Optimum tuning of damped side-branch silencer using equivalent discrete model and considering open-end correction

Yamada, Keisuke; Shimizu, Tatsuya; Utsuno, Hideo; Kurata, Junichi; Murakami, Yoshihiro

doi:10.1299/mej.20-00417

Cited by 2 publications

(1 citation statement)

References 10 publications

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“…where f is the natural frequency ratio, γ is the characteristic impedance ratio, h ω is the natural angular frequency of the targeted acoustic mode of the host acoustic field, and s ω is the natural angular frequency of the Helmholtz silencer, considering the effect of the residual acoustic modes of the host acoustic field and cavity of the Helmholtz silencer. The simplified equivalent discrete model and transfer functions p G and v G are identical to those obtained in the study of the damped side branch silencer (Yamada et al, 2021). Therefore, the optimum natural frequency ratio and optimum loss factor can be derived in the same manner.…”

Section: Optimum Tuning Using Two Fixed Point Methodsmentioning

confidence: 89%

Optimum tuning of damped Helmholtz silencer using an equivalent discrete model and considering open-end correction

Yamada

Shimizu

Utsuno

et al. 2021

Mechanical Engineering Journal

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This paper describes the optimum tuning of damped Helmholtz silencers. In this study, Helmholtz resonators are used as silencers that suppress acoustic resonance in host acoustic fields. Side branch silencers and Helmholtz silencers are commonly known as a type of vibration absorber; however, damped silencers have not been thoroughly studied thus far. Therefore, prior to this paper, we reported the optimum tuning of damped side branch silencers using modal analysis and two fixed point method. In this paper, we additionally describe the optimum tuning of damped Helmholtz silencers in a similar fashion as in our previous paper. The resonance mechanism of Helmholtz silencers is different from that of side branch silencers. The coupled vibration between the host acoustic field and Helmholtz silencer was theoretically analyzed using modal analysis in this study. An equivalent discrete model was obtained using the equations of motion using modal coordinate systems. Using the equivalent discrete model, the open-end correction of the neck of the Helmholtz silencer was considered, and the number of degrees of freedom of the equivalent discrete model was reduced to two to derive optimum tuning conditions using the two fixed point method. The optimum natural frequency ratio and loss factor of the Helmholtz silencer were derived using the vibration model with two degrees of freedom. The theoretical analysis was validated through simulations and experiments.

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Section: Optimum Tuning Using Two Fixed Point Methodsmentioning

confidence: 89%

Optimum tuning of damped Helmholtz silencer using an equivalent discrete model and considering open-end correction

Yamada

Shimizu

Utsuno

et al. 2021

Mechanical Engineering Journal

Self Cite

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Substructure elimination method for vibration systems governed by a one-dimensional wave equation

YAMADA,

2023

Mechanical Engineering Journal

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This paper presents a vibration analysis using the substructure elimination method for vibration systems governed by a one-dimensional wave equation. The utilization of a one-dimensional continuous body serves as a suitable approach for understanding the fundamental aspects of physical phenomena. Consequently, the significance of one-dimensional computer-aided engineering has witnessed a noticeable upsurge in recent years. The vibration analysis of continuous bodies through modal analysis is effective for reducing the degrees of freedom (DOFs). In addition, modal analysis of continuous bodies using the substructure elimination method can reduce the DOFs further, compared with modal analysis using the substructure synthesis method. However, the substructure elimination method was reported only briefly by the first author, and several problems remained. Focusing on continuous bodies governed by one-dimensional wave equations, this study aimed to address the aforementioned problems by devising solutions and establishing criteria for the effective utilization of the substructure elimination method. As a versatile method for setting arbitrary boundary conditions, a new formulation method based on constraint conditions was proposed. In addition, appropriate material properties of the elimination regions and highest order of the eigenmode were determined through a simulation-based investigation. The effectiveness of the substructure elimination method was verified by comparing the simulation results obtained using the substructure elimination method and exact solutions obtained using the boundary conditions. To investigate the advantage of low DOFs, the simulation results obtained using the substructure elimination method were also compared with those obtained using the substructure synthesis method. As an example, in a simulation of a 0.85 m one-dimensional acoustic field with a non-reflective boundary, highly precise results were obtained below 1200 Hz using 15 DOFs and the substructure elimination method.

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Optimum tuning of damped side-branch silencer using equivalent discrete model and considering open-end correction

Cited by 2 publications

References 10 publications

Optimum tuning of damped Helmholtz silencer using an equivalent discrete model and considering open-end correction

Optimum tuning of damped Helmholtz silencer using an equivalent discrete model and considering open-end correction

Substructure elimination method for vibration systems governed by a one-dimensional wave equation

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