Related Experiment Video
Updated: Jun 6, 2026
10:16
Synthetic, Multi-Layer, Self-Oscillating Vocal Fold Model Fabrication
Published on: December 2, 2011
Implementation of a constrained Ritz series modeling technique for acoustic cavity-structural systems
1GW Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, USA.
The Journal of the Acoustical Society of America
|November 30, 2010
Summary
This study presents methods to convert complex differential-algebraic equations for acoustic cavities into standard ordinary differential equations. This simplifies analysis of structural acoustics and vibratory systems for improved accuracy.
Area of Science:
- Structural Acoustics
- Vibrational Mechanics
- Computational Physics
Background:
- Prior work utilized Ritz series and Hamilton's principle for acoustic cavity dynamics.
- Governing equations were derived as a differential-algebraic system with velocity continuity constraints.
Purpose of the Study:
- To develop methods for transforming differential-algebraic equations into standard ordinary differential equations.
- To explore different boundary condition enforcement options for structural acoustics analysis.
- To validate solution accuracy and convergence for a 1D waveguide model.
Main Methods:
- Application of Ritz series and Hamilton's principle.
- Formulation of constraint equations for velocity continuity.
- Development of three methods to convert differential-algebraic equations to ordinary differential equations.
- Analysis of a 1D waveguide with an oscillator boundary.
Main Results:
- Successful conversion of governing equations to standard forms.
- Demonstration of options for enforcing boundary conditions.
- Examination of natural frequencies and mode functions for accuracy and convergence.
- Validation of the proposed methods using a 1D waveguide example.
Conclusions:
- The presented methods effectively transform complex acoustic cavity equations.
- The formulation allows flexibility in boundary condition implementation.
- The study confirms the accuracy and convergence of the derived solutions for structural acoustics problems.
Related Concept Videos
01:28Standing Waves in a Cavity
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
01:12Double Resonance Techniques: Overview
Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
Spin decoupling is usually achieved by...
01:14Sound Waves: Resonance
Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
01:24Characteristics of Series Resonant Circuit
Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:
01:07Unsymmetric Loading of Thin-Walled Members: Problem Solving
The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
02:16Resonance and Hybrid Structures
According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.