Elsevier

Applied Acoustics

Volume 182, November 2021, 108179
Applied Acoustics

Numerical simulation of impact sound transmission control across a smart hybrid double floor system equipped with a genetically-optimized NES absorber

https://doi.org/10.1016/j.apacoust.2021.108179Get rights and content

Abstract

An idealized detailed 2D formulation is presented for suppression of transient impact sound transmission across a hybrid smart double-leaf sandwich beam (floor-ceiling) structure into a rectangular (receiving) room with ideally flat and rigid walls. The smart double wall structure, which is mechanically inter-connected at an arbitrary point with a lightweight nonlinear energy sink (NES) absorber, incorporates spatially distributed and electrically independent non-collocated semiactive (electro-rheological fluid- or ERF-incorporated) and fully-active (piezoceramic- or PZT-incorporated) actuator layers functioning in a closed loop control framework. Extensive time-domain numerical simulations initially calculate both the uncontrolled and controlled transient acoustic pressure fields in absence of the dynamic vibration absorber for four separate settings of the active (PZT-) and semiactive (ERF-) actuation elements. Subsequently, the remarkable performance of the GA-optimized hybrid smart active/semi-active/passive (PZT/ERF/NES) configuration, which benefits from the multi-mode targeted energy transfer (TET) mechanism of the NES, in significant broadband (low frequency) attenuation of the transmitted shock energy with a much lower actuator energy demand, is demonstrated. Furthermore, some important aspects of the transient fluid-structure interaction (TFSI) control problem like weakening of the acoustic shock focusing effects (focal zones) within the source room are illustrated through selected early-to-late-times 2D images and animations of the cavity pressure fields. Limiting situations are studied and correctness of the derivations is established against accessible data in addition to numerical (FEM) simulations.

Introduction

Inter-floor impact noise is an essential factor in acoustic building design that has also turned into a major social issue. It has been considered as a serious environmental factor in multistoried residential buildings and industrial complexes where the structure-borne energy can travel with small attenuation to different sections of the building and then simply be reradiated at low frequencies [1], [2]. Numerous researchers have employed various numerical, analytical, and experimental methods to investigate (passive) impact noise insulation in floors of different constructions. For example, Neves-e-Sousa and Gibbs [3] experimentally validated his modal-based analytical model that examined the effects of floating floor and room characteristics on the low frequency impact sound transmission. Díaz-Cereceda et al. [4] presented a deterministic model based on modal analysis to investigate the influence of elastic structural floor connections (i.e., studs and joints) in reduction of impact noise transmission. Yoo and Jeon [5] used field measurements and finite element simulations to study the effects of viscoelastic damping materials and resilient isolators on the low-frequency impact sound insulation in reinforced concrete floor structures. More recently, Wang et al. [2] examined the state-of-the-art methodologies for calculation of structural vibration, impact forces, and radiated sound power in rooms with impacted timber joist floors.

The structural vibration control strategies may be divided into three general categories, namely, passive (inactive) control, semiactive control, and active control, all of which include various energy depletion devices [6], [7], [8], [9]. Also, based on dissimilar properties of damping and stiffness damping elements, energy depletion devices can be separated into two main groups: linear energy dissipative dampers and devices (e.g., tuned mass dampers, or TMDs [10], [11]; and tuned liquid dampers, or TLDs [12], [13], [14], [15]) and nonlinear energy dissipative dampers and devices (e.g., nonlinear energy sinks and viscous dampers, and particle impact dampers [9]). The applications of first class (linear dampers) are largely restricted due to their weak performance under some specific conditions. The second class of energy dissipation devices (i.e., the nonlinear dampers) circumvent the above shortcoming and are thus increasingly utilized in practical engineering applications, due to their simplicity, modularity, lightweightness, broadband response, robustness, and adaptivity [9], [16]. Accordingly, the nonlinear energy sink (NES) [17] has recently been extensively employed as an efficient type of high performance strongly nonlinear passive vibration absorber with an extremely high wideband vibration energy absorption capacity under transient excitations [9], [18], [19], [20], [21], [22]. A basic NES is generally composed of a local lightweight inertial attachment (i.e., a small mass coupled to the primary vibrating structure through a viscous linear damper), and an essential (non-linearizable) stiffness nonlinearity. It utilizes the notion of targeted energy transfer (TET) based on nonlinear mode localization and internal resonance (resonance capture) to irreversibly and locally transfer a major portion of the shock energy from different modes of the vibrating structure to the NES, where the kinetic energy of the main system is eventually dissipated [9], [18], [19], [20], [21], [22].

