Finite Cylindrical Shell Research Articles

Broadband vibration isolation in cylindrical shells embedded with total reflection elastic meta-shells

In this research, we propose a pioneering conceptual design paradigm of elastic meta-shells for broadband elastic wave control in cylindrical shells. We theoretically reveal the mechanism for wave isolation in cylindrical shells, which arises from the closure of all transmission channels (i.e., total reflection) when 0th-order diffraction is the only remaining diffraction mode. In addition, to solve the dynamic coupling behavior between multi-order diffraction modes, we extend the acoustic mode-coupling theory to elastic waves in cylindrical shells. Based on the diffraction theory and multiple reflection effect, we construct a total reflection elastic meta-shell and numerically demonstrate efficient broadband elastic wave isolation in the frequency range of 5 k–7 kHz. Finally, the vibration isolation performance is experimentally verified by embedding a total reflection elastic meta-shell in a finite thin-walled cylindrical shell waveguide. Results confirm the feasibility of the elastic meta-shell design concept and its ability to achieve fully passive, high-efficiency, and broadband vibration isolation. Our vibration isolation strategy could broaden the applicable scope of elastic meta-structures and open new horizons for vibration isolation, mechanical energy filtering, and elastic wave signal processing in cylindrical shells.

The assignment of zero sound pressure frequencies using measured sound pressure receptances and structural receptances

In structural receptances, the zeros (antiresonances) define those frequencies at which vibrations disappear. In this paper, the zero sound pressure frequency is defined as the frequency at which the sound pressure is zero at certain locations. A method for the assignment of zero sound pressure frequencies using measured sound pressure receptances and structural receptances is proposed through two forms of structural modifications: rank-one modification and higher-rank modification. In rank-one modification, the sound pressure receptances of the modified structure are obtained by using the structural receptances with the Sherman-Morrison formula. In higher-rank modification, the modifications are determined by an analysis of the null space of a matrix consisting of structural receptances and sound pressure receptances. This method requires only a few structural receptances and sound pressure receptances, and no structural models or acoustic models are needed. Numerical examples involving a baffled plate vibrating in air and a fluid-loaded finite cylindrical shell are used to demonstrate the methods. Numerical results show that the zero sound pressure frequencies can be assigned to specific frequencies by structural modification.

Отражение звука от упругой конечной цилиндрической оболочки различной относительной длины

A calculation of the sound pressure frequency dependences scattered by a finite elastic cylindrical shell placed in a liquid medium is presented. The shell has hemispherical ends and is considered either hollow or filled with gas or liquid. The scattered sound pressure under conditions of hydroelastic contact on the shell surfaces is found by jointly using the Kirchhoff integral and the integral equation for the elastic medium displacement vector, obeying the Lamé equation. Boundary conditions regarding stresses and displacements are formulated for each of the shell contact surfaces with the external and internal environments. Considerating approach is based on the numerical transformation of continuous integral equations into a system of linear algebraic equations using curvilinear isoparametric boundary elements. In this case, the elements geometry and the main variables (displacements and stresses) are specified using the same interpolating relations (shape functions). The scattered sound pressure frequency dependences are calculated and analyzed for various ratios of the length and shell diameter.

Acoustic radiation from a baffled finite shell in an underwater waveguide

Analytical modelling of vibroacoustic systems can help us to understand the physical phenomena involved in more complex problems, and it provides a benchmark solution and reference upon which more complex systems can be built. In the present work, the system of interest consists of a finite elastic cylindrical shell inserted in infinitely rigid cylindrical baffles and immersed in an underwater acoustic waveguide. The latter consists of a finite fluid layer bounded by an upper free surface and a lower rigid floor. In such a fluid domain, the acoustic waves radiated from the excited shell will exhibit reflections off the boundaries. This phenomenon is modelled by the image-source theory and embedded in the fluid loading term, which intervenes in the shell equations. Investigations into the influence on the finiteness of the elastic shell, types of supports (i.e., simply supported, clamped, free, and combinations of these), and depth of the waveguide on the shell’s acoustic radiation are presented.

Investigation of sound transmission through a finite length cylindrical shell in the presence of an exterior turbulent boundary layer

This paper studies sound transmission through a thin cylindrical shell of finite length. The structure is subjected to an exterior turbulent boundary layer (TBL) excitation and the boundary conditions of its two ends are considered as simply-supported. The classical shell theory (CST) is employed to derive wave propagation in the cylindrical shell, and the Corcos model is applied to describe pressure fluctuation due to TBL. According to the existence of two axial and radial modes, a complete convergence study is presented. To examine sound transmission through the structure, a comprehensive parameters study is provided on the resulting power spectral density (PSD) of the kinetic energy. To validate the results of the present method, the statistical energy analysis (SEA) method is used. For this purpose, modeling is performed by SEA in VA One software, which shows the high accuracy of the results of the present method. The analytical predictions suggest that the sound insulation performance of such a finite length structure is enhanced considerably by increasing the thickness of the shell in a broad-band frequency range. Similar effects on sound transmission are observed for Young’s modulus and density of the shell particularly in the low and high-frequency ranges, respectively. Whereas, enhancing the turbulent pressure and freestream velocity adversely affects sound radiation into the structure.

