Nonlinear Response of CNT Cantilever Based Nano-Resonators

2013 ◽  
Author(s):  
Il Kwang Kim ◽  
Soo Il Lee
Keyword(s):  
Applied Voltage ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Van Der Waals Interactions ◽  
Conducting Plane ◽  
Near Resonance ◽  
Resonance Response ◽  
Theoretical Finding ◽  
Inertial Nonlinearities

This paper presents nonlinear dynamic response of carbon nanotube (CNT) cantilevers incorporating electrostatic forces and van der Waals interactions between the CNT and the conducting plane. The CNT cantilever models including geometric and inertial nonlinearities for predicting unexpected phenomena when the deflection of the CNT is increased. As a result, the CNT cantilever shows complex dynamic responses due to the applied voltage. At the low voltages, the cantilever has only linear response at fundamental resonance except the superharmonic response due to the harmonic excitation of electrostatic field. The secondary resonance response branches off through period-doubling (PD) bifurcation, and becomes softened through saddle-node (SN) bifurcation when the applied voltage is increased. After SN bifurcation, the lower branch of the solution near resonance loses its stability and becomes unstable. This theoretical finding can help the prediction of complex response of the nano-resonators.

Dynamic responses of clearance-type non-linear systems subjected to base harmonic excitation and their experimental verification

2021 ◽  
pp. 107754632110128
Author(s):  
K Renji
Keyword(s):  
Linear Systems ◽  
Experimental Verification ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Maximum Response ◽  
Base Excitation ◽  
Mathematical Expressions ◽  
Non Linear Systems ◽  
Propellant Tank ◽  
Different Levels

Realistic joints in a spacecraft structure have clearances at the interfacing parts. Many such systems can be considered to be having bilinear stiffness. A typical example is the propellant tank assembled with the structure of a spacecraft. However, it is seen that the responses of such systems subjected to base excitation are rarely reported. In this work, mathematical expressions for theoretically estimating the amplitude of its response, the frequency at which the response is the maximum and the maximum response when it is subjected to base sine excitation are derived. Several experiments are conducted on a typical such system subjecting it to different levels of base sine excitation. The frequency at which the response is the maximum reduces with the magnitude of excitation. The expressions derived in this work can be used in estimating the amplitudes of responses and their characteristics reasonably well.

scholarly journals Optimal switch timing for piezoelectric-based semi-active vibration reduction techniques

2017 ◽  
Vol 28 (16) ◽  
pp. 2275-2285 ◽  
Author(s):  
Christopher R Kelley ◽  
Jeffrey L Kauffman
Keyword(s):  
Vibration Reduction ◽  
Harmonic Excitation ◽  
Peak Displacement ◽  
Reduction Techniques ◽  
At Resonance ◽  
Near Resonance ◽  
Switch Time ◽  
Vibration Sensing ◽  
Dimensional Parameters ◽  
Active Vibration

Piezoelectric-based semi-active vibration reduction techniques typically rely on rapid changes in the electrical boundary conditions or corresponding stiffness state. Approaches such as state switching and synchronized switch damping on a resistor or an inductor require four switching events per vibration cycle, with switch timing associated with displacement extrema. Any deviation from this switch timing affects the performance of these techniques. Typical harmonic forcing analyses focus on the energy dissipation and only evaluate the performance at resonance. This study evaluates displacement reduction for harmonic excitation, both at resonance and for frequencies near resonance. Furthermore, it examines the effect of sub-optimal switch timings. Numerical simulations of a non-dimensional model are performed, and an analytical solution is derived for any switch time. This analysis shows that the optimal switch timing depends on the forcing frequency relative to the natural frequency of the structure. Thus, the classical switch time at peak displacement is only optimal when the excitation is exactly at resonance. Even when the optimal switch timing is known, uncertainties in vibration sensing cannot guarantee that switches will occur at the desired moment. Therefore, this work characterizes the degradation in vibration reduction performance when switching away from the optimal switch time based on global, non-dimensional parameters.

Superharmonic Resonance of Fractional-Order Mathieu–Duffing Oscillator

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Jiangchuan Niu ◽  
Xiaofeng Li ◽  
Haijun Xing
Keyword(s):  
Fractional Order ◽  
Order Term ◽  
Duffing Oscillator ◽  
Steady State Solution ◽  
Harmonic Excitation ◽  
Frequency Equation ◽  
Superharmonic Resonance ◽  
Duffing System ◽  
Resonance Response ◽  
Kbm Method

The superharmonic resonance of fractional-order Mathieu–Duffing oscillator subjected to external harmonic excitation is investigated. Based on the Krylov–Bogolubov–Mitropolsky (KBM) asymptotic method, the approximate analytical solution for the third superharmonic resonance under parametric-forced joint resonance is obtained, where the unified expressions of the fractional-order term with fractional order from 0 to 2 are gained. The amplitude–frequency equation for steady-state solution and corresponding stability condition are also presented. The correctness of the approximate analytical results is verified by numerical results. The effects of the fractional-order term, excitation amplitudes, and nonlinear stiffness coefficient on the superharmonic resonance response of the system are analyzed in detail. The results show that the KBM method is effective to analyze dynamic response in a fractional-order Mathieu–Duffing system.

