Double Panel Structure Research Articles

An analytical method for the vibration characteristics of double panel structures with uniform elastic boundary supports

ABSTRACT In this paper, the methods for solving the free vibration and forced vibration of double panel structures under arbitrary boundaries are studied. Based on the Mindlin plate theory, the natural boundary between plates and plates is constrained by artificial springs, and the theoretical model of the structure is derived. The displacement function of in-plane vibration and bending vibration is expressed by a modified Fourier series expansion. The effectiveness and reliability of this method are verified by a series of numerical calculations and comparison with those of the finite element method. Through the parameter analysis, it can be seen that the vibration isolation effect can be increased by properly increasing the coupling height or making the connecting plate closer to the boundary of the bottom plate. The method presented in this paper can be used in vibration absorption and structural design of such structures.

Sound transmission loss optimization of clamped double-panels

The panel cavity structure is one of the key components of the aircraft (vehicle) body and is among the main noise transmission pathways. Based on the modal superposition and Galerkin method, this paper realizes the theoretical model of sound insulation of the clamped, double-panel structure. The non-dominated sorting genetic algorithm-II (NSGA-II) is used to realize the sound insulation of the clamped double-panel structure. Through optimization, the fitting function and law of structural surface density and the optimized normal weighted sound insulation Pareto fronts were obtained. The results show that among the optimization, for the Pareto front cases, their double-panel thickness ratio h1/ h2 is relatively far away from 1, and the corresponding cavity thickness H is relatively large. The influence of boundary conditions and size effects of lightweight sound insulation optimization are also discussed. The research on the influence of boundary and size indicates that the difference in the optimal weighted sound insulation Pareto fronts corresponding to the same surface density is mostly within the 1 dB range. Both the boundary and thickness of the panel will affect the frequency STL, while the boundary conditions or structure size changed, even the total thickness of panels needs to be the same, and the structure can also have similar weighted sound transmission loss ( Rw) when the thickness ratio of the double-panel structure is chosen properly. The difference of material effects is also discussed. This research provides a method for the sound insulation optimization of clamped double-panel structures concerning the boundary and size effect.

Design optimization for broadband sound insulation by double-panel structure with a slot-type Helmholtz resonator array at low frequency range

Design optimization for broadband sound insulation by double-panel structure with a slot-type Helmholtz resonator array at low frequency range

Nonlinear vibro-acoustic analysis of a double-panel structure with an enclosure cavity

Nonlinear vibro-acoustic analysis of a double-panel structure with an enclosure cavity

Broadening Low-Frequency Band Gap of Double-Panel Structure Using Locally Resonant Sonic Crystal Comprised of Slot-Type Helmholtz Resonators

An approach is presented to form and broaden the low-frequency band gap of the double panel structure (DPS) by using a locally resonant sonic crystal (LRSC) in this work. The LRSC is made of cylindrical Helmholtz resonators arranged on square lattice. Their designs are similar to a slot-type resonator, but have different depths of slot. Elongating the slit neck inward and distributing the depths of slots produce a broad local resonant band gap at low frequencies: an average insertion loss (IL) of 10.9 dB covering 520 Hz to 1160 Hz with a LRSC of 12 cm width. Next, the effect of porous material filled into the resonators on the local resonant band gap is evaluated. It is shown that filling of porous material into the resonators decreases the height and width of the local resonant band gap. Finally, the transmission losses (TLs) through the DPS with LRSC are calculated as a function of the incident angle of the sound wave for LRSC embedded in porous material and not. The results show that the porous material can be significantly reduce the incident angle dependency of TL through the DPS with LRSC.

Relationship Between the Sound Transmission Through the Finite Double-Panel Structure with a Cylindrical Shell Array and the Vibro-Acoustic Characteristics of its Constituents

Relationship Between the Sound Transmission Through the Finite Double-Panel Structure with a Cylindrical Shell Array and the Vibro-Acoustic Characteristics of its Constituents

Double Panel Structure for Active Control of Noise Transmission

Passive noise reduction means are commonly used to reduce noise in the industry but, unfortunately, their effectiveness is poor in the low frequency range. By applying active structural acoustic control to the enclosure walls significant improvement of the insulating properties in this frequency range can be achieved. In this paper a model of double panel structure with ASAC is presented. The structure consists of two aluminium plates separated by an air gap. Two inertial magnetoelectric actuators and two piezoceramic MFC sensors were used for controlling the structure. A multichannel FxLMS algorithm with virtual error microphone technique is used as a control algorithm. The signal of a virtual error microphone is extrapolated basing on signals from MFC sensors. Performance of this actively controlled structure for tonal signals at selected frequencies is presented in the article. During the study, a double panel structure was mounted on one wall of sound insulating enclosure located in an acoustic chamber. During the measurements local and global reduction of noise test signal was investigated.

