scholarly journals Oscillation Phenomena of Rayleigh Equation Disturbed by Superposition of Two Harmonic Excitation

2019 ◽  
Vol 1417 ◽  
pp. 012014
Author(s):  
A Alfan ◽  
N A C Dewi
Keyword(s):  
Harmonic Excitation ◽  
Rayleigh Equation

scholarly journals Nonlinear vibration of knitted spacer fabric under harmonic excitation

2020 ◽  
Vol 15 ◽  
pp. 155892502098356
Author(s):  
Fuxing Chen ◽  
Hong Hu
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Polyurethane Foams ◽  
Excitation Level ◽  
Harmonic Amplitude ◽  
Damping Force ◽  
Spacer Fabric ◽  
Fabric System ◽  
Quadratic Stiffness

Knitted spacer fabrics can be an alternative material to typical rubber sponges and polyurethane foams for the protection of the human body from vibration exposure, such as automotive seat cushions and anti-vibration gloves. To provide a theoretical basis for the understanding of the nonlinear vibration behavior of the mass-spacer fabric system under harmonic excitation, experimental, analytical and numerical methods are used. Different from a linear mass-spring-damper vibration model, this study builds a phenomenological model with the asymmetric elastic force and the fractional derivative damping force to describe the periodic solution of the mass-spacer fabric system under harmonic excitation. Mathematical expression of the harmonic amplitude versus frequency response curve (FRC) is obtained using the harmonic balance method (HBM) to solve the equation of motion of the system. Parameter values in the model are estimated by performing curve fit between the modeled FRC and the experimental data of acceleration transmissibility. Theoretical analysis concerning the influence of varying excitation level on the FRCs is carried out, showing that nonlinear softening resonance turns into nonlinear hardening resonance with the increase of excitation level, due to the quadratic stiffness term and the cubic stiffness term in the model, respectively. The quadratic stiffness term also results in biased vibration response and causes an even order harmonic distortion. Besides, the increase of excitation level also results in elevated peak transmissibility at resonance.

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

Effects of noise and harmonic excitation on the growth of Bacillus subtilis biofilm

Biosystems ◽  
2021 ◽  
Vol 201 ◽  
pp. 104329
Author(s):  
Qiubao Wang ◽  
Xing Zhang ◽  
Yuejuan Yang
Keyword(s):  
Bacillus Subtilis ◽  
Harmonic Excitation

Multi-Stable Magnetic Spring-Based Energy Harvester Subject to Harmonic Excitation: Comparative Study and Experimental Evaluation

2018 ◽  
Author(s):  
Hieu Nguyen ◽  
Hamzeh Bardaweel
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
Comparative Study ◽  
Experimental Evaluation ◽  
Chaotic Motion ◽  
Energy Harvester ◽  
Electric Energy ◽  
Harmonic Excitation ◽  
Jump Frequency ◽  
Piezoelectric Elements

The work presented here investigates a unique design platform for multi-stable energy harvesting using only interaction between magnets. A solid cylindrical magnet is levitated between two stationary magnets. Peripheral magnets are positioned around the casing of the energy harvester to create multiple stable positions. Upon external vibration, kinetic energy is converted into electric energy that is extracted using a coil wrapped around the casing of the harvester. A prototype of the multi-stable energy harvester is fabricated. Monostable and bistable configurations are demonstrated and fully characterized in static and dynamic modes. Compared to traditional multi-stable designs the harvester introduced in this work is compact, occupies less volume, and does not require complex circuitry normally needed for multi-stable harvesters involving piezoelectric elements. At 2.5g [m/s2], results from experiment show that the bistable harvester does not outperform the monostable harvester. At this level of acceleration, the bistable harvester exhibits intrawell motion away from jump frequency. Chaotic motion is observed in the bistable harvester when excited close to jump frequency. Interwell motion that yields high displacement amplitudes and velocities is absent at this acceleration.

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

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