Transient Radiation from Pistons in an Infinite Planar Baffle
01 Jul 1970-Journal of the Acoustical Society of America (Acoustical Society of America)-Vol. 49, pp 1629-1638
TL;DR: In this article, an approach to compute the near and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle is presented.
Abstract: An approach is presented to compute the near‐ and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integrals. A simple expression is developed for an impulse response function, which is the time‐dependent velocity potential at a spatial point resulting from an impulse velocity of a piston of any shape. The time‐dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the appropriate impulse response. The response of an array may be computed using superposition. Several examples illustrating the usefulness of the approach are presented. The farfield time‐dependent radiation from a rectangular piston is discussed for both continuous and pulsed velocity conditions. For a pulsed velocity of time duration T it is shown that the pressure at several of the field points can consist of two separate pulses of the same duration, when T is less than the travel time across the piston.
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TL;DR: A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested, which relies on the Tupholme-Stepanishen method for calculating pulsing pressure fields and can also handle the continuous wave and pulse-echo case.
Abstract: A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested. It relies on the Tupholme-Stepanishen method for calculating pulsed pressure fields, and can also handle the continuous wave and pulse-echo case. The field is calculated by dividing the surface into small rectangles and then Summing their response. A fast calculation is obtained by using the far-field approximation. Examples of the accuracy of the approach and actual calculation times are given. >
2,340 citations
TL;DR: Pulsed wave time-reversal focusing is shown using reciprocity valid in inhomogeneous medium to be optimal in the sense that it realizes the spatial-temporal matched filter to the inhomogeneity propagation transfer function between the array and the target.
Abstract: Time reversal of ultrasonic fields represents a way to focus through an inhomogeneous medium. This may be accomplished by a time-reversal mirror (TRM) made from an array of transmit-receive transducers that respond linearly and allow the incident acoustic pressure to be sampled. The pressure field is then time-reversed and re-emitted. This process can be used to focus through inhomogeneous media on a reflective target that behaves as an acoustic source after being insonified. The time-reversal approach is introduced in a discussion of the classical techniques used for focusing pulsed waves through inhomogeneous media (adaptive time-delay techniques). Pulsed wave time-reversal focusing is shown using reciprocity valid in inhomogeneous medium to be optimal in the sense that it realizes the spatial-temporal matched filter to the inhomogeneous propagation transfer function between the array and the target. The research on time-reversed wave fields has also led to the development of new concepts that are described: time-reversal cavity that extends the concept of the TRM, and iterative time-reversal processing for automatic sorting of targets according to their reflectivity and resonating of extended targets. >
1,407 citations
TL;DR: A new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion is described.
Abstract: The paper describes a new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation. The movement of the object is determined from a field with spatial oscillations in both the axial direction of the transducer and in one or two directions transverse to the axial direction. By using a number of pulse emissions, the inter-pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The method is based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion. Such a transverse modulation can be generated by using apodization on individual transducer array elements together with a special focusing scheme. A method for making such a field is presented along with a suitable two-dimensional velocity estimator. An implementation usable in medical ultrasound is described, and simulated results are presented. Simulation results for a flow of 1 m/s in a tube rotated in the image plane at specific angles (0, 15, 35, 55, 75, and 90 degrees) are made and characterized by the estimated mean value, estimated angle, and the standard deviation in the lateral and longitudinal direction. The average performance of the estimates for all angles is: mean velocity 0.99 m/s, longitudinal S.D. 0.015 m/s, and lateral S.D. 0.196 m/s. For flow parallel to the transducer the results are: mean velocity 0.95 m/s, angle 0.10, longitudinal S.D. 0.020 m/s, and lateral S.D. 0.172 m/s.
470 citations
Cites methods from "Transient Radiation from Pistons in..."
...The simulation is performed using the impulse response method developed by Tupholme [24] and by Stepanishen [ 25 ] in the implementation developed by Jensen and Svendsen [23]....
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TL;DR: The authors have undertaken a theoretical investigation of the focusing and steering properties of pulsed 2-D arrays to characterize the parameters required for medical imaging, such as element size, spacing, and number of elements.
Abstract: The major problem facing the development of 2-D arrays for imaging is the complexity arising from the large number of elements anticipated in such transducers. The authors have undertaken a theoretical investigation of the focusing and steering properties of pulsed 2-D arrays to characterize the parameters required for medical imaging, such as element size, spacing, and number of elements. Details of the computational methods employed are presented, as well as a discussion of the steered beam properties of wideband 2-D arrays. The effects of apodization and element cross-coupling on the beam properties of a 2-D transducer array are examined. The beam properties of various sparse arrays with elements randomly distributed over the aperture of the transducer are discussed. >
309 citations
TL;DR: The transducer is probably the single most important component of any ultrasonic imaging system and the techniques for modeling the electromechanical impulse response are reviewed, with emphasis on the spatio-temporal impulse response technique.