Wave Propagation in a LRPC Composite Double Panel Structure with Periodically Attached Pillars and Etched Holes

The locally resonant phononic crystal (LRPC) composite double panel structure (DPS) made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower composite plates is proposed. The plates are composed of two kinds of materials and periodically etched holes. In order to reveal the bandgap properties of structure theoretically, the band structures, displacement fields of eigenmodes and transmission power spectrums of corresponding 8 × 8 finite structure are calculated and displayed by using finite element method (FEM). Numerical results and further analysis demonstrate that if the excitation and response points are picked on different sides of the structure, a wide band gap with low starting frequency is opened, which can be treated as the coupling between dominant vibrations of pillars and plate modes. In addition, the influences of filled-in rubber, etched hole and viscidity of soft material on band gap are studied and understood with the help of “base-spring-mass” simplified model.

Influence of Double-Panel Structure Modification on Vibroacoustical Properties of a Rigid Device Casing

Nowadays, noise generated by devices is a serious issue in industry and in everyday life, because it may cause health damage to humans. In this research, a cubic rigid device casing built of double-panel thin steel walls is employed to reduce noise emitted from an enclosed noise source. Double-panel structure is used because of good sound insulation it provides. There exist three main groups of noise reduction methods, i.e. passive, semi-active and active. In this paper, a semi-active modification of double-panel structure is applied and examined. The bistable actuator (solenoid) mounted between incident and radiating plates changes its state due to applied constant voltage, causing the coupling of plates. Experimentally measured natural frequencies and modeshapes of the structure are compared to the simulation results. The influence of proposed modification on dynamical properties of the structure is analyzed and discussed.

Improving Sound Transmission Through Triple-Panel Structure Using Porous Material and Sonic Crystal

Main aim of this study is to combine the characteristics of the sonic crystal (SC) with acoustic panels and porous materials to improve the sound transmission loss (STL) through the triple-panel structure. SCs cause a bandgap centered around a certain frequency (Bragg’s frequency) due to generation of destructive interference. Initially, an analytical method is developed that extends the previous theory of double-panel structure to predict STL through a triple-panel structure. Finite element (FE) simulations are performed to obtain the STL through the triple-panel, which are validated with the analytical predictions. Various configurations are analyzed using the FE method based on the method of inserting the porous material and SCs between the panels to address the combined effect. STL through the triple-panel structure is compared with that through the double-panel structure having the same total weight and total thickness. It is found that the combined structure of the triple panel and the SC with glass wool as filler gives the best soundproof performance for the same external dimensions. For narrow air gaps, filing with glass wool is more advantageous than inserting one row of SC. In addition, the triple panel combined with a SC has better soundproofing than the two-panel counterparts.

Acoustic optimization design of porous materials on sandwich panel under flow-induced vibration

In this study, porous sound-absorbing materials used as a lining in double-panel structure applications (such as high-speed train body structures) to limit flow-induced vibration interior noise were studied, and acoustic optimization design was performed. First, in the wavenumber domain, the cross-spectrum Corcos model was used to characterize the dynamic hydrodynamic pressure of turbulence. Biot’s theory is used to model the porous materials. The transmission loss (TL) of the sandwich panel were also determined based on the model superposition method. Three types of sandwich panel structures were considered: air–air (A–A), bonded-bonded (B–B), and bonded-air (B–A). The TL of the three structure types under hydrodynamic pressure was used to evaluate the suppression of flow-induced vibration interior noise in porous materials. The effects of flow velocity, thickness and density of the porous material, and three types of polyimide foam on the TL characteristics of the sandwich panel were investigated. The results show that the flow velocity has a significant influence on the TL of the sandwich panel. The TL of the sandwich panel decreases by 3–4 dB when the flow velocity increases by 100 km/h The B–A configuration has satisfactory sound insulation performance at most frequencies. With an increase in material thickness, the TL of the sandwich panel structure first increases and then decreases, and the material density mainly affects the TL of the structure at intermediate and high frequencies. Based on the objectives of maximizing the average transmission loss (TLavg) and minimizing the structural weight, the acoustic optimization design of the B–A structure was performed, and the balance between the two objective functions was achieved by a nondominated sorting genetic algorithm (NSGA-Ⅱ). The TLavg s of the sandwich panel structure increased by 5.2 dB when the total mass of the structure was decreased by 0.2 kg.

