Lagrangian meshfree particle method for modeling acoustic wave propagation in moving fluid

Zhang, Yongou; Hou, Qing Zhi; Gong, Zhixiong; Zhang, Tao; Li, Tianyun; Wei, Jihong; Dang, Jian Wu

doi:10.1121/1.4988230

Cited by 2 publications

(3 citation statements)

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“…The cantilever oscillates back and forth and forms a hyperbolic curve with the noticeable structures that a tangent to the end of the cantilever always intersects its point along the middle axis. The corresponding Lagrangian equation is given as [26–30] shown below:

\begin{matrix} true \\ right L & = & left \frac{1}{2} m {false(L_{e} θ false)}^{2} \\ left - ({}, \frac{1}{2} k {(L_{e} θ)}^{2} - μ B \cos ((), θ - β) + k_{u} V \sin^{2} β) \end{matrix}

where m is the mass of poles in cantilever beam, V is the volume of the particle, k is the constant of the cantilever, L e is the length of the cantilever, μ is the angular momentum. The Lagrangian equation consists of two variables θ and β , and the corresponding equation for the two variables is given as:

\frac{d}{d t} \frac{\partial L}{\partial \dot{β}} = \frac{\partial L}{\partial β} = μ B \sin false(θ - β false) - 2 k_{u} V \sin β \cos β

β = \frac{B θ}{B + H_{k}}

H_{k} = \frac{2 k_{u} V}{μ}

Let, θ be the angle, and as the function of the Lagrangian equation, it is given as follows:

θ - β = \frac{θ H_{k}}{B + H_{k}}

then,

\frac{d}{d t} \frac{\partial L}{\partial \dot{θ}} = \frac{\partial L}{\partial θ}

…”

Section: Modelling and Function Of The Proposed Piezoelectric Energy ...mentioning

confidence: 99%

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Piezoelectric energy harvester converting wind aerodynamic energy into electrical energy for microelectronic application

Sitharthan

Yuvaraj

Padmanabhan

et al. 2021

IET Renewable Power Gen

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Piezoelectric Energy Harvesting Systems play a vital role in energizing microelectronic devices with the low-frequency operation. Here, a novel piezoelectric energy harvesting device has been developed for low power electronic devices. The developed Piezoelectric Energy Harvesting Systems consists of a cantilever with poles projecting outwards and the cantilevers one end is connected to the wind-catcher, and another end is connected to the torsional spring. The developed Piezoelectric Energy Harvesting Systems signifies its application in energizing microelectronic devices. The cantilever is placed inwards to the piezoelectric crystal stack. When the wind strikes, a vortex is created in the windcatcher, which oscillates the cantilever and generates stress in the piezoelectric crystal stack to develop electric energy. The output voltage obtained from the Piezoelectric Energy Harvesting Systems does not affect any input frequency of the piezoelectric crystal. The result obtained shows that the developed Piezoelectric Energy Harvesting Systems generates 120-200 eV with 2.9 × 10 16 -4.84 × 10 16 Hz frequency considering an elementary charge unit as 40 for a variable wind flow of 4-9 m/s. This research aims to develop an efficient wind-based Piezoelectric Energy Harvesting Systems for low powered microelectronic devices.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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\begin{matrix} true \\ right L & = & left \frac{1}{2} m {false(L_{e} θ false)}^{2} \\ left - ({}, \frac{1}{2} k {(L_{e} θ)}^{2} - μ B \cos ((), θ - β) + k_{u} V \sin^{2} β) \end{matrix}

\frac{d}{d t} \frac{\partial L}{\partial \dot{β}} = \frac{\partial L}{\partial β} = μ B \sin false(θ - β false) - 2 k_{u} V \sin β \cos β

β = \frac{B θ}{B + H_{k}}

H_{k} = \frac{2 k_{u} V}{μ}

Let, θ be the angle, and as the function of the Lagrangian equation, it is given as follows:

θ - β = \frac{θ H_{k}}{B + H_{k}}

then,

\frac{d}{d t} \frac{\partial L}{\partial \dot{θ}} = \frac{\partial L}{\partial θ}

…”

Section: Modelling and Function Of The Proposed Piezoelectric Energy ...mentioning

confidence: 99%

Section: Modelling and Function Of The Proposed Piezoelectric Energy ...mentioning

confidence: 99%

Piezoelectric energy harvester converting wind aerodynamic energy into electrical energy for microelectronic application

Sitharthan

Yuvaraj

Padmanabhan

et al. 2021

IET Renewable Power Gen

View full text Add to dashboard Cite

show abstract

“…Hahn [22] used the smoothed particle hydrodynamics (SPH) method to obtain the pressure disturbance. Zhang et al [23] solved the LFDE with a PCA method, namely the SPH method, to simulate the acoustic propagation in moving media, and the Doppler Effect was solved well. However, because the sound pressure magnitude is much smaller than the pressure magnitude in most engineering problems, for the DNS, a high requirement is imposed on the computational memory and accuracy.…”

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confidence: 99%

Lagrangian Meshfree Particle-based Computational Acoustics for Two-dimensional Sound Propagation and Scattering Problems

Zhang¹,

Li²,

Zhang³

2017

Preprint

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Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of using the PCA method to solve two-dimensional acoustic problems, and realize the particle representation with a hybrid meshfree and finite-difference time-domain (FDTD) method for acoustic boundary conditions at both the plane and curved surface. As a widely used Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) based on the support domain and the kernel function has developed rapidly in recent years. The traditional SPH method is easily implements parallel processing and has been applied in sound wave simulation. As a corrective method with higher accuracy than SPH, the acoustic propagation and scattering in the time domain is simulated with the corrective smoothed particle method (CSPM). Moreover, a hybrid meshfree-FDTD boundary treatment technique is utilized to represent different acoustic boundaries in the Lagrangian approach.In this boundary treatment technique, the parameter value of virtual particles is obtained with the FDTD method, which concerns truncation errors based on the Tayler series expansion. Soft, rigid, and Mur's absorbing boundary conditions are developed to simulate sound waves in finite and infinite domain. Results of modeling acoustic propagation and scattering show that CSPM is accurate and convergence with exact solutions, and different acoustic boundaries are validated to be effective in the computation.

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Lagrangian meshfree particle method for modeling acoustic wave propagation in moving fluid

Cited by 2 publications

References 0 publications

Piezoelectric energy harvester converting wind aerodynamic energy into electrical energy for microelectronic application

Piezoelectric energy harvester converting wind aerodynamic energy into electrical energy for microelectronic application

Lagrangian Meshfree Particle-based Computational Acoustics for Two-dimensional Sound Propagation and Scattering Problems

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