Band structure and defect states in acoustic phononic crystals using expansion and micro-perforated chamber mufflers

2021 ◽  
Vol 263 (5) ◽  
pp. 1194-1205
Author(s):  
Adriano Mitsuo Goto ◽  
Victor Gustavo Ramos Costa Dos Santos ◽  
José Maria Campos Dos Santos
Keyword(s):  
Sound Propagation ◽  
Transmission Loss ◽  
Dynamic Stiffness ◽  
Forced Response ◽  
Phononic Crystals ◽  
Defect States ◽  
Sound Control ◽  
Duct Systems ◽  
Stiffness Matrices ◽  
Periodic Arrangement

The expansion and the micro-perforated chamber mufflers are acoustic silencers designed to attenuate the sound propagation at duct systems. These silencers can show interesting phononic crystals behavior when set periodically. The concept of phononic crystals still is an emerging topic in vibration and sound control. The periodic arrangement of acoustic silencers can provide a significant enhancement of the sound absorption due to the "wave filtering" property where the wave cannot propagate at certain frequency ranges, called stopbands or bandgaps. However, these properties may be affected by defects, like the break of the periodicity due to manufacturing errors. For the present work, the influence of some defects on the acoustic efficiency is investigated numerically for expansion and micro-perforated chamber mufflers. A direct and efficient approach is used to obtain the transfer and dynamic stiffness matrices. Simulated examples are used to calculate the forced response, transmission loss, and dispersion diagram, which are verified by other methods.

Flow-dependent modeling of acoustic propagation based on DG-FEM method

2021 ◽  
Author(s):  
Zichen Wang ◽  
Jian Xu ◽  
Xuefeng Zhang ◽  
Can Lu ◽  
Kangkang Jin ◽  
...  
Keyword(s):  
Sound Propagation ◽  
Transmission Loss ◽  
Acoustic Propagation ◽  
Water Area ◽  
Current Speed ◽  
Propagation Model ◽  
Propagation Loss ◽  
Two Dimensional ◽  
Underwater Sound ◽  
Ocean Environment

AbstractThis paper proposes a two-dimensional underwater sound propagation model using the Discontinuous Galerkin Finite Element Method (DG-FEM) to investigate the influence of current on sound propagation. The acoustic field is calculated by the convected wave equation with the current speed parameter. Based on the current speed data from an assimilation model, a two-dimensional coupled acoustic propagation model in the Fram Strait water area is established to observe the variability in propagation loss under different seasonal velocities in the real ocean environment. The transmission loss and signal time structure are examined. The results obtained in different source frequencies are also compared. It appears that the current velocity, time and range variation all have an effect on underwater sound propagation.

A New Finding on the Dynamic Stiffness Matrices of Asymmetric and Axisymmetric Shafts

2001 ◽  
Author(s):  
Francesco A. Raffa ◽  
Furio Vatta
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Rotational Inertia ◽  
Dynamic Stiffness Matrix ◽  
Rayleigh Beam ◽  
Principal Moments Of Inertia ◽  
Stiffness Matrices ◽  
New Finding

Abstract In this paper the dynamic stiffness method is developed to analyze a rotating asymmetric shaft, i.e. a shaft whose transverse section is characterized by dissimilar principal moments of inertia. The shaft is modeled according to the Rayleigh beam theory including the effects of both translational and rotational inertia, and gyroscopic moments. The mathematical description is carried out in a reference system rotating at the shaft speed and is based on the exact solution of the governing differential equations of motion. The exact expressions of the shaft displacements are utilized for deriving the 8 × 8 complex dynamic stiffness matrix of the shaft. A new relationship is obtained which links the dynamic stiffness matrix of the asymmetric shaft to the 4 × 4 real dynamic stiffness matrix of the axisymmetric shaft.

Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain

2019 ◽  
Vol 19 (09) ◽  
pp. 1950106 ◽  
Author(s):  
Zejun Han ◽  
Mi Zhou ◽  
Xiaowen Zhou ◽  
Linqing Yang
Keyword(s):  
Dynamic Response ◽  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Stiffness ◽  
Dynamic Responses ◽  
Rigid Foundation ◽  
Layered Soils ◽  
Stiffness Matrices ◽  
The Time Domain ◽  
Arbitrary Shapes

Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

A numerical method for static and free-vibration analysis of non-uniform Timoshenko beam–columns

2006 ◽  
Vol 33 (3) ◽  
pp. 278-293 ◽  
Author(s):  
Z Canan Girgin ◽  
Konuralp Girgin
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Beam Columns ◽  
Geometrical Properties ◽  
Stiffness Matrices

A generalized numerical method is proposed to derive the static and dynamic stiffness matrices and to handle the nodal load vector for static analysis of non-uniform Timoshenko beam–columns under several effects. This method presents a unified approach based on effective utilization of the Mohr method and focuses on the following arbitrarily variable characteristics: geometrical properties, bending and shear deformations, transverse and rotatory inertia of mass, distributed and (or) concentrated axial and (or) transverse loads, and Winkler foundation modulus and shear foundation modulus. A successive iterative algorithm is developed to comprise all these characteristics systematically. The algorithm enables a non-uniform Timoshenko beam–column to be regarded as a substructure. This provides an important advantage to incorporate all the variable characteristics based on the substructure. The buckling load and fundamental natural frequency of a substructure subjected to the cited effects are also assessed. Numerical examples confirm the efficiency of the numerical method.Key words: non-uniform, Timoshenko, substructure, elastic foundation, geometrical nonlinearity, stiffness, stability, free vibration.

scholarly journals Exact and Direct Modeling Technique for Rotor-Bearing Systems with Arbitrary Selected Degrees-of-Freedom

1994 ◽  
Vol 1 (6) ◽  
pp. 497-506 ◽  
Author(s):  
Shilin Chen ◽  
Michel Géradin
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Modeling Technique ◽  
Dynamic Stiffness Matrix ◽  
Global Dynamic ◽  
Combination Methods ◽  
Stiffness Matrices ◽  
Direct Modeling ◽  
Rotor Bearing

An exact and direct modeling technique is proposed for modeling of rotor-bearing systems with arbitrary selected degrees-of-freedom. This technique is based on the combination of the transfer and dynamic stiffness matrices. The technique differs from the usual combination methods in that the global dynamic stiffness matrix for the system or the subsystem is obtained directly by rearranging the corresponding global transfer matrix. Therefore, the dimension of the global dynamic stiffness matrix is independent of the number of the elements or the substructures. In order to show the simplicity and efficiency of the method, two numerical examples are given.

Derivation of New Transcendental Member Stiffness Determinant for Vibrating Frames

2003 ◽  
Vol 03 (02) ◽  
pp. 299-305 ◽  
Author(s):  
F. W. Williams ◽  
D. Kennedy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Infinite Order ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Structural Stiffness ◽  
Trial And Error ◽  
Stiffness Matrices ◽  
Vibration Problems

Transcendental dynamic member stiffness matrices for vibration problems arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretization errors. Assembling them into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or their squares) are found with certainty using the Wittrick–Williams algorithm. This paper gives equations for the recently discovered transcendental member stiffness determinant, which equals the appropriately normalized FEM dynamic stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall transcendental stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. The present paper gives the first ever derivation of the Bernoulli–Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

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