Smoothed boundary conditions for low‐frequency coherent scatter

The low-frequency vibration and radiation performance of a locally resonant (LR) plate with periodic multiple resonators is studied in this paper, with both infinite and finite structure properties examined. For the finite cases, taking the LR plate attached with two periodic arrays of resonators as an example, the forced vibration response and the radiation efficiency are theoretically derived by adopting a general model with elastic boundary conditions. Through a comparison with the band structures calculated by the plane-wave-expansion method, it shows that the band gaps in the infinite LR plate are in good agreement with the vibration-attenuation bands in the finite LR plate, no matter what boundary conditions are applied to the latter. In contrast to the vibration reduction in the band gaps, the radiation efficiency of the finite LR plate is sharply increased in the band-gap frequency ranges. Furthermore, the acoustic power radiated from the finite LR plate can be seriously affected by its boundary conditions. For the LR plate with greater constraints, the acoustic power is reduced in the band-gap frequency ranges, while that from the one with fully free boundary conditions is increased. When further considering the damping loss factors of the resonators, the attenuation performance can be improved for both the vibration and radiation of the LR plate.

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Use of experimental dynamic substructuring to predict the low frequency structural dynamics under different boundary conditions

Mathematics and Mechanics of Solids ◽

10.1177/1081286517727147 ◽

2017 ◽

Vol 23 (11) ◽

pp. 1444-1455

Author(s):

Walter D’Ambrogio ◽

Annalisa Fregolent

Keyword(s):

Boundary Conditions ◽

Rigid Body ◽

Frequency Response ◽

Response Function ◽

Frequency Response Function ◽

Low Frequency ◽

Response Functions ◽

Frequency Response Functions ◽

Different Boundary Conditions ◽

Rigid Body Modes

Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low frequency dynamics of the free-free structure. To overcome this problem, substructure decoupling can be used, that allows us to identify the dynamics of a substructure (i.e. the free-free structure) after measuring the frequency response functions on the complete structure (i.e. the structure plus the supports) and from a dynamic model of the residual substructure (i.e. the supporting structure). Subsequently, the effect of additional boundary conditions can be predicted using a frequency response function condensation technique. The procedure is tested on a reduced scale model of a space solar panel.

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

Journal of Vibration and Acoustics ◽

10.1115/1.4042927 ◽

2019 ◽

Vol 141 (4) ◽

Cited By ~ 1

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.

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Can Bias Correction of Regional Climate Model Lateral Boundary Conditions Improve Low-Frequency Rainfall Variability?

Journal of Climate ◽

10.1175/jcli-d-16-0654.1 ◽

2017 ◽

Vol 30 (24) ◽

pp. 9785-9806 ◽

Cited By ~ 22

Author(s):

Eytan Rocheta ◽

Jason P. Evans ◽

Ashish Sharma

Keyword(s):

Boundary Conditions ◽

Regional Climate Model ◽

Bias Correction ◽

Climate Model ◽

Regional Climate ◽

Low Frequency ◽

Lateral Boundary ◽

Model Simulations ◽

Low Frequency Variability ◽

Climate Model Simulations

Global climate model simulations inherently contain multiple biases that, when used as boundary conditions for regional climate models, have the potential to produce poor downscaled simulations. Removing these biases before downscaling can potentially improve regional climate change impact assessment. In particular, reducing the low-frequency variability biases in atmospheric variables as well as modeled rainfall is important for hydrological impact assessment, predominantly for the improved simulation of floods and droughts. The impact of this bias in the lateral boundary conditions driving the dynamical downscaling has not been explored before. Here the use of three approaches for correcting the lateral boundary biases including mean, variance, and modification of sample moments through the use of a nested bias correction (NBC) method that corrects for low-frequency variability bias is investigated. These corrections are implemented at the 6-hourly time scale on the global climate model simulations to drive a regional climate model over the Australian Coordinated Regional Climate Downscaling Experiment (CORDEX) domain. The results show that the most substantial improvement in low-frequency variability after bias correction is obtained from modifying the mean field, with smaller changes attributed to the variance. Explicitly modifying monthly and annual lag-1 autocorrelations through NBC does not substantially improve low-frequency variability attributes of simulated precipitation in the regional model over a simpler mean bias correction. These results raise questions about the nature of bias correction techniques that are required to successfully gain improvement in regional climate model simulations and show that more complicated techniques do not necessarily lead to more skillful simulation.

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An Optimization Method for Maximizing the Low Frequency Sound Insulation of Plate Structures

Shock and Vibration ◽

10.1155/2018/7849327 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Dayi Ou

Keyword(s):

Genetic Algorithm ◽

Boundary Conditions ◽

Low Frequency ◽

Sound Transmission ◽

Sound Insulation ◽

Plate Structures ◽

Arbitrary Boundary ◽

Frequency Sound ◽

Arbitrary Boundary Conditions ◽

Element Method

A combined approach based on finite element method, boundary element method, and genetic algorithm (FEM-BEM-GA) is proposed for optimizing the low frequency sound (LFS) insulation performance of plate structures. This approach can identify the optimal structural parameters (especially concerning the effects of arbitrary boundary conditions) so as to maximize the structural overall LFS insulation. The basic ideas of this approach are as follows: (1) the sound transmission loss (TL) analysis of a plate with arbitrary boundary conditions is conducted by the coupled FEM-BEM method; (2) the single-number rating method (such as low frequency sound transmission class) is used to assess the plate’s overall LFS insulation; and (3) the genetic algorithm (GA) is employed for searching the optimal solutions of the multiple-parameter optimization problem. The proposed approach is subsequently illustrated by numerical studies. The results show the effectiveness of consideration of the effects of boundary condition in the plate’s LFS insulation optimization and demonstrate the feasibility and effectiveness of this approach as a structure design tool.

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