حل دقيق ميدان صوتي نامتقارن تابش يافته از كره كشسان ضخيم مستغرق

EXACT SOLUTION FOR NONAXISYMMETRIC ACOUSTIC RADIATION FROM A SUBMERGED HOLLOW SPHERE

به‌منظور بررسي خصوصيات تابش صوتي‌ هارمونيك نامتقارن از كره كشسان ضخيم، پر‌شده از سيال ايده‌آل و مستغرق در سيال ايده‌آل ديگر و تحت تحريك‌ هارمونيك دلخواه روي سطوح داخلي و/يا خارجي، از روش نظريه‌ي كشساني سه‌بعدي و نيز روش جداسازي متغيرها بهره گرفته شده است. با به كار‌گيري تبديلات لژاندر و فوريه در دو جهت محيطي حول كره به فرم كلي پاسخ در حوزه‌ي فركانس رسيده و با اعمال شرايط مرزي و حل دستگاه معادلات خطي، حل دقيقي براي ميدان‌هاي فشار سيال داخل و خارج، و نيز جابه‌جايي ميدان جامد كشسان حاصل مي‌‌شود. به‌منظور صحت‌يابي، نتايج حاصله با اطلاعات ارايه‌شده توسط ديگر محققين مقايسه‌ شد. نتايج تحليلي براي چندين مثال عددي بيان شده و تاثير نوع و فركانس تحريك روي فشار براي سيال خارج، الگوي فشار دوردست و قدرت صوتي حاصله مورد بحث قرار گرفته است.

In this paper, an analytical vibro-acoustic model, based on 3D elasticity theory, is formulated for acoustic radiation from a fluid-loaded arbitrary thick hollow sphere driven by internal/external distributed/concentrated harmonic loads. The classical Navier equations of linear elasticity and the Helmholtz equation for the internal/external acoustic domains are employed to present an exact solution for three dimensional non-axisymmetric steady-state sound radiation from an arbitrarily thick hollow elastic sphere submerged in an unbounded compressible ideal acoustic medium, filled with another compressible ideal acoustic fluid, and subjected to arbitrary time-harmonic distributed/concentrated mechanical drives at its internal and/or external surfaces. The Legendre Fourier Transform in the azimuthal and circumferential direction is utilized to obtain an expression for the radiated pressure field in the frequency domain. The analytical results are illustrated with numerical examples, in which air-filled, water-submerged, thick-walled steel spheres are driven by harmonic concentrated or distributed radial internal/external loads. The numerical results reveal the important effects of loading configuration and excitation frequency on the sound radiation characteristics of the submerged structure. Limited cases are considered and the validity of results is established with the aid of comparison with the data in the existing literature. The proposed model is of basic academic interest due to its inherent value as a canonical problem in structural acoustics. It can be of practical value for understanding the fundamental physics of the interaction of acoustic waves with real structures. The presented exact solution can provide an invaluable guide for structural acoustic engineers involved in the dynamic analysis and design of submerged thick-walled spherical vessels, storage tanks, underwater lab rooms, and sonar transducers. It can also serve as a benchmark for comparison to solutions obtained by costly numerical methods or approximate asymptotic approaches. Furthermore, it can aid in solving the corresponding transient radiation problem with different configurations of internal cavity.