Abstract: The transducer is probably the single most important component of any ultrasonic imaging system. A basic introduction to the problems and paradoxes of transducer design is given. After introducing the piezoelectric equations and discussing important transducer material such as lead zirconate titanate and polyvinylidene difluoride, the techniques for modeling the electromechanical impulse response are reviewed. Quarter-wave matching and short pulse techniques are discussed. The prediction of the ultrasound field of plane, spherical, and conical transducers is reviewed with emphasis on the spatio-temporal impulse response technique. Finally, the use of the above approaches is illustrated in a very practical fashion for three interesting transducer geometries: 1) a split aperture device with two focal lengths, 2) a five-element annular array, and 3) a 37.5 degree conical/annular array hybrid transducer.
232 citations
References
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TL;DR: In this article, an approach to compute the time-dependent force acting on a piston in a rigid infinite planar baffle as a result of the specified velocity of the piston is presented.
Abstract: An approach is presented to compute the time‐dependent force acting on a piston in a rigid infinite planar baffle as a result of the specified velocity of the piston. The approach to computing the force is applicable to both sinusoidal and nonsinusoidal velocity pulses and is valid for all piston shapes. The approach, which is based on a Green's‐function solution to the time‐dependent boundary value problem, utilizes a transformation of coordinates to simplify the evaluation of the double surface integrals. An impulse response function is defined such that the time‐dependent force can be obtained by differentiating the convolution of the impulse response and piston velocity time functions. A closed‐form expression for the impulse response of a circular piston is derived and discussed. Numerical results for the impulse response and the forces on large square pistons resulting from sinusoidal piston velocities are then presented and discussed to compare the transient and steady‐state behavior of the forces. Finally, an approach is presented to compute the radiation impedance as a function of normalized frequency from the impulse response data, and the approach is used to obtain the normalized radiation resistance and reactance for square pistons.
186 citations
TL;DR: In this article, it was shown that a form of reciprocity exists between the structure of the acoustic signal at a point in the field of a pulsed transducer when transmitting and the electrical signal when the same transducers receive an acoustic signal.
Abstract: When a single pulse is applied to a plane radiator in a large rigid baffle or to a convexly curved baffled radiator having dimensions and radii of curvature large compared with the relevant wavelengths, the pressure at a field point is shown theoretically to consist, generally, of a sequence of pulses, each of which is, approximately, a scaled replica of the applied pulse. The number of pulses and their relative size and spacing are functions of position of the field point. In the direction of the main beam, if the radiating surface is plane, these pulses are not resolved and a single nearly undistorted pulse is obtained. A form of reciprocity is shown to exist between the structure of the acoustic signal at a point in the field of a pulsed transducer when transmitting and the structure of the electrical signal when the same transducer receives an acoustic pulse. Simple relationships are presented between the formulas for pulsed radiation, reception, and backscattering from a plane surface.
41 citations
TL;DR: In this article, an approach is presented to computing the time-dependent force acting on a piston as a result of the velocity of an adjacent piston which may be any specified timedependent function, based on a Green's function solution to the timedependent boundary value problem for an impulsive piston velocity motion.
Abstract: An approach is presented to computing the time‐dependent force acting on a piston as a result of the velocity of an adjacent piston which may be any specified time‐dependent function. The method is based on a Green's function solution to the time‐dependent boundary‐value problem for an impulsive piston velocity motion. An asymptotic expression for the mutual radiation impedance between square pistons has been obtained using the method. A numerical approach is also presented to obtain the mutual radiation impedance coefficients from the time‐dependent solution of the boundary‐value problem. Numerical results obtained from the asymptotic expression are shown to agree with previously published numerical results and the results obtained using the numerical approach indicated in the paper. Numerical results for time‐dependent interaction forces resulting from sinusoidal piston velocities are also presented and discussed.
24 citations
TL;DR: In this article, the Laplace transform is used to determine the time history required to produce a step in the velocity of a circular piston mounted in an infinite baffle, and the inverse problem of the velocity response to a step force is calculated approximately.
Abstract: The force‐time history required to produce a step in the velocity of a circular piston mounted in an infinite baffle is determined with the aid of the Laplace transform. Working from this result, the inverse problem of the velocity response to a step force is calculated approximately. These two results suffice to treat arbitrary distributions of applied force or velocity by Duhamel superposition. The application of the results to a loudspeaker model shows that a system designed for critical damping on the “steady‐state” approximation for the air loading will actually be slightly overdamped in its initial motion, but that the characteristic time during which the design assumption is inadequate is of the order of 10−3 second.
11 citations
TL;DR: When a submerged solid body is subjected to a translational velocity step, it radiates oscillatory, transient acoustic pressures whose natural period is proportional to the travel time of a sound pulse around the accelerated solid as mentioned in this paper.
Abstract: When a submerged solid body is subjected to a translational velocity step, it radiates oscillatory, transient acoustic pressures, whose natural period is proportional to the travel time of a sound pulse around the accelerated solid. Transient velocities displaying more‐complicated distributions over the radiating surface give rise to acoustic‐wave harmonics that, with the exception of the breathing mode, are also oscillatory, and characterized by one or more “natural” frequencies proportional to the ratio of the sound velocity to the characteristic dimension of the radiator. These pressures are analogous to room reverberation attenuated by radiation damping but their phase velocities and attenuation are reminiscent of creeping waves. If the initial velocity impulse is modified by subsequent gradual accelerations (or decelerations) as embodied, for example, in an exponentially decaying or “pulsed CW” velocity, the “reverberant” oscillatory‐sound field is superimposed on an acoustic field whose time history...
4 citations