
Shamim Mashrouteh ◽  
Ahmad Barari ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Nonlinear Vibration ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Beam Theory ◽  
Harmonic Excitation ◽  
Free Form ◽  
B Splines ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Euler Bernoulli Beam

This paper focuses on nonlinear forced vibration analysis of a free-form conveying fluid nanotube. Non-Uniform Rational B-Splines (NURBS) is used to model the free-form curvature of the nanotube, analytically. In order to develop the ordinary differential equations of motion, the Euler-Bernoulli beam theory and Galerkin method are implemented and the frequency response and the primary resonance of the nanotube under a harmonic excitation are studied. The effects of the free-form curvature of the nanotube and its physical characteristic on the nonlinear vibration behavior of the system are discussed as a parametric study.

Nonlinear Forced Vibration Analysis of Smart Curved CNTs Conveying Fluid

2021 ◽  
Author(s):  
Vahid Mohamadhashemi ◽  
Amir Jalali ◽  
Habib Ahmadi
Keyword(s):  
Carbon Nanotube ◽  
Velocity Vector ◽  
Multiple Scales ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Maximum Amplitude ◽  
Beam Theory ◽  
Physical Parameters ◽  
Conveying Fluid

In this study, the nonlinear vibration of a curved carbon nanotube conveying fluid is analyzed. The nanotube is assumed to be covered by a piezoelectric layer and the Euler–Bernoulli beam theory is employed to establish the governing equations of motion. The influence of carbon nanotube curvature on structural modeling and fluid velocity vector is considered and the slip boundary conditions of CNT conveying fluid are included. The mathematical modeling of the structure is developed using Hamilton’s principle and then, the Galerkin procedure is employed to discretize the equation of motion. Furthermore, the frequency response of the system is extracted by applying the multiple scales method of perturbation. Finally, a comprehensive study is carried out on the primary resonance and piezoelectric-based parametric resonance of the system. It is shown that consideration of nanotube curvature may lead to an increase in nonlinearity. Implementing the fluid velocity vector in which nanotube curvature is included highly affects the maximum amplitude of the response and should not be ignored. Furthermore, different system parameters have evident impacts on the behavior of the system and therefore, selecting the reasonable geometrical and physical parameters of the system can be very useful to achieve a favorable response.

scholarly journals Nonlinear Free and Forced Vibration Behavior of Shear-Deformable Composite Beams with Shape Memory Alloy Fibers

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren Yongsheng ◽  
Du Chenggang ◽  
Shi Yuyan
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Shear Deformation ◽  
Forced Vibration ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Composite Beams ◽  
Vibration Behavior ◽  
Shear Deformable

The nonlinear free and forced vibration of the composite beams embedded with shape memory alloy (SMA) fibers are investigated based on first-order shear deformation beam theory and the von Kármán type nonlinear strain-displacement equation. A thermomechanical constitutive equation of SMA proposed by Brinson is used to calculate the recovery stress of the constrained SMA fibers. The equations of motion are derived by using Hamilton’s principle. The approximate solution is obtained for vibration analysis of the composite beams based on the Galerkin approach. The parametric study is carried out to display the effect of the actuation temperature, the volume fraction, the initial strain of SMA fibers, and the length-to-thickness ratio. The shear deformation is shown to have a significant contribution to nonlinear vibration behavior of the composite beams with SMA fibers.

Dynamic Behavior of Vehicles Travelling on Bridges

1993 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Mehrdaad Ghorashi
Keyword(s):  
Boundary Conditions ◽  
Dynamic Behavior ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parameter System ◽  
Moving Vehicle ◽  
Lumped Parameter ◽  
Euler Bernoulli Beam ◽  
Two Degree Of Freedom

Abstract An investigation into the dynamic behavior of a bridge with simply supported boundary conditions, carrying a moving vehicle, is performed. The vehicle has been modelled as a two degree of freedom lumped-parameter system travelling at a uniform speed. Furthermore, the bridge is assumed to obey the Euler-Bernoulli beam theory of vibration. This analysis may well be applied to a beam with different boundary conditions, but the computer simulation results given in this paper are set for only the case of freely hinged ends. Numerical solutions for the derived differential equations of motion are obtained and their close agreement, in some extreme cases, with those reported earlier by the authors are observed. Finally, the effect of speed on the maximum dynamic deflection of bridge is shown to be of much importance and hence an estimation for the critical speed of the vehicle is presented.

scholarly journals Theoretical and experimental investigation of parametrically excited piezoelectric energy harvester

2018 ◽  
Vol 211 ◽  
pp. 02009
Author(s):  
Anshul Garg ◽  
Santosha K. Dwivedy
Keyword(s):  
Cantilever Beam ◽  
Energy Harvester ◽  
Multiple Scales ◽  
Resonance Condition ◽  
Beam Theory ◽  
State Response ◽  
Piezoelectric Energy ◽  
Arbitrary Position ◽  
Fixed End ◽  
Euler Bernoulli Beam

In the present work, a cantilever beam based piezoelectric energy harvester is investigated both theoretically and experimentally. The harvester is consists of a harmonically base excited vertical cantilever beam with a piezoelectric patch at the fixed end and a mass attached at an arbitrary position. The Euler-Bernoulli beam theory is applied considering the cantilever beam to be slender. The temporal nonlinear electromechanical governing equation of motion is obtained by using generalized Galerkin’s method considering two-mode approximation. Here for principal parametric resonance condition the steady state response of the voltage is obtained by using the method of multiple scales. The results are validated by developing an experimental setup of the harvester. For the harvester having a dimension of 295 mm×24 mm×7.6 mm, a maximum voltage of 40 V is obtained for a base motion of 9 mm with a frequency of 10.07 Hz when 15 gm mass is attached at a distance of 140 mm from the fixed end.

On the forced vibration of carbon nanotubes via a non-local Euler—Bernoulli beam model

2010 ◽  
Vol 224 (2) ◽  
pp. 497-503 ◽  
Author(s):  
P Karaoglu ◽  
M Aydogdu
Keyword(s):  
Carbon Nanotubes ◽  
Forced Vibration ◽  
Beam Theory ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
Non Local ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Walled Cnts

This article studies the forced vibration of the carbon nanotubes (CNTs) using the local and the non-local Euler—Bernoulli beam theory. Amplitude ratios for the local and the non-local Euler—Bernoulli beam models are given for single- and double-walled CNTs. It is found that the non-local models give higher amplitudes when compared with the local Euler—Bernoulli beam models. The non-local Euler—Bernoulli beam model predicts lower resonance frequencies.

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