Analytical Model for Low-Frequency Transmission Loss Calculation of Zero-Prestressed Plates With Arbitrary Mass Loading

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
William T. Edwards ◽  
Chia-Ming Chang ◽  
Geoffrey McKnight ◽  
Steven R. Nutt
Keyword(s):  
Boundary Conditions ◽  
Analytical Model ◽  
Transmission Loss ◽  
Mass Density ◽  
Low Frequency ◽  
Sound Attenuation ◽  
Mode Shapes ◽  
Natural Mode ◽  
Rectangular Plates ◽  
Acoustic Metamaterials

As the importance of sound attenuation through weight-critical structures has grown and mass law based strategies have proven impractical, engineers have pursued alternative approaches for sound attenuation. Membrane-type acoustic metamaterials have demonstrated sound attenuation significantly higher than mass law predictions for narrow, tunable bandwidths. Similar phenomena can be achieved with plate-like structures. This paper presents an analytical model for the prediction of transmission loss through rectangular plates arbitrarily loaded with rigid masses, accommodating any combination of clamped and simply supported boundary conditions. Equations of motion are solved using a modal expansion approach, incorporating admissible eigenfunctions given by the natural mode shapes of single-span beams. The effective surface mass density is calculated and used to predict the transmission loss of low-frequency sound through the plate–mass structure. To validate the model, finite element results are compared against analytical predictions of modal behavior and shown to achieve agreement. The model is then used to explore the influence of various combinations of boundary conditions on the transmission loss properties of the structure, revealing that the symmetry of plate mounting conditions strongly affects transmission loss behavior and is a critical design parameter.

scholarly journals Low-Frequency Bandgaps of the Lightweight Single-Phase Acoustic Metamaterials with Locally Resonant Archimedean Spirals

Materials ◽  
2022 ◽  
Vol 15 (1) ◽  
pp. 373
Author(s):  
Haoqiang Gao ◽  
Qun Yan ◽  
Xusheng Liu ◽  
Ying Zhang ◽  
Yongtao Sun ◽  
...  
Keyword(s):  
Single Phase ◽  
Transmission Loss ◽  
Low Cost ◽  
Low Frequency ◽  
Mode Shapes ◽  
Frequency Noise ◽  
Acoustic Metamaterials ◽  
Acceleration Sensors ◽  
Attenuation Mechanism ◽  
Control Equation

In order to achieve the dual needs of single-phase vibration reduction and lightweight, a square honeycomb acoustic metamaterials with local resonant Archimedean spirals (SHAMLRAS) is proposed. The independent geometry parameters of SHAMLRAS structures are acquired by changing the spiral control equation. The mechanism of low-frequency bandgap generation and the directional attenuation mechanism of in-plane elastic waves are both explored through mode shapes, dispersion surfaces, and group velocities. Meanwhile, the effect of the spiral arrangement and the adjustment of the equation parameters on the width and position of the low-frequency bandgap are discussed separately. In addition, a rational period design of the SHAMLRAS plate structure is used to analyze the filtering performance with transmission loss experiments and numerical simulations. The results show that the design of acoustic metamaterials with multiple Archimedean spirals has good local resonance properties, and forms multiple low-frequency bandgaps below 500 Hz by reasonable parameter control. The spectrograms calculated from the excitation and response data of acceleration sensors are found to be in good agreement with the band structure. The work provides effective design ideas and a low-cost solution for low-frequency noise and vibration control in the aeronautic and astronautic industries.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Hydroelastic Vibration of Rectangular Plates

1996 ◽  
Vol 63 (1) ◽  
pp. 110-115 ◽  
Author(s):  
Moon K. Kwak
Keyword(s):  
Boundary Conditions ◽  
Approximate Formula ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Ritz Method ◽  
Plate Boundary ◽  
Rigid Wall ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Virtual Mass

This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

Development of Hybrid Semi-Analytical and Finite Element Analysis to Calculate Sound Radiation from Vibrating Structure

2013 ◽  
Vol 845 ◽  
pp. 71-75 ◽  
Author(s):  
Azma Putra ◽  
Nurain Shyafina ◽  
Noryani Muhammad ◽  
Hairul Bakri ◽  
Noor Fariza Saari
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Analytical Model ◽  
Complex Geometry ◽  
Sound Radiation ◽  
Vibration Velocity ◽  
Rectangular Plates ◽  
Element Analysis

Simple analytical model of plate dynamics usually applies for rectangular plate with simply supported edges. Analytical model of sound radiation from rectangular plate is also convenient, but not for other geometries and other boundary conditions. This paper presents a hybrid mathematical model which combines a semi-analytical model with the Finite Element Analysis (FEA) method to determine sound radiation from a vibrating structure. The latter is employed to calculate the vibration velocity of a structure with a rather complex geometry. The results are then used as the input in the semi-analytical model to calculate the radiated sound pressure through the Rayleigh integral. Results from the proposed model are presented here for the radiation efficiency of rectangular plates with different boundary conditions.