Engineering structures have progressed very far from the traditional passive (inactive) structural to active ones. Recent advances in the development and applications of sensor and actuator (smart material) technologies in conjunction with advanced control systems and high-power computing machineries have significantly extended multi-functionality and integration of mechatronic systems and devices. Two well-known control strategies are generally pursued for active control of the radiated/transmitted noise, depending on the type of applied actuators, namely, ANC or Active Noise Control [23], [24], [25] and ASAC or Active Structural Acoustic Control [26], [27], [28]. The more costly and intrusive ANC is normally appropriate for low-frequency sound field cancellation, where the system structural dynamics actually remain unaffected, and attaining global noise attenuation in a complex sound field becomes impractical. In the ASAC methodology, on the other hand, structural actuators interfere with the modal pattern of the vibrating structure, aiming at direct attenuation of the radiated sound levels [29]. This method is particularly regarded as a more efficient approach to treat the structure-borne noise problems with complex sound fields. In contrast to the extensively applied passive methods [5], relatively few researchers have entered the field of active inter-floor impact noise control. For example, Akishita et al. [30] developed and experimentally tested an independently controlled active modular panel feedback system utilizing piezoelectric actuators and acceleration sensors for insulation of residential floor panel impact noise. Kageyama et al. [31] applied the so-called Direct Adaptive Algorithm (DAA) in both simulations and experiments for ANC of impact noise in the low frequency range. Pinte et al. [32] used a numerically optimized configuration of inertia actuators and sensors (accelerometers) to present a non-collocated active structural acoustic control method based on different Iterative Learning Control (ILC) algorithms for mitigation of transient noise due to repetitive structural impact excitations. Kamura et al. [33] employed a frequency domain adaptive algorithm to actively control impact noise. The effectiveness of proposed active noise control method was confirmed through simulations and experiments. Min et al. [34] employed Filtered-XLMS-ANC algorithm for reducing floor impact noise. The adopted algorithm was experimentally verified by reducing floor impact noise at the error microphone. More recently, Xue [35] proposed a modal filtering approach for active suppression of floor vibration subjected to impact loading.

The above review clearly demonstrates that while there is a sizeable mass of research works that utilize a wide variety of merely passive or fully active methodologies for suppression of airborne and impact sound transmission through single and double floor partitions, rigorous numerical or theoretical solutions for enhanced hybrid active-semiactive-passive transient sound transmission reduction through these structures appear to be missing. The main purpose of present manuscript is to cover this significant dearth in the literature. To do this, the associated acoustoelastic model is first analytically developed and validated. Subsequently, the transient impact sound transmission across the double beam partition is expediently suppressed through the closed loop control of a PZT-actuator layer in conjunction with the semiactive modification of the stiffness/damping properties of an ERF-actuator layer, while taking advantage of a genetically-optimized inter-connected NES (see Fig. 1). The proposed hybrid design philosophy enables the noise control engineer to simultaneously profit from the dissimilar characteristics of different classes of common actuation and absorption mechanisms that cannot be perceived by utilizing a single class alone [36], [37], [38], [39]. It can ultimately assist in development of new smart acoustic materials and systems with superior broadband low-frequency impact sound insulation characteristics [22], [30], [32], [34], [35], [40], [41], [42] despite lower actuation energy demands. The adopted hybrid control approach incorporates the accuracy and high performance of the active PZT-incorporated structure with low price, efficiency, and robustness (stability) of the semiactive ERF-incorporated structure inter-coupled with a simple, lightweight, and inherently robust NES damper. Lastly, the presented extensive time-domain simulation output can offer a dependable benchmark for assessment of principally approximate or numerical techniques [5], [29].

Section snippets

Formulation

Rectangular enclosures typify acoustic mediums for living rooms, bedrooms, dwellings, and test laboratories. Therefore, the study of vibro-acoustic insulation counteracting floor impact is typically performed in constructions with rectangular cavities [3], [5], [43]. In particular, double-floor structures with an intermediate air cavity are among the most common structural elements used for sound insulation in lightweight constructions [44], [45], [46]. Accordingly, we shall consider a

Input parameters and convergence

Having noticed the large number of input parameters involved in the presented coupled acoustoelastic formulation, and keeping in mind our computational limitations, we shall only consider some specific numerical examples. Except where otherwise stated, the geometrical and material properties of the hybrid double beam-cavity system (Fig. 1) are taken from Table 1. Here, the commercially produced and widely used soft piezoceramic PZT (lead zirconate titanate)-5H is selected as the material for

Conclusions

A novel 2D theoretical formulation is put forward for assessing the transient impact sound transmission control performance of a smart hybrid sandwich double-beam floor construction inter-coupled with a simple lightweight NES. The presented electro-acousto-mechanical model is based on Maxwell's electrodynamics equations, the linear acoustic wave theory, the relevant fluid/structure boundary conditions, the Kelvin-Voigt viscoelastic material, and the pertinent continuum-based thin beam models.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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