Noise and Contact in Dynamic AFM Operations

2011 ◽  
Author(s):  
Ishita Chakraborty ◽  
Balakumar Balachandran
Keyword(s):  
White Noise ◽  
Evolution Equations ◽  
Stochastic Dynamics ◽  
Gaussian White Noise ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Dynamic Mode ◽  
Grazing Impacts ◽  
Representative System

In this article, the authors study the effects of Gaussian white noise on the dynamics of an atomic force microscope (AFM) cantilever operating in a dynamic mode by using a combination of numerical and analytical efforts. As a representative system, a combination of Si cantilever and HOPG sample is used. The focus of this study is on understanding the stochastic dynamics of a micro-cantilever, when the excitation frequencies are away from the first natural frequency of the system. In the previous efforts of the authors, period-doubling bifurcations close to grazing impacts have been reported for micro-cantilevers when the excitation frequency is in between the first and the second natural frequencies of the system. In the present study, it is observed that the addition of Gaussian white noise along with a harmonic excitation produces a near-grazing contact, when there was previously no contact between the tip and the sample with only the harmonic excitation. Moment evolution equations derived from a Fokker-Planck system are used to obtain numerical results, which support the statement that the addition of noise facilitates contact between the tip and the sample.

Inflight Deicing of Self-Actuating Aircraft Wing Structures With Piezoelectric Actuators

2002 ◽  
Author(s):  
Y. J. Lin ◽  
Suresh V. Venna
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Piezoelectric Actuators ◽  
Element Model ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Underlying Structure ◽  
Shear Stresses ◽  
Modeling And Analysis

Self-actuating aircraft wings for in-flight deicing with minimal power requirements are proposed. Lightweight piezoelectric actuators are utilized to excite the wing structure to its natural frequencies to induce shear stresses on the surface of the wing. The shears are generated in such a way that they are sufficient to break the weak bond between the ice layer and the wing surface. A laminated composite cantilever plate is used for the modeling and analysis. Analytical model is developed to predict the natural frequencies and shear stresses on the surface of the plate and finite element modal analysis is carried out to verify the results. In addition, finite element model involving the ice deposited on the underlying structure is built. The dynamic responses of the structure to harmonic excitation to its first five natural frequencies are investigated. It is observed that significant amount of ice de-bonding from the substrate occurs in the third mode, or the second symmetric mode. Moreover, the energy requirements of the piezoelectric actuators to actuate an adaptive composite structure with given weight are evaluated.

Simplified frequency-independent model for vertical vibrations of surface circular foundations

2019 ◽  
Vol 16 (5) ◽  
pp. 592-603
Author(s):  
Amina Zahafi ◽  
Mohamed Hadid
Keyword(s):  
Half Space ◽  
Harmonic Excitation ◽  
Vertical Vibration ◽  
Dynamic Responses ◽  
Simplified Model ◽  
Content Type ◽  
Frequency Independent ◽  
Modes Of Vibration ◽  
Embedded Foundations ◽  
Independent Model

Purpose This paper aims to simplify a new frequency-independent model to calculate vertical vibration of rigid circular foundation resting on homogenous half-space and subjected to vertical harmonic excitation is presented in this paper. Design/methodology/approach The proposed model is an oscillator of single degree of freedom, which comprises a mass, a spring and a dashpot. In addition, a fictitious mass is added to the foundation. All coefficients are frequency-independent. The spring is equal to the static stiffness. Damping coefficient and fictitious mass are first calculated at resonance frequency where the response is maximal. Then, using a curve fitting technique the general formulas of damping and fictitious mass frequency-independent are established. Findings The validity of the proposed method is checked by comparing the predicted response with those obtained by the half-space theory. The dynamic responses of the new simplified model are also compared with those obtained by some existing lumped-parameter models. Originality/value Using this new method, to calculate the dynamic response of foundations, the engineer only needs the geometrical and mechanical characteristics of the foundation (mass and radius) and the soil (density, shear modulus and the Poisson’s ratio) using just a simple calculator. Impedance functions will no longer be needed in this new simplified method. The methodology used for the development of the new simplified model can be applied for the resolution of other problems in dynamics of soil and foundation (superficial and embedded foundations of arbitrary shape, other modes of vibration and foundations resting on non-homogeneous soil).