Analysis of the Vibro-Acoustic Behavior of a Stiffened Double Panel-Cavity System

An analytical solution for the vibro-acoustic behavior analysis of a stiffened double panel-cavity coupled system is presented. Unlike existing methods, this method is flexible with parameter analysis and can simulate the elastic boundary conditions of a stiffened double panel structure. The displacements of the stiffened double panel structures and the sound pressure of two inner acoustic cavities are expressed by two-dimensional (2D) and three-dimensional (3D) improved Fourier series methods, respectively. Then, the unknown coefficients of the vibro-acoustic control equation are solved by the Rayleigh–Ritz method based on the virtual works principle applied to the coupled system. In numerical results, the accuracy and effectiveness of the proposed method are validated by several comparison examples. Finally, the influence of some parameters on the vibro-acoustic behavior of the coupled system is investigated. Numerical results show that the external acoustic excitation at a certain angle can stimulate more resonant responses of the panel-cavity coupled system. This work can predict quickly the vibro-acoustic behavior of the stiffened double panel-cavity coupled system with a small truncation number. Some new results can be used as reference data for future work.

Influence Mechanism of a New-Style Resonator on Band Gap of Locally Resonant Phononic Crystal Double Panel Structure

Based on the previous studies on the stubbed-on locally resonant phononic crystal (LRPC) double panel structure (DPS) made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower plates, the stubbed-on LRPC DPS with soft shell surrounded and simplified model with additional springs surrounded are proposed. According to the changes in structural form, the wider band gap is opened, and the novel formation mechanism of the band gap is revealed. Finite element method (FEM) is applied to calculate the band structures. Numerical results and further analysis demonstrate that the soft shell only affects the bands corresponding to symmetric vibration mode and makes the bands shift up. In addition, the influences of density and Poisson’s ratio of soft shell on the band gap can be ignored, but the starting frequency keeps still, and band gap width increases first and then keeps constant with the increase of elasticity modulus. All the results provide a theoretical basis for the study of vibration and noise resistance in engineering.

From mechanics to acoustics: Critical assessment of a robust metamaterial for acoustic insulation application

The increasing popularity of sandwich and composite double panel structures stems from their better sound insulation properties over a wide frequency range with respect to their single panel counterparts. However, in the design of such multi-layer panels particular attention must be paid to the resonance dominated region of the Sound Transmission Loss (STL), where the Mass-Spring-Mass resonance causes a frequency region of poor acoustic performance. In the present contribution, a metamaterial unit cell endowed with an ultra-wide band gap is integrated with faceplates to create a novel acoustic insulation sandwich panel. The panel is realized with a single material and with a properly designed mechanical stiffness that does not affect results in terms of acoustic wave attenuation over a wide frequency range, making at the same time the internal core self-sustained. The STL of the panel is numerically evaluated through a plane wave tube model. The solid-air interaction in terms of resonance frequencies is critically assessed and accurately described by the proposed lumped-parameter model. The model represents a simple tool to predict and optimize the behaviour of the panel in the resonance dominated region of the STL. The acoustic performances of the panel are validated through an experimental campaign on a Nylon prototype, which is 3D printed through Selective Laser Sintering technique.

Analytical model of the diffuse sound transmission loss of finite double panel structures

An analytical model for the forced sound transmission loss of finite single-leaf walls using a variational technique was previously developed and validated. As the double panel is one of the most used structures in building acoustics, the aim of this paper is to extend the analytical model to consider double panel structures. Analytical formulas for the forced part of the airborne sound insulation of finite sized double panel structures are derived using a variational technique based on the integral-differential equation of the fluid loaded panels. The formulas are valid in the entire audible frequency range. The results are compared to alternative analytical models and measurements, with reasonable agreement.

