
Analytical solution of black hole equation and some consequences
A complete set of fundamental solutions of the bending oscillating rod equation, sharpened by parabolic law, is suggested. Cutoff frequency, from which and above, this parabolically sharpened rod becomes a black hole, capable to absorb vibrational energy, is defined. These solutions
are used to calculate the elements of the input matrix impedance of this rod. For an ideal black hole, corresponding to the sharpening rod strictly to zero value, the impedance is determined by use only two fundamental solutions. For a real black hole, corresponding to the cutting of the sharpening
at a finite (non-zero) thickness, the impedance is determined by all four fundamental solutions. Spectrum of eigenfrequencies of a real black hole is calculated. A modified WKB approximation solutions of a rod equation with arbitrary smoothly varying cross-section is proposed.
The requested document is freely available to subscribers. Users without a subscription can purchase this article.
- Sign in below if you have already registered for online access
Sign in
Document Type: Research Article
Publication date: 21 August 2016
The Noise-Con conference proceedings are sponsored by INCE/USA and the Inter-Noise proceedings by I-INCE. NOVEM (Noise and Vibration Emerging Methods) conference proceedings are included. All NoiseCon Proceedings one year or older are free to download. InterNoise proceedings from outside the USA older than 10 years are free to download. Others are free to INCE/USA members and member societies of I-INCE.
- Membership Information
- INCE Subject Classification
- Ingenta Connect is not responsible for the content or availability of external websites
- Access Key
- Free content
- Partial Free content
- New content
- Open access content
- Partial Open access content
- Subscribed content
- Partial Subscribed content
- Free trial content