Coherent wave reflection in integrable or chaotic symmetrical acoustical billiards

This study is concerned with the distribution of flexural vibrations in plates excited with a Gaussian white noise. The distribution of energy can be characterized by its homogeneity and isotropy. Some particular geometries like the Bunimovitch stadium generate a field that is both homogeneous and isotropic. But other geometries produce a field that is homogeneous but not isotropic (like the rectangle panel) or non-isotropic and not homogeneous (like the circular panel). It is known that these features drive the establishment of diffuse field. However, in the present work, we show that even at high frequency and for these three particular geometries, the diffuse field cannot be reached rigorously. Owing to symmetries, the vibrational response is always enhanced on some particular lines and points by the effect of coherence between rays. The enhancement factors are predicted theoretically with the image-source method. The presence of energy enhancement is also shown experimentally by measuring the vibrational energy density in the 20 Hz–4 kHz frequency range for these three plates excited with a random white noise. Measurement of enhancement factors shows a good agreement with their theoretical predictions.

Flexible Fiber Fabric for FRP–Concrete Connection of Thin Hybrid Slabs

In order to combat corrosion issues, several studies on progressively replacing steel reinforcement elements with composite ones have been conducted in recent years. Hybrid steel–concrete thin slabs in which the steel acts as formwork are also candidates for update in the coming years. Achieving a reliable connection between fiber-reinforced polymer (FRP) and cast-in-place concrete is key to promoting this technology. This study analyzed different connection systems and proposes the novel approach of embedding a flexible fiber fabric as a superficially distributed connector between concrete and FRP. Eight specimens with four different connection strategies were tested using an experimental modal analysis and a quasi-static three-point bending test. The impact of the connection system on the vibrational response, flexural ultimate load, moment response, neutral axis position, shear and dissipated energy was obtained and compared. The results show that the use of an embedded mesh increases the frictional mechanism and produces the best performance in terms of load-bearing capacity and ductility.

The vibrational response of a fluid-loaded baffled plate near a free surface

An analytical model to predict the vibrational response of a simply supported rectangular plate embedded in an infinite baffle with an upper free surface under heavy fluid loading and excited by a point force is presented. The equations of motion of a thin plate are solved using­­­­­­ modal decomposition technique by employing admissible functions for an in-vacuo plate and by directly solving the Helmholtz equation for acoustic waves in a fluid. The vibrational response for a flat plate in an infinite baffle and unbounded domain (semi-infinite domain) using analytical formulation available in literature is initially computed. These results are then compared against present results to observe the effect of a free surface. Predictions from analytical models are validated by comparison with results obtained by numerical models. The proposed analytical approach presents a novel formulation to describe a fluid-loaded flat plate in a waveguide and an efficient method for predicting its vibrational response.

Influence of the plate thickness and material properties on the violin top plate modes

In this paper we analyze the vibrational behavior of the violin top plate, for varying plate thickness and material properties via finite element method (FEM) numerical simulations. It is well known that the vibrational properties of the top plates of string instruments influence their sound emission characteristics. Due to the impact of global warming on wood formation and due to their configurability, many manufacturers investigate the use of composite materials to produce musical instruments. Therefore, composite, carbon fiber reinforced epoxy (CFRE) prepreg along with traditional wooden material, such as spruce, are adopted in this study. FEM modal analysis along with a frequency response function (FRF) FEM analysis are performed. The vibrational variations of the plate's response are computed under free conditions. The main vibrational modes and the natural frequencies obtained by the simulations show the influence of the different mechanical and geometric properties on the top plate's vibrational response. The resulting eigenmode frequencies and shapes of the plate in relation to the varying thickness and the material properties used, are discussed. The results of this study offer valuable information on the evaluation of the acoustical characteristics of violins and may be further used on their vibrational behavior optimization and control.

On the extension of the mode-matching procedure for modeling a wave-bearing cavity

The present work highlights the scattering of fluid–structure coupled waves through a wave-bearing cavity in rigid waveguide. The cavity is filled with compressible fluid and comprises horizontal as well as vertical elastic boundaries. The mode-matching technique is extended by tailored-Galerkin and Galerkin procedures to incorporate the vibrational response of the vertical elastic components having different sets of edge conditions. It is found that in mode-matching tailored-Galerkin (MMTG) method, a unique general description of the displacement of vertical elastic component can deal with a variety of edge conditions, whereas the mode-matching Galerkin (MMG) technique relies upon the orthogonal basis a priori whose description varies by changing the edge conditions of vertical elastic components. Accordingly, for some sets of edge conditions the eigenvalues cannot be expressed explicitly and must be found numerically. The eigenmodes of the cavity region satisfy the generalized orthogonal conditions which ensure the point-wise convergence of MMTG and MMG approaches. Moreover, the truncated MMTG and MMG solutions reconstruct the matching conditions as well as satisfying the conserved power identity. It confirms the accuracy of performed algebra and retained solutions. From the numerical results it is found that by varying the conditions on the edges of bridging elastic components, the stopbands can be enhanced and shifted as well as broadened over the certain frequency regimes.

Electric Field and Temperature Effects on the Ab Initio Spectroscopy of Liquid Methanol

Although many H-bonded systems have been extensively investigated by means of infrared (IR) spectroscopy, the vibrational response to externally applied electric fields of polar liquids remains poorly investigated. However, local electric fields along with quantum-mechanical interactions rule the behavior of H-bonded samples at the molecular level. Among the many H-bonded systems, liquid methanol holds a key place in that it exhibits a very simple H-bond network where, on average, each molecule acts as a single H-bond donor and, at the same time, as a single H-bond acceptor. Here we report on the IR spectra emerging from a series of state-of-the-art ab initio molecular dynamics simulations of bulk liquid methanol under the action of static and homogeneous electric fields. In addition, the same analysis is here conducted in the absence of the external field and for different temperatures. Although some electric-field-induced effects resemble the response of other polar liquids (such as the global contraction of the IR spectrum upon field exposure), it turns out that, distinctly from water, the “electrofreezing” phenomenon is unlikely to happen in liquid methanol. Finally, we provide atomistic analyses magnifying the completely different nature of electric-field- and temperature-induced effects on bulk liquid methanol and on its vibrational response.

Finite element analysis of a single conductor with a Stockbridge damper under Aeolian vibration

A finite element model is developed to predict the vibrational response of a single conductor with a Stockbride damper. The mathematical model accounts for the two-way coupling between the conductor and the damper. A two-part numerical analysis using MATLAB is presented to simulate the response of the system. The first part deals with the vibration of the conductor without a damper. The results indicate that longer span conductors without dampers are susceptible to fatigue failure. In the second part, a damper is attached to the conductor and the effects of the excitation frequency, the damper mass, and the damper location are investigated. This investigation shows that the presence of a properly positioned damper on the conductor significantly reduces fatigue failure.

Finite element analysis of a single conductor with a Stockbridge damper under Aeolian vibration

A finite element model is developed to predict the vibrational response of a single conductor with a Stockbride damper. The mathematical model accounts for the two-way coupling between the conductor and the damper. A two-part numerical analysis using MATLAB is presented to simulate the response of the system. The first part deals with the vibration of the conductor without a damper. The results indicate that longer span conductors without dampers are susceptible to fatigue failure. In the second part, a damper is attached to the conductor and the effects of the excitation frequency, the damper mass, and the damper location are investigated. This investigation shows that the presence of a properly positioned damper on the conductor significantly reduces fatigue failure.