José Roberto de França Arruda

Application of acoustic radiation modes in the directivity control by a spherical loudspeaker array

This work concerns the theoretical analysis and synthesis of sound fields by a compact spherical loudspeaker array. Such an electroacoustic device consists of several transducers mounted on a sphere-like structure, which are driven independently in order to achieve non-uniform directivity patterns. The control strategy usually adopted is to provide the array with some preprogrammed basic directivities corresponding to spherical harmonic functions. Thus, an arbitrary radiation pattern can be approximately achieved by changing the gains associated with these basic directivities. Here, a different approach based on the acoustic radiation modes of the array is proposed. Unlike spherical harmonics, radiation modes constitute a finite set of vectors that spans a subspace on which any radiation pattern the array is able to reproduce can be projected. Furthermore, radiation modes radiate sound energy independently. Since the eigenvalue analysis that must be carried out in order to obtain the modes leads also to their radiation efficiencies, the low frequency constraint in the directivity synthesis by a spherical array is naturally evaluated. Finally, it is useless to drive inefficient radiation modes. Therefore, the radiation mode approach leads to a reduced number of active channels, and to minimum source voltages for a given target directivity pattern.

Theoretical and experimental analysis of the electromechanical behavior of a compact spherical loudspeaker array for directivity control

Sound directivity control is made possible by a compact array of independent loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. The radiation pattern of spherical loudspeaker arrays has been predicted from the surface velocity pattern by approximating the drivers membranes as rigid vibrating spherical caps, although a rigorous assessment of this model has not been provided so far. Many aspects concerning compact array electromechanics remain unclear, such as the effects on the acoustical performance of the drivers interaction inside the array cavity, or the fact that voltages rather than velocities are controlled in practice. This work presents a detailed investigation of the electromechanical behavior of spherical loudspeaker arrays. Simulation results are shown to agree with laser vibrometer measurements and experimental sound power data obtained for a 12-driver spherical array prototype at low frequencies, whereas the non-rigid body motion and the first cavity eigenfrequency yield a discrepancy between theoretical and experimental results at high frequencies. Finally, although the internal acoustic coupling affects the drivers vibration in the low-frequency range, it does not play an important role on the radiated sound power.

Vibration Analysis of Flexible Rotating Rings Using a Spectral Element Formulation

In this work, the forced response of rotating rings exhibiting nonperiodic and periodic variations in material properties and geometry is assessed by means of the spectral element method (SEM). Based on the Euler–Bernoulli beam theory, a spectral element for a planar rotating ring is derived. This spectral element allows the investigation of the effects of structural damping, internal pressure and elastic foundations in the harmonic response of rotating rings. The dynamic response of rotating rings including periodic imperfections that lead to band gap effects is addressed. The spectral element formulation provides exact solutions within the range of validity of the applied theory using a reduced number of degrees-of-freedom. Thus, it contributes to reducing the computational time. It also provides a straightforward way to solve structural dynamics problems including arbitrary boundary conditions and discontinuities. The proposed formulation is validated by comparison with analytical solutions, which are available only for uniform homogenous rings.

Structural damage detection using energy flow models

The presence of a crack in a structure modifies the energy dissipation pattern. As a consequence, damaged structures can present high localized damping. Experimental tests have revealed that crack nucleation and growth increase structural damping which makes this phenomenon useful as a damage locator. This paper examines the energy flow patterns caused by localized damping in rods, beams and plates using the Energy Finite Element Method (EFEM), the Spectral Element Method (SEM) and the Energy Spectral Element Method (ESEM) in order to detect and locate damage. The analyses are performed at high frequencies, where any localized structural change has a strong influence in the structural response. Simulated results for damage detection in rods, beams, and their couplings calculated by each method and using the element loss factor variation to model the damage, are presented and compared. Results for a simple thin plate calculated with EFEM are also discussed.

Power flow estimation using pulsed ESPI

Measurements performed using a double pulse ESPI (Electronic Speckle Pattern Interferometry) are used to estimate the power flow maps in a square plate excited harmonically. The pulse ESPI was equipped with one camera providing no information about the phase of the measured displacement field. A procedure based on the solution of a system of transcendental equations which corresponds to two measurements with a known time delay is used to determine the magnitude and phase. In order to spatially smooth the operational modes and reduce the noise spikes, a smoothing technique and a median filter are used, respectively. The active power flow is estimated for two frequencies. The reactive power flow due to the bending moments, twisting moments and shear forces are obtained separately. A finite element model based on the theory of thin plates is used for qualitative comparison of the reactive power flow maps.

