Broadband and Enhanced Energy Harvesting Using Inerter Pendulum Vibration Absorber

2020 ◽  
Author(s):  
Aakash Gupta ◽  
Wei-Che Tai
Keyword(s):  
Large Scale ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Vibration Absorber ◽  
Frequency Bandwidth ◽  
Energy Harvesters ◽  
New Type ◽  
Electrical Damping ◽  
Relationship Of

Abstract Inerter-based vibration energy harvesters (VEHs) have been widely studied to harvest energy from large-scale structural vibrations. Recently, there have been efforts to increase the operation frequency bandwidth of VEHs by introducing a variety of stiffness and inertia nonlinearity. This paper proposes a new inerter-based VEH comprising an epicyclic-gearing inerter and a pendulum vibration absorber. The centrifugal force of the pendulum introduces a new type of inertia nonlinearity that broadens the frequency bandwidth. This inerter-pendulum VEH (IPVEH) is incorporated in a single-degree-of-freedom structure to demonstrate its performance and the equations of motion of the system are derived. The method of multiple scales is applied to derive the amplitude–frequency response relationship of the harvested power in the primary resonance. The harvested power is optimized through tuning the harvester’s electrical damping and the optimum power is benchmarked with that of conventional linear inerter-based VEHs. The results show that the IPVEH has larger bandwidth and harvested power and the improvement is correlated with the strength of its inertia nonlinearity.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

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.

Characterizing the Effective Bandwidth of Tri-Stable Energy Harvesters

2016 ◽  
Author(s):  
Meghashyam Panyam ◽  
Mohammed F. Daqaq
Keyword(s):  
Magnetic Field ◽  
Analytical Solutions ◽  
Energy Harvester ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Experimental Studies ◽  
Effective Bandwidth ◽  
Frequency Bandwidth ◽  
Effective Frequency ◽  
Energy Harvesters

This paper aims to investigate the response and characterize the effective frequency bandwidth of tri-stable vibratory energy harvesters. To achieve this goal, the method of multiple scales is utilized to construct analytical solutions describing the amplitude and stability of the intra- and inter-well dynamics of the harvester. Using these solutions, critical bifurcations in the parameter’s space are identified and used to define an effective frequency bandwidth of the harvester. A piezoelectric tri-stable energy harvester consisting of a uni-morph cantilever beam is considered. Stiffness nonlinearities are introduced into the harvesters design by applying a static magnetic field near the tip of the beam. Experimental studies performed on the harvester are presented to validate some of the theoretical findings.

Nonlinear Vibrations of a Beam-Spring-Large Mass System

2017 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Large Mass ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Response Curves ◽  
Mass System ◽  
Spring System

This paper presents the nonlinear vibration of a simply supported Euler-Bernoulli beam with a mass-spring system subjected to a primary resonance excitation. The nonlinearity is due to the mid-plane stretching and cubic spring stiffness. The equations of motion and the boundary conditions are derived using Hamiltons principle. The nonlinear system of equations are solved using the method of multiple scales. Explicit expressions are obtained for the mode shapes, natural frequencies, nonlinear frequencies, and frequency response curves. The validity of the results is demonstrated via comparison with results in the literature. Exact natural frequencies are obtained for different locations, rotational inertias, and masses.

Nonlinear Vibration Absorber Design: An Asymptotic Approach

2015 ◽  
Author(s):  
Arnaldo Casalotti ◽  
Walter Lacarbonara
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Sensitivity Analyses ◽  
Vibration Absorber ◽  
Asymptotic Approach ◽  
Nonlinear Vibration Absorber ◽  
The One ◽  
Two Degree Of Freedom ◽  
Good Agreement

The one-to-one internal resonance occurring in a two-degree-of-freedom (2DOF) system composed by a damped non-linear primary structure coupled with a nonlinear vibration absorber is studied via the method of multiple scales up to higher order (i.e., the first nonlinear order beyond the internal/external resonances). The periodic response predicted by the asymptotic approach is in good agreement with the numerical results obtained via continuation of the periodic solution of the equations of motion. The asymptotic procedure lends itself to manageable sensitivity analyses and thus to versatile optimization by which different optimal tuning criteria for the vibration absorber can possibly be found in semi-closed form.

Multimode Interactions in Suspended Cables

2002 ◽  
Vol 8 (3) ◽  
pp. 337-387 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Haider N. Arafat ◽  
Char-Ming Chin ◽  
Walter Lacarbonara
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Internal Resonances ◽  
Out Of Plane ◽  
Space Formulation ◽  
Suspended Cables ◽  
One To One ◽  
Plane Mode

We investigate the nonlinear nonplanar responses of suspended cables to external excitations. The equations of motion governing such systems contain quadratic and cubic nonlinearities, which may result in two-to-one and one-to-one internal resonances. The sag-to-span ratio of the cable considered is such that the natural frequency of the first symmetric in-plane mode is at first crossover. Hence, the first symmetric in-plane mode is involved in a one-to-one internal resonance with the first antisymmetric in-plane and out-of-plane modes and, simultaneously, in a two-to-one internal resonance with the first symmetric out-of-plane mode. Under these resonance conditions, we analyze the response when the first symmetric in-plane mode is harmonically excited at primary resonance. First, we express the two governing equations of motion as four first-order (i.e., state-space formulation) partial-differential equations. Then, we directly apply the methods of multiple scales and reconstitution to determine a second-order uniform asymptotic expansion of the solution, including the modulation equations governing the dynamics of the phases and amplitudes of the interacting modes. Then, we investigate the behavior of the equilibrium and dynamic solutions as the forcing amplitude and resonance detunings are slowly varied and determine the bifurcations they may undergo.

