Related Experiment Video
Updated: Jul 3, 2026

Measurement of Chladni Mode Shapes with an Optical Lever Method
Published on: June 5, 2020
Statistics of nodal points of in-plane random waves in elastic media
Dmitrii N Maksimov1, Almas F Sadreev
1Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russia.
Abstract:
We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.
Related Concept Videos
Standing Electromagnetic Waves
Suppose a sheet of a perfect conductor is placed in the yz-plane, and a linearly polarized electromagnetic wave traveling in the...
Nodal Analysis
Consider, for instance, a simple circuit composed of three nodes and three resistors, as shown in...
Standing Waves
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Plane Electromagnetic Waves I
The EM field is assumed to be a...
Nodal Analysis with Voltage Sources
Consider a circuit that contains four resistors and two voltage sources, as shown in Figure 1. One of these voltage sources is connected between a...