Effects of enclosure design on the directivity synthesis by spherical loudspeaker arrays

Spherical loudspeaker arrays have been used to generate non‐uniform directivity patterns. It is known that the poor radiation efficiency of spherical sources and the loudspeaker electroacoustic behavior impose constraints on the directivity synthesis at low frequencies, which are aggravated as the source volume is made smaller. In this work, the effects of the enclosure design on the loudspeaker signal powers are analyzed. Two different approaches have been reported in literature, although quantitative comparisons have not been provided. In the first approach, the drivers share the same enclosure volume and in the second, they have their own independent sealed cavities. Here, an analytical model that takes into account the interior and exterior acoustic coupling is used in order to evaluate the voltages that must feed the array drivers. It is shown that the signal powers can be reduced at low frequencies by letting the drivers share the same enclosure volume. However, this leads to controllability problem...

Optimal array pattern synthesis with desired magnitude response

Letting Euclidean norm be the performance parameter, the task of finding the best approximation of a complex function in a finite dimension subspace leads to a convex optimization problem that can be easily solved by the least‐squares method. However, this procedure leads to a sub‐optimal solution in applications that have no phase requirements on the approximated function. In this case, semidefinite programming has been used to obtain optimal magnitude responses. In this work, this non‐convex optimization problem is dealt with by using an iterative method based on the least‐squares, which is illustrated on directivity synthesis by spherical loudspeaker arrays. Usually, instead of synthesize directly the desired pattern, the strategy adopted is to reproduce its truncated spherical harmonic representation. The truncation order is determined by the number of drivers of the spherical array. It is shown that truncation error and signal powers can be significantly reduced if phase error is neglected, providing...

Energetic analysis of an actively controlled one-dimensional acoustic waveguide

Abstract The aim of this work is to show the energetic behavior when an active noise controller is applied in a one-dimensional waveguide, namely an ideal duct under the first critical frequency. In order to model the duct, a spectral element method, which is shown to be more practical for analyzing pipe networks than other commonly used analytical models, was used. The model used here consists of a duct with two sources, the primary source at one end of the duct, and the secondary source at the middle section. The error sensor was placed downstream from secondary source, and the other end of the duct was open with no flange. Three optimal control methods were applied: minimization of the potential energy density, minimization of the active intensity, and minimization of the total acoustic power radiated by the sources. It was observed that the three control methods achieved the same final result, and when the volume velocity of the secondary source was driven to the optimal volume velocity, neither the primary source nor the secondary source radiated any acoustic power. Furthermore, the controlled duct was equivalent to a duct opened-ended at the secondary source position with radiation impedance equal to zero.

Wave and Vibration Analysis of Rotating Periodic Structures by Wave-Based Methods

The vibration of flexible rotating structures has been extensively investigated by the rotordynamics community. The analysis is usually performed via the finite element method using normal mode superposition. However, some interesting features of these structures may be hidden using a modal approach. In this paper, a wave-based approach is used to study the dynamic behavior of flexible rotating structures. Using a wave description, it is straightforward to show that the gyroscopic effect inherent to flexible rotating structures breaks the time-reversal symmetry. This corresponds to an asymmetric wave propagation, i.e., a forward-going wave and its corresponding backward-going pair travel with different wave speeds. In this paper, we show that this feature of flexible rotating structures makes them a natural mechanical circulator. On the other hand, we show that in the case of inhomogeneous flexible rotating structures designed as spectral gap elastic materials, i.e., phononic crystals or locally resonant metamaterials, the rotational speed has a strong influence in the location and width of the band gaps. The mathematical formulation of these problems have been presented by the authors elsewhere. Here, the conceptual aspects of these investigations are discussed under the light of original numerical simulation results.

Boundary modes in quasiperiodic elastic structures

Topological metamaterials are a new class of materials that support topological modes such as edge modes and interface modes, which are commonly immune to scattering and imperfections. This novelty has been the subject of extensive research in many branches of physics such as electronics, photonics, phononics, and acoustics. The nontrivial topological properties related to the presence of topological modes are tipically found in periodic media. However, it was recently demonstrated that structures called quasicrystals may also exhibit nontrivial topological behavior attributed to dimensions higher than that of the quasicrystal. While quasiperiodicity has received a lot of attention in the fields of crystallography and photonics, research into quasiperiodic elastic structures has been scarce. In this paper, we show how the concepts of quasiperiodicity may be applied to the design of topological mechanical metamaterials. We start by investigating the boundary modes present in quasiperiodic 1D phononic lattices. These modes have the interesting property of being localized at either one of the two different boundaries depending on the value of an additional parameter, which is remnant of the higher dimension. A smooth variation of this parameter in either time or a spatial dimension can lead to a robust transfer of energy between two sites of the structure. We present an idealized mechanical system composed by an array of coupled rods that may be used as a platform for realizing this kind of robust transfer of energy. These are preliminary investigations into a entirely new class of structures which may lead to novel engineering applications.