Calculation of the shape of a towed underwater acoustic array

Howard, B.E.; Syck, James M.

doi:10.1109/48.126976

Cited by 38 publications

(9 citation statements)

References 2 publications

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“…Generally, Array Element Localization (AEL) sensors are attached to an array and used to determine the depth of the array elements below the sea surface, the array heading and the straightness of the array [45] [46]. However, in some of the experiments, these sensors are not available or are sometimes malfunctioning.…”

Section: Array Element Localizationmentioning

confidence: 99%

Low-frequency bottom backscattering data analysis using multiple constraints beamforming

Li¹

1995

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Section: Array Element Localizationmentioning

confidence: 99%

Low-frequency bottom backscattering data analysis using multiple constraints beamforming

Li¹

1995

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“…[6][7][8][9] Another is based on distributed measurements from nonacoustic sensors along the array ͑e.g., depth gauges and compasses͒. 10,11 Generally, these techniques rely on solving the Paidoussis equation and/or interpolating between known points with polynomials or splines. The acoustic approaches involve a variety of signal-processing techniques using acoustic signals received at the hydrophones in two general categories-͑a͒ from nearfield controlled sources, and ͑b͒ from far-field noncontrolled sources of opportunity.…”

Section: Introductionmentioning

confidence: 99%

Performance of sinusoidally deformed hydrophone line arrays

Caveny

Balzo

Leclere

et al. 1999

The Journal of the Acoustical Society of America

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It is well known that array deformations can distort beam patterns and introduce bearing errors if the beamformer assumes linearity. It is also known that deformed arrays can resolve left-right ambiguities, provided the shape is known. In this work, these two effects are studied for undamped and damped sinusoidally deformed arrays with small deformation amplitudes in the horizontal (x,y) plane only. By use of fixed arc-length separations along the array, the hydrophone (x,y) coordinates are determined numerically and the error in assuming equal x spacing is summarized for a sample array. Array-response patterns are analyzed for two conditions: ͑1͒ when the deformed array shape is assumed linear and ͑2͒ when the deformed array shape is known exactly. Degradations resulting from assuming linearity and the ability to resolve left-right ambiguities are discussed in terms of reduced gain, degraded angular resolution, and bearing errors. Shape-unknown signal-gain degradation ranges to 7 dB at broadside, but is less than 1 dB near endfire. For the shape-known case, signal gain for the true peak is greater than signal gain for the ambiguous peak by up to 9 dB for sources at broadside and to just over 2.5 dB for arrivals near endfire.

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“…Rather, an additional linear and tridiagonal system of equations are necessary to ensure smoothness at the node points. The construction of these inter-element constraints for twisted splines is discussed in detail in Howard and Syck (1983). Considering the piezo-beam section of Figure 2, the inter-element constraint equations use boundary conditions on the tangent of the beam section, r 0 ðN A Þ and r 0 ðN B Þ , and the node positions of the assembled piezo-beam section, r ðN A Þ through r ðN B Þ , to define the node curvatures, r 00 ðN B Þ through r 00 ðN B Þ , that yield C 1 (s) and C 2 (s) continuity as per the method of Buckham et al (2004).…”

Section: Condensing the Element Equationsmentioning

confidence: 99%

Finite Element Modeling of a Slewing Non-linear Flexible Beam for Active Vibration Control with Arrays of Sensors and Actuators

Gilardi

Buckham

Park

2009

Journal of Intelligent Material Systems and Structures

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In this article, a new finite element model (FEM) of an EulerBernoulli beam, developed through an absolute nodal coordinate formulation (ANCF), is presented for simulation and analysis of the performance of surface-bonded piezoelectric actuators in suppressing non-linear transverse vibrations that are induced by very fast slewing. The elastic deformations experienced are an order of magnitude larger than cases considered to date, and the model employs a unique cubic spline approximation to the beam's deformed elastic line that is in terms of node positions and curvatures. To ensure relevant commentary on the vibration suppression properties of the distributed piezoelectric actuators, a material damping model was introduced in the continuum equations to capture the non-linear damping of the very slender beam that is observed in experiments. Following the ANCF methodology, the constitutive damping moment is formulated in terms of the absolute nodal coordinates with care taken to ensure the calculation is singularity free. Galerkin's method of weighted residuals is applied to discretize the revised equations of motion derived for the beam continuum. The FE beam model exploits a synergy between the twisted spline geometry and the lumped mass approximation to halve the size of the matrix equations that must be solved on each time step. However, this condensation of the matrix equations requires the use of interelement boundaries at the edges of the surface-bonded piezos. Using a single-link flexible manipulator as an example, a number of static and dynamic simulation examples that illustrate the validity of our FEM are presented, including comparisons to theoretical and other existing numerical solutions in literature. In addition, active vibration control examples are presented using proportional-and derivative-based hub motion and piezoelectric actuator controls in suppressing dramatic vibrations induced by fast slewing.

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Calculation of the shape of a towed underwater acoustic array

Cited by 38 publications

References 2 publications

Low-frequency bottom backscattering data analysis using multiple constraints beamforming

Low-frequency bottom backscattering data analysis using multiple constraints beamforming

Performance of sinusoidally deformed hydrophone line arrays

Finite Element Modeling of a Slewing Non-linear Flexible Beam for Active Vibration Control with Arrays of Sensors and Actuators

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