Optimal geometric parameters for a double panel structure with low frequency forbidden characteristics

In this paper, a locally resonant phononic crystal (LRPC) double panel structure with optimal geometric parameters is investigated. The present LRPC structure can open band gaps (BGs) with low frequency forbidden characteristics. The effects of several parameters such as the thickness of steel and aluminum plates, the width of elastic beams, the side length and height of cuboid scatterer onto BGs are analyzed. The thickness of the steel and aluminum plates as well as the width of elastic beams is identified to be the most influential factors on BGs. Seventy-seven experimental runs based on the three-factor and seven-level experimental design are performed to complete response surface analysis, three functional relationships are obtained between the three-factor and the terminating frequency of the second BG, the bandwidth of the first BG, and the bandwidth of the second BG. Additionally, the interior point method is also applied to optimize the closed-form expressions of functional relationships to obtain the optimal LRPC double panel structure with the low-frequency forbidden properties from 90 Hz to 250 Hz.

Chladni Figures in Modal Analysis of a Double-Panel Structure.

Analysis of the structural vibration, under the sound excitation is an important part of the quality assurance during the design process of devices. One of the most commonly used method is Laser Doppler Vibrometry (LDV). However, under the rapid fluctuations of temperature, structural resonances are shifted into the other frequencies. In such situation LDV method may be inconvenient, due to the scanning time. In this paper the authors proposed Chladni figures to modal analysis of the double-panel structure, excited by the loudspeaker enclosed inside the casing with a rigid frame. Double-panel structure has been proven to be particularly useful for noise and vibration reduction applications. Vision images, obtained during the experiments are converted to binary patterns, using GLCM matrix, and compared with simulations performed in ANSYS.

Spectral Analysis of Macro-Fiber Composites Measured Vibration of Double-Panel Structure Coupled with Solenoids.

Noise may have a negative impact on humans health and well being. Noise is a direct result of the vibration of structures. Many industrial workers and people using household appliances may be exposed to these harmful factors. To minimize their negative consequences, different approaches to noise and vibration reduction may be applied, e.g., active, semi-active or passive methods. In this research, a semi-active approach to vibration reduction of a cubic rigid casing enclosing a noise- and vibration-generating device is presented. One of the casing walls consists of double thin steel panels, coupled with the use of electromagnetic dampers—solenoids installed in the space between the panels. Other casing walls are built of single plywood panels. Vibrations of the outer (radiating) panel of the wall are measured by Macro-Fiber Composite patches. Spectral analysis of structure vibration is carried out to identify the benefits of the proposed coupling solution in terms of vibration reduction of the wall. The frequency range, where vibration reduction is observed, depends on the number of activated solenoids and the duty cycle of a Pulse Width Modulation (PWM) signal. Advantages and drawbacks of the proposed method are discussed and future improvements of the examined setup are suggested.

Sound transmission through a stiff double-panel structure periodically stabilized by negative stiffness module: Theoretical modeling

Analytic expressions are derived for models predicting the influence of periodically spaced structural links on sound transmission through a double-panel structure. The double panel has been configured to have two sets of structural links: a rib stiffener and negative stiffness component. The stiffener is identical and is spaced periodically at a distance. However, the negative element component is shifted by an amount q from the other set. The dynamic equation of the vibroacoustic of the system is formulated in terms of the space harmonics and by the principle of virtual work. The model is validated by comparing the model predictions with the existing result from the literature. Then, influences of the negative element, engineering safety, offset, and elevation angle are investigated. A new antiresonance with a huge sound transmission loss value can be engineered at the low-frequency region when these parameters are varied. In addition, the application of the stiff model is implemented for a periodic acoustic metamaterial structure. The negative stiffness inclusion can prevent wave propagation at low frequency. The periodic structure can be designed to obtain more and wider frequency bandgaps.

Comparative Study of Sound Transmission Losses of Sandwich Composite Double Panel Walls

The increasing motivation behind the recently wide industrial applications of sandwich and composite double panel structures stems from their ability to absorb sounds more effectively. Meticulous selection of the geometrical and material constituents of both the core and panels of these structures can produce highly desirable properties. A good understanding of their vibro-acoustic response and emission index such as the sound transmission loss (STL) is, therefore, a requisite to producing optimal design. In this study, an overview of recent advances in STL of sandwich and composites double panels is presented. At first, some salient explanation of the various frequency and controlled regions are given. It then critically examines a number of parameter effects on the STL of sandwich and composite structures. Literatures on the numerical, analytical and experimental solutions of STL are systematically presented. Efficient and more reliable optimization problems that maximize the STL and minimize the objective functions capable of degrading the effectiveness of the structure to absorb sounds are also provided.