Ministry of Science and
Higher Education
of the Russian Federation
Russian Academy of Sciences
Department of power engineering, mechanical engineering, mechanics and control processes
Mechanical Engineering Research
Institute of the Russian
Academy of Sciences
for english » Research Departments » Department of Vibrational Acoustics of Machines » Structure of the Department » Wave Mechanics of Machines Lab. » Scientific Achievements » Development of analytical methods for calculating the forced oscillations of the hull of a submarine, represented as a finite elastic cylindrical shell in a liquid emitted by the hull of the primary and secondary fields and their active damping
Development of analytical methods for calculating the forced oscillations of the hull of a submarine, represented as a finite elastic cylindrical shell in a liquid emitted by the hull of the primary and secondary fields and their active damping
The following is being developed: Physico-mathematical model (FMM) of oscillations and radiation of cylindrical shells in liquids, algorithms and programs for calculating the primary and secondary hydroacoustic fields of the submarine created by the object in the low-frequency sound range (up to 500 Hz).
Developments are aimed at solving the task of detecting an object in the shallow sea using low-frequency sonar (NCHGL). The need to solve the problem is dictated by the following circumstances: a) the expected zones of action are shallow seas; B) low-frequency sonar is effective in the shallow sea (high-frequency does not work); C) resonance oscillations of the elastic body of the object are strongly manifested at low frequencies; D) at low frequencies the passive coating of the hull does not work, so it is impossible to do without active quenching methods.
In the USA, since the 1990s, active methods of detecting objects (submarines) on the secondary hydroacoustic field have been intensively developed, and for acoustic protection of objects, "intelligent (smart) coatings" are being developed.
The secondary field is understood as the following (Fig. 1): Aprobing sound signal from a radiating antenna is incident on an object from a certain point in space. Under the impact of this signal, forced oscillations of the object's hull are generated, creating a scattered field. The scattered field is recorded by receiving antennas located at other points in space with different observation angles, i.e. in bistatic (or multistatic) mode. The object itself (a submarine) can be noiseless (by the primary field), but it is detected by its acoustic shadow, i.e. by the secondary (re-emitted) field.
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| Fig. 1 |
The characteristic features of the dynamic model being developed and the method of solving it, which determine the novelty and usefulness:
- The basis of the dynamic model is a finite, elastic, cylindrical shell with free ends that floats in a fluid (unlike an infinite shell or with boundary Navier boundary conditions),
- The object in the complete dynamic model is represented in the form of a shell structure consisting of compartments modeled by cylindrical shells connected by bulkheads. The bulkheads are modeled by elastic rings on which the amortized equipment is fixed. The equipment is modeled by concentrated masses. Cylindrical shells of compartments are supported by frames (Fig. 2).
- Analytical and numerical-analytical methods of calculation (in contrast to the finite element method) are applied.
- A method for solving the integro-differential equation is proposed, and a dispersion equation is obtained that determines the "wet roots" for a finite cylindrical shell in a fluid.
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| Fig. 2 |
Theoretical basis. The complete equations of the theory of elasticity of cylindrical shells are used [1]. When determining the fluid pressure on the surface of the shell and solving the diffraction problem, papers [2,3] are used. The secondary field in the remote zone is determined by the Kirchhoff-Green integral formula using [3].
Experimental studies were not conducted.
As a result of calculations, the parameters of the vibro-acoustic state of the hull of the object (the shell design model) and the characteristics of the secondary hydroacoustic far zone are determined:
1. Frequency response of hull oscillations in accelerations of 4 coordinates (U, V, W, W '). (Fig. 3).
2. Forms of oscillations of the hull according to the same coordinates.
3. Angular distribution of the pressure of the scattered field along the observation angle.
4. Frequency response of the maximum pressure levels (based on the calculation of angular distributions of pressure) (Fig. 4).
5. Directional diagrams of the secondary field by the sum of the first 15 circle harmonics (Fig. 5).
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| АЧХ fluctuations | АЧХ Рmax pressures |
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| Fig. 4 | |
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| Fig. 5 | |
Developed methods for calculating primary and secondary fields can be used for acoustic design of objects and development of active methods of field damping. The developed mathematical model of radiation of the submarine's hull can be used as an object of observation in the development of a computer model of a low-frequency geolocation system.
