Sommerfeld effect in a single-DOF system with base excitation from motor driven mechanism

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

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

Journal of Vibration and Control ◽

10.1177/10775463211012877 ◽

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.

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Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

10.21203/rs.3.rs-527826/v1 ◽

2021 ◽

Author(s):

K. Zhou ◽

H.R. Yi ◽

Huliang Dai ◽

H Yan ◽

Z.L. Guo ◽

...

Keyword(s):

Theoretical Model ◽

Flow Velocity ◽

Absolute Nodal Coordinate Formulation ◽

Strong Relationship ◽

Excitation Amplitude ◽

Pipe Conveying Fluid ◽

Base Excitation ◽

Absolute Nodal Coordinate ◽

Nonlinear Behaviors ◽

Conveying Fluid

Abstract By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of the cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability, and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that the period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

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Dynamic Analysis of a Protein-Ligand Molecular Chain Attached to an Atomic Force Microscope

Journal of Vibration and Acoustics ◽

10.1115/1.1804999 ◽

2004 ◽

Vol 126 (4) ◽

pp. 496-513 ◽

Cited By ~ 1

Author(s):

Deman Tang ◽

Earl H. Dowell

Keyword(s):

Nonlinear Systems ◽

Atomic Force Microscope ◽

Reduced Order Model ◽

Molecular Chain ◽

Static Equilibrium ◽

Reduced Order Models ◽

Base Excitation ◽

Order Model ◽

Reduced Order ◽

Atomic Force

Dynamic numerical simulation of a protein-ligand molecular chain connected to a moving atomic force microscope (AFM) has been studied. A sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. A comparison between results for a single molecule and those for multiple molecules has been made. For a small number of molecules, multiple stable static equilibrium positions are observed and chaotic behavior may be generated via a period-doubling cascade for harmonic base excitation of the AFM. For many molecules in the chain, only a single static equilibrium position exists. To enable these calculations, reduced-order (dynamic) models are constructed for fully linear, combined linear/nonlinear and fully nonlinear systems. Several distinct reduced-order models have been developed that offer the option of increased computational efficiency at the price of greater effort to construct the particular reduced-order model. The agreement between the original and reduced-order models (ROM) is very good even when only one mode is included in the ROM for either the fully linear or combined linear/nonlinear systems provided the excitation frequency is lower than the fundamental natural frequency of the linear system. The computational advantage of the reduced-order model is clear from the results presented.

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