A class of cylindrically symmetric exact solutions of the wave equation. (17th February 2023)

• Record Type: Journal Article
• Authors: Rienstra, Sjoerd W.
• Is Part Of: Journal of sound and vibration. Volume 545(2023)
• Publication Date: 2023-02-17
• Subjects: Two dimensional wave equation -- Exact solutions; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2022.117430
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: A class of analytically exact solutions is derived of the two-dimensional wave equation. The solutions are due to a point source (i.e. a uniform line source in 3D) at the origin r = 0 with polynomial time dependence that starts at t = 0 . They are essentially similarity solutions in the variable c 0 t / r . Their explicit formulation is supported by analytical results for large t and small r behaviour. By taking advantage of linearity, sources of finite duration can be modelled by subtracting from a solution its delayed version. For illustration, some examples are given graphically as functions of r, of t, and of t − r / c 0, for a number of points in time and location, respectively. Highlights: A class of analytically exact solutions of the 2D wave equation with a point source. Explicit examples for pulse type sources. Asymptotic behaviour of solutions for general and pulse type sources. Graphical examples.