The Influence of Nonlinear Boundary Conditions on the Nonplanar Autoparametric Responses of an Inextensible Beam

2001 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Nonlinear Behavior ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Springs ◽  
Out Of Plane

Abstract The nonplanar responses of a beam clamped at one end and restrained by nonlinear springs at the other end is investigated under a primary resonance base excitation. The beam’s geometry and the springs’ linear stiffnesses are such that the system possesses a one-to-one autoparametric resonance between the nth in-plane and out-of-plane modes. The beam is modeled using Euler-Bernoulli theory and includes cubic geometric and inertia nonlinearities. The objective is to assess the influence of the nonlinear boundary conditions on the beam’s oscillations. To this end, the method of multiple scales is directly applied to the integral-partial-differential equations of motion and associated boundary conditions. The result is a set of four nonlinear ordinary-differential equations that govern the slow dynamics of the system. Solutions of these modulation equations are then used to characterize the system’s nonlinear behavior.

Nonlinear Dynamics of Closed Spherical Shells

2005 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Haider N. Arafat
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Resonance Excitation ◽  
Internal Resonances ◽  
Spherical Shells ◽  
Linear Eigenvalue Problem ◽  
Nonlinear Responses ◽  
Nonlinear Equations Of Motion ◽  
Primary Resonance Excitation

We investigate the axisymmetric dynamics of forced closed spherical shells. The nonlinear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the possibility of the activation of two-to-one internal resonances between the different types of modes. Lastly, we examine the shell’s nonlinear responses to an axisymmetric primary-resonance excitation and analyze their bifurcations.

USING ENERGY-PHASE METHOD TO STUDY GLOBAL BIFURCATIONS AND SHILNIKOV TYPE MULTIPULSE CHAOTIC DYNAMICS FOR A NONLINEAR VIBRATION ABSORBER

2012 ◽  
Vol 22 (01) ◽  
pp. 1250001 ◽  
Author(s):  
S. B. LI ◽  
W. ZHANG ◽  
M. H. YAO
Keyword(s):  
Nonlinear Vibration ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Standard Form ◽  
Primary Resonance ◽  
Phase Method ◽  
Vibration Absorber ◽  
Global Bifurcations ◽  
Modulation Equation ◽  
Nonlinear Vibration Absorber

Global bifurcations and Shilnikov type multipulse chaotic dynamics for a nonlinear vibration absorber are investigated by using the energy-phase method for the first time. A two-degree-of-freedom model of a nonlinear vibration absorber is considered. After the nonlinear nonautonomous equations of this model are given, the method of multiple scales is used to derive four first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases of the two interacting modes in the presence of 1:1 internal resonance and primary resonance. Using several coordinate transformations to transform the modulation equation into a standard form, we can apply the energy-phase method to show the existence of the multipulse chaotic dynamics by identifying Shilnikov-type multipulse orbits in the perturbed phase space. We are able to obtain the explicit restriction on the damping, forcing excitation and the detuning parameters, under which the multipulse chaotic dynamics is expected. These multipulse orbits represent the repeated departure from purely vertical oscillations for the nonlinear vibration absorber. Numerical simulations also indicate that there exist different forms of the multipulse chaotic responses and jumping phenomena for the nonlinear vibration absorber.

scholarly journals Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach

2021 ◽  
Vol 11 (20) ◽  
pp. 9486
Author(s):  
Andrea Arena
Keyword(s):  
Nonlinear Dynamic ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Resonance Excitation ◽  
Dynamic Features ◽  
Response Curves ◽  
Internal Resonances ◽  
The Third ◽  
Fold Bifurcation

The nonlinear dynamic features of compression roller batteries were investigated together with their nonlinear response to primary resonance excitation and to internal interactions between modes. Starting from a parametric nonlinear model based on a previously developed Lagrangian formulation, asymptotic treatment of the equations of motion was first performed to characterize the nonlinearity of the lowest nonlinear normal modes of the system. They were found to be characterized by a softening nonlinearity associated with the stiffness terms. Subsequently, a direct time integration of the equations of motion was performed to compute the frequency response curves (FRCs) when the system is subjected to direct harmonic excitations causing the primary resonance of the lowest skew-symmetric mode shape. The method of multiple scales was then employed to study the bifurcation behavior and deliver closed-form expressions of the FRCs and of the loci of the fold bifurcation points, which provide the stability regions of the system. Furthermore, conditions for the onset of internal resonances between the lowest roller battery modes were found, and a 2:1 resonance between the third and first modes of the system was investigated in the case of harmonic excitation having a frequency close to the first mode and the third mode, respectively.

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