Related Experiment Video
Updated: Jul 21, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
A four-element array design for the implementation of the third-order super-cardioid beam pattern
Qiumu Wang1, Yu Lan2, Jun Fan1
1State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
Abstract:
This paper presents a practical acoustic source that can implement the third-order super-cardioid beam pattern (SCBP). Based on the product theorem of the array, the third-order dipole beam pattern can be implemented based on the first-order and second-order dipole beam patterns so that a four-element array is designed. In addition, the second-order dipole beam pattern can also be implemented by the same four-element array. Hence, a four-element array is designed to implement the third-order SCBP. Subsequently, the single-sided radiation flextensional transducer-which is a type of low-frequency underwater acoustic transducer-is selected as the array element of the four-element array that is studied and analyzed by means of the finite element method. Finally, a four-element array prototype is fabricated and tested leading to the conclusion that the special four-element array combined with the product theorem provides a practical way for the implementation of the third-order SCBP.
Related Concept Videos
Load along a Single Axis
Consider a beam of length L subjected to a varying load, which is a combination of parabolic and trapezoidal load distribution along the x-axis. In this case, it is essential to determine the resultant loads, their locations, and...
Design of Prismatic Beams for Bending
Prismatic Beams: Problem Solving
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the designer...
Shear on the Horizontal Face of a Beam Element
Beams with Symmetric Loadings
The M/EI...
Polar Coordinates: Problem Solving

