Analytical and Experimental Investigation on Sound Transmission of Double Thin Plates with Magnetic Negative Stiffness

2018 ◽  
Vol 10 (05) ◽  
pp. 1850054 ◽  
Author(s):  
Akintoye Olumide Oyelade ◽  
Yi Chen ◽  
Ruojun Zhang ◽  
Gengkai Hu
Keyword(s):  
Finite Element ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Interaction Force ◽  
Negative Stiffness ◽  
Thin Plates ◽  
Acoustic Metamaterials ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Wave Condition

Transmission loss of acoustic metamaterials (AM) made of double thin plates with magnetic (negative) stiffness was analyzed using theory, finite element analysis and experimental techniques. The theoretical formulation was done using a rectangular duct below the first cut off frequency, the model is then validated against finite element method and experiment. Two cubic magnets were used, their interaction force and the resulted magnetic stiffness were calculated. The sound transmission loss (STL) of the structure is calculated for plane wave condition, the addition of magnetic mass shifts STL peaks to the lower frequency compared to a structure without mass. The slight increase in STL for small negative stiffness in experiment is not enough to cancel the effect of air compressibility. However, a significant enhancement could be expected if negative stiffness can be made large enough in the double thin plates. The developed AM can be employed as a prospective sound engineering control at low frequency.

A FINITE ELEMENT PLATE FORMULATION FOR THE ACOUSTICAL INVESTIGATION OF THIN AIR LAYERS

2013 ◽  
Vol 21 (04) ◽  
pp. 1350014 ◽  
Author(s):  
PING RONG ◽  
OTTO VON ESTORFF ◽  
LORIS NAGLER ◽  
MARTIN SCHANZ
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Transmission Loss ◽  
Fluid Layer ◽  
Single Layer ◽  
Shell Element ◽  
Thin Plates ◽  
Element Analysis ◽  
Shell Elements ◽  
Double Wall

Double wall systems consisting of thin plates separated by an air gap are common light-weighted wall structures with high transmission loss. Generally, these plate-like structures are modeled in a finite element analysis with shell elements and volume elements for the air (fluid) layer. An alternative approach is presented in this paper, using shell elements for the air layer as well. First, the element stiffness matrix is obtained by removing the thickness dependence of the variational form of the Helmholtz equation by use of a power series. Second, the coupling between the acoustical shell element and the elastic structure is described. To verify the new shell element, a simple double wall system is considered. Comparing the predicted sound field with the results from a commercial FE software (with a single layer of volume elements) a very good agreement is observed. At the same time, employing the new elements with a third-order power series (4 DOFs per node), the calculation time is reduced.

Dual Representation Methods for Efficient and Automatable Analysis of 3D Plates

2010 ◽  
Vol 10 (4) ◽  
Author(s):  
Vikalp Mishra ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Computer Aided Design ◽  
Dimensional Space ◽  
Reduction Process ◽  
Thin Plates ◽  
Design Environment ◽  
Element Analysis ◽  
Cross Sectional ◽  
Dual Representation ◽  
3D Finite Element

It is well recognized that 3D finite element analysis is inappropriate for analyzing thin structures such as plates and shells. Instead, a variety of highly efficient and specialized 2D methods have been developed for analyzing such structures. However, 2D methods pose serious automation challenges in today’s 3D design environment. Specifically, analysts must manually extract cross-sectional properties from a 3D computer aided design (CAD) model and import them into a 2D environment for analysis. In this paper, we propose two efficient yet easily automatable dual representation methods for analyzing thin plates. The first method exploits standard off-the-shelf 3D finite element packages and achieves high computational efficiency through an algebraic reduction process. In the reduction process, a 3D plate bending stiffness matrix is constructed from a 3D mesh and then projected onto a lower-dimensional space by appealing to standard 2D plate theories. In the second method, the analysis is carried out by integrating 2D shape functions over the boundary of the 3D plate. Both methods do not entail extraction of the cross-sectional properties of the plate. However, the user must identify the plate or thickness direction. The proposed methodologies are substantiated through numerical experiments.