Capillary–gravity Kelvin–Helmholtz waves close to resonance

1990 ◽  
Vol 217 ◽  
pp. 71-91 ◽  
Author(s):  
V. Bontozoglou ◽  
T. J. Hanratty
Keyword(s):  
Gravity Waves ◽  
Second Harmonic ◽  
Period Doubling ◽  
Current Speed ◽  
Period Doubling Bifurcation ◽  
Helmholtz Instability ◽  
Horizontal Pipe ◽  
Near Resonance ◽  
Gas Liquid Flow ◽  
Permanent Form

Capillary–gravity waves of permanent form at the interface between two unbounded fluids in relative motion are considered. The range of wavelengths for an internal resonance with the second harmonic and a period-doubling bifurcation are found to depend on the current speed. The Kelvin–Helmholtz instability of short waves becomes strongly subcritical near resonance. It is speculated that this instability is needed to trigger a period-doubling bifurcation. This notion is used to explain the development of waves at short fetch and the initiation of liquid slugs for gas–liquid flow in a horizontal pipe.

Nonlinear Dynamics of High-Dimensional Models of a Rotating Euler-Bernoulli Beam Under the Gravity Load

2014 ◽  
Author(s):  
J. L. Huang ◽  
W. D. Zhu
Keyword(s):  
Slope Angle ◽  
Period Doubling ◽  
Dynamic Responses ◽  
Phase Portraits ◽  
High Dimensional ◽  
Bernoulli Beam ◽  
Gravity Load ◽  
Dimensional Models ◽  
Euler Bernoulli Beam ◽  
Ihb Method

Nonlinear dynamic responses of an Euler-Bernoulli beam attached to a rotating rigid hub with a constant angular velocity under the gravity load are investigated. The slope angle of the centroid line of the beam is used to describe its motion, and the nonlinear integro-partial differential equation that governs the motion of the rotating hub-beam system is derived using Hamilton’s principle. Spatially discretized governing equations are derived using Lagrange’s equations based on discretized expressions of kinetic and potential energies of the system, yielding a set of second-order nonlinear ordinary differential equations with combined parametric and forced harmonic excitations due to the gravity load. The incremental harmonic balance (IHB) method is used to solve for periodic responses of high-dimensional models of the system and period-doubling bifurcation. The multivariable Floquet theory along with the precise Hsu’s method is used to investigate the stability of the periodic responses. Phase portraits and bifurcation points obtained from the IHB method agree very well with those from numerical integration.

Large-Amplitude Vibrations of Thin Panels

2006 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Boundary Conditions ◽  
Lyapunov Exponents ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Time Integration ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Different Boundary Conditions ◽  
Model C

Geometrically nonlinear vibrations of circular cylindrical panels with different boundary conditions and subjected to harmonic excitation are numerically investigated. The Donnell's nonlinear strain-displacement relationships are used to describe geometric nonlinearity; in-plane inertia is taken into account. Different boundary conditions are studied and the results are compared; for all of them zero normal displacements at the edges are assumed. In particular, three models are considered in order to investigate the effect of different boundary conditions: Model A for free in-plane displacement orthogonal to the edges, elastic distributed springs tangential to the edges and free rotation; Model B for classical simply supported edges; Model C for fixed edges and distributed rotational springs at the edges. Clamped edges are obtained with the Model C for very high value of the stiffness of rotational springs. The nonlinear equations of motion are obtained by the Lagrange multi-mode approach, and are studied by using the code AUTO based on pseudo-arclength continuation method. Convergence of the solution with the number of generalized coordinates is numerically verified. Complex nonlinear dynamics is also investigated by using bifurcation diagrams from direct time integration and calculation of the Lyapunov exponents and the Lyapunov dimension. Interesting phenomena such as (i) subharmonic response, (ii) period doubling bifurcations, (iii) chaotic behavior and (iv) hyper-chaos with four positive Lyapunov exponents have been observed.

Dynamic Characteristics of Fluid-Conveying Pipes with Piecewise Linear Support

2016 ◽  
Vol 16 (06) ◽  
pp. 1550025 ◽  
Author(s):  
Zhan-Ying Li ◽  
Jian-Jun Wang ◽  
Ming-Xing Qiu
Keyword(s):  
Dynamic Characteristics ◽  
Piecewise Linear ◽  
Time Integration ◽  
Measurement Data ◽  
Element Model ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Fluid Structure ◽  
Pipe System ◽  
Fluid Conveying Pipes

For the analysis of dynamic characteristics of fluid-conveying pipes with piecewise linear support, a fluid–structure coupling dynamic model based on the finite element method is proposed. A user-defined pipe element based on Euler–Bernoulli beam is developed for modeling the pipes, considering the dynamic flow conditions. A nonlinear spring element is utilized to model the clamp between the pipe and the base. The dynamic responses of the system are obtained through the direct time integration. The stiffness of the clamp support is investigated by the analytical method and the experimental method, in which it is found that the clamp stiffness is piecewise linear. For different pipe geometries the user-defined element model, analytical model and measurement data are compared. The results show high quality of the element developed in this paper. Finally, the dynamic characteristics of the pipe system with piecewise linear support subjected to base harmonic excitation are calculated and the effects of the system parameters on pipe behaviors have also been studied. As a consequence, the model proposed in this paper can represent the piecewise linear nonlinearity of the clamp support and be used conveniently to investigate the effects of the fluid–structure coupling on the system behaviors.

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