Broadband fractal acoustic metamaterials for low-frequency sound attenuation

2016 ◽  
Vol 109 (13) ◽  
pp. 131901 ◽  
Author(s):  
Gang Yong Song ◽  
Qiang Cheng ◽  
Bei Huang ◽  
Hui Yuan Dong ◽  
Tie Jun Cui
Keyword(s):  
Low Frequency ◽  
Sound Attenuation ◽  
Acoustic Metamaterials ◽  
Frequency Sound

Multi-cavity coupling acoustic metamaterials with low-frequency broad band gaps based on negative mass density

2016 ◽  
Vol 30 (23) ◽  
pp. 1650317
Author(s):  
Chuanhui Yang ◽  
Jiu Hui Wu ◽  
Songhua Cao ◽  
Li Jing
Keyword(s):  
Band Gap ◽  
Mass Density ◽  
Resonant Cavity ◽  
Broad Band ◽  
Low Frequency ◽  
Band Gaps ◽  
Acoustic Metamaterials ◽  
Negative Mass ◽  
Closed Cavity ◽  
Cavity Coupling

This paper studies a novel kind of low-frequency broadband acoustic metamaterials with small size based on the mechanisms of negative mass density and multi-cavity coupling. The structure consists of a closed resonant cavity and an open resonant cavity, which can be equivalent to a homogeneous medium with effective negative mass density in a certain frequency range by using the parameter inversion method. The negative mass density makes the anti-resonance area increased, which results in broadened band gaps greatly. Owing to the multi-cavity coupling mechanism, the local resonances of the lower frequency mainly occur in the closed cavity, while the local resonances of the higher frequency mainly in the open cavity. Upon the interaction between the negative mass density and the multi-cavity coupling, there exists two broad band gaps in the range of 0–1800 Hz, i.e. the first-order band gap from 195 Hz to 660 Hz with the bandwidth of 465 Hz and the second-order band gap from 1157 Hz to 1663 Hz with the bandwidth of 506 Hz. The acoustic metamaterials with small size presented in this paper could provide a new approach to reduce the low-frequency broadband noises.

An exact solution for free vibration of thin functionally graded rectangular plates

2010 ◽  
Vol 225 (3) ◽  
pp. 526-536 ◽  
Author(s):  
A Hasani Baferani ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Different Boundary Conditions

The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been shown that the effects of in-plane displacements on natural frequencies of functionally graded plates under different boundary conditions have been studied.

scholarly journals An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

2017 ◽  
Vol 61 (4) ◽  
pp. 309 ◽  
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Mass Density ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Multiwalled Carbon ◽  
Simply Supported ◽  
Pasternak Model ◽  
Multi Walled Carbon Nanotubes

In the present work, vibration characteristics of functionally graded (FG) sandwich rectangular plates reinforced by multiwalled carbon nanotubes (MWCNTs) resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation is used to evaluate the Young’s modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The mass density and Poisson’s ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. The proposed sandwich rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the sandwich plates are investigated.

scholarly journals Sound Attenuation of Membranes Loaded with Square Frame-Shaped Masses

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
J. S. Chen ◽  
D. W. Kao
Keyword(s):  
Effective Mass ◽  
Sound Wave ◽  
Present Model ◽  
Transmission Loss ◽  
Mass Density ◽  
Sound Attenuation ◽  
Loss Peak ◽  
In Series ◽  
Thin Membranes ◽  
Multiple Transmission

This study examines sound transmission of thin membranes with square frame-shaped masses. Numerical results indicate that multiple transmission loss peaks can be generated by adding more frame mass inclusions. The number and the location of the peaks are controlled by the number of frames, the frame distribution, and the frame width. Near the transmission loss peak frequencies, the dynamic effective mass density turns from positive to negative. The validity of the present model has been verified by comparing the analytical results with FE results. Two types of cell arrangements are also considered in this study, namely, cells in series and cells in array. It is seen that either the stacked or array configurations can produce better sound attenuation than single-celled structures. Moreover, the frequency band where sound wave is blocked can be broadened by stacking more layers with different mass magnitudes. Furthermore, additional frequency bands due to the periodicity of the structure are found in the stacked configurations.

Sign in / Sign up

Export Citation Format

Share Document