Sound Barrier Applications of Recycled Plastics

1998 ◽  
Vol 1626 (1) ◽  
pp. 85-92 ◽  
Author(s):  
M. Ala Saadeghvaziri ◽  
Keith Macbain
Keyword(s):  
Finite Element ◽  
Analytical Model ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Finite Element Analyses ◽  
Sound Barrier ◽  
Recycled Plastics ◽  
Material Tests

An innovative noise wall design that uses recycled plastic and takes advantage of multilayering to increase stiffness and sound effectiveness is proposed and analyzed. Prototypes of the proposed design were constructed and tested for sound transmission to determine their effectiveness and show the desirability of a multilayered approach. The results show that, acoustically, the transmission loss of the proposed design is as effective as traditional designs. Furthermore, finite element analyses as well as an analytical model developed specifically for recycled plastics indicate that, structurally, the proposed design can increase spans between posts resulting in a design that is potentially more economical than current designs. Results of material tests conducted in support of the analytical model and noise wall development are also discussed.

scholarly journals Elastic buckling of thin plate with circular holes in bending

2019 ◽  
Vol 136 ◽  
pp. 04043
Author(s):  
Guo Yanli ◽  
Song Xiaoqing ◽  
Li Xiao ◽  
Yao Xingyou ◽  
Xia Zhifan ◽  
...  
Keyword(s):  
Finite Element ◽  
Perforated Plate ◽  
Thickness Ratio ◽  
Thin Plates ◽  
Elastic Buckling ◽  
Buckling Mode ◽  
Element Analysis ◽  
Short Side ◽  
Finite Element Software ◽  
Circular Holes

Stress redistribution will occur around the hole for the perforated plate under bending, and the buckling mode of bending plate is changed, which makes the design of bending plate more complicated. The finite element software ABAQUS is used to establish the perforated plate under bending model, analyze the degree of influence of the plate aspect ratio, width-thickness ratio, size and position of the holes, meanwhile, the distance between holes is also discussed. The results show that the thickness of the plate size and width-thickness ratio have little influence on the elastic buckling performance of thin plates with holes in bending. As the size of the holes increase, the influence is greater, and there is a certain regularity. The opening position is closer to the short side of the plate, the buckling coefficient of plate will be significantly decreased. The effect is greater with the increase of opening size, the distance between holes have a safe value, the position of the opening is more obvious for the buckling of the bending plate. Finally, based on the data from finite element analysis, the proposed formula of buckling stability coefficient k for the bending perforated plate is given.

On the comprehensive static characteristic analysis of a translational bistable mechanism

2016 ◽  
Vol 230 (20) ◽  
pp. 3803-3817 ◽  
Author(s):  
Guangbo Hao ◽  
John Mullins
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Negative Stiffness ◽  
Beam Length ◽  
Rotational Stiffness ◽  
Characteristic Analysis ◽  
Element Analysis ◽  
Primary Motion ◽  
Bistable Mechanism ◽  
Inclined Angle

Bistable mechanisms have two stable positions and their characteristic analysis is much harder than the traditional spring system due to their postbuckling behaviour. As the strong nonlinearity induced by the postbuckling, it is difficult to establish a correct model to reveal the comprehensive nonlinear characteristics. This paper deals with the in-plane comprehensive static analysis of a translational bistable mechanism using nonlinear finite element analysis. The bistable mechanism consists of a pair of fixed-clamped inclined beams in symmetrical arrangement, which is a monolithic design and works within the elastic deformation domain. The displacement-controlled finite element analysis method using Strand7 is first discussed. Then the force–displacement relation of the bistable mechanism along the primary motion direction is described followed by the detailed primary translational analysis for different parameters. A simple analytical (empirical) equation for estimating the negative stiffness is obtained, and experimental testing is performed for a case study. It is concluded that (a) the negative stiffness magnitude has no influence from the inclined angle, but is proportional to the product of the Young’s modulus, beam depth, and cubic ratio for in-plane thickness to the beam length; (b) the unstable position is proportional to the product of the beam length and the Sine function of the inclined angle, and is not affected by the in-plane thickness and the material (or the out-of-plane thickness). The in-plane off-axis (translational and rotational) stiffness is further analysed to show the stiffness changes over the primary motion and the off-axis motion, and a negative rotational stiffness domain has been obtained.

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