Modelling and analysis of electromagnetic vibration in long sheet secondary tubular linear induction motors

AbstractThis paper aims to clarify the behaviour and mechanism of electromagnetic vibration in long sheet secondary tubular linear induction motors (LSS‐TLIMs). Firstly, the spatial and temporal characteristics of electromagnetic force acting in the stator are analysed. Secondly, based on the wave propagation method, an analytical model is established to calculate the vibration response of the stator, which is simplified as a finite cylindrical shell. The accuracy of the proposed model, as well as the rationality of the simplification, are verified by 3D FEM simulation. It is indicated that the electromagnetic vibration response of LSS‐TLIMs mainly depends on the “axial breathing mode” (ABM) and corresponding “modal participation factor”. Moreover, the influences of the spatial distribution of electromagnetic force and the structural dimensions on the vibration are investigated. Finally, the “static vibration test” is performed to validate the above analysis. It is concluded that, compared with a rotary motor, the low‐frequency vibration of LSS‐TLIMs can be easily controlled since the natural frequency of ABMs tends to be much higher than that of the circumferential mode.

Vibration and Sound Radiation of Cylindrical Shell Covered with a Skin Made of Micro Floating Raft Arrays Excited by Turbulence

To reduce the vibration and sound radiation of underwater cylindrical shells, a skin composed of micro floating raft arrays and a compliant wall is proposed in this paper. A vibroacoustic coupling model of a finite cylindrical shell covered with this skin for the case of turbulence excitation is established based on the shell theories of Donnell. The model is solved with the modal superposition method to investigate the effects of the structural parameters of micro floating raft elements on the performance of reducing vibration and sound radiation of the cylindrical shell of this skin. The results indicate that increasing the stiffness ratio, damping ratio, mass ratio, or decreasing the interval between micro floating raft elements can improve the vibration and sound radiation reduction performance of this skin over the frequency range 0~2000 Hz. Moreover, the mean quadratic velocity level and sound radiation power level of the finite cylindrical shell with this skin can be reduced by 12.00 dB and 9.65 dB respectively compared to the finite cylindrical shell with homogeneous viscoelastic coating in the frequency range from 0~2000 Hz, implying a favorable performance of this skin for reducing the vibration and sound radiation of cylindrical shells.

Determination and analysis of the thermoelastic state of layered orthotropic cylindrical shells

The fundamental relations of the quasi-static problem of thermoelasticity are written for a finite layered orthotropic cylindrical shell of an antisymmetric structure. Under convective heat transfer on the surfaces of this shell and under a linear dependence of temperature on the transverse coordinate, the basic system of equations for the integral characteristics of temperature is given. The method is proposed for solving the formulated problems of thermoelasticity and thermal conductivity, using the double finite integral Fourier transform with respect to the corresponding coordinates of the transformation and Laplace transform with respect to the time. The results of a numerical analysis of temperature, deflections, and stresses for the considered two-layer shell hinged at the edges under local heating by the initially specified temperature field are presented.

Dumbbell-Shaped Damage Effect of Closed Cylindrical Shell Subjected to Far-Field Side-On Underwater Explosion Shock Wave

In naval warfare, underwater explosion (UNDEX) shock waves significantly influence the stability and safety of the pressure hull structure of the equipment. This study investigated the unique dynamic buckling of a closed cylindrical shell subjected to a far-field side-on UNDEX shock wave using a three-dimensional numerical simulation based on acoustic–structural arithmetic. In particular, the flow-field response characteristics, plastic deformation, and yield characteristics of the cylindrical shell were determined under the influence of the UNDEX shock wave. Subsequently, the failure mode of the cylindrical shell was analyzed to propose the dumbbell-shaped damage effect. The results revealed that when the UNDEX shock wave encounters a finite cylindrical shell, the fluid exhibits a perturbation such as pressure division, stress wave deflection, and flow in the surroundings of the circular cylinder. However, the fluid cannot produce a sizeable instantaneous displacement that yields certain strong constraints at both ends of the cylindrical shell. These constraints generate an irregular distribution of the flow field pressure, and the cylindrical shell tends to exhibit an “arch” deformation along the direction of shock wave propagation. Owing to the flow surrounding the circular cylinder, a negative pressure zone is generated in the flow field at both ends of the cylindrical shell, which induces a “sucking disc” shape at both ends of the cylindrical shell and ultimately produces a dumbbell-shaped damage effect. The present findings will aid in the structural design and impact resistance of submarines, unmanned undersea vehicles, and additional equipment under the impact load of the UNDEX.

Vibroacoustic modeling and radiation impedances of a finite cylindrical shell filled with flowing fluid

This paper presents an analytical study of the acoustic radiation modeling of a finite cylindrical shell with infinite rigid extensions. An infinite fluid at rest surrounds the shell, which contains a flowing fluid and excited by a harmonic driving force. The external pressure is calculated with a single layer integral equation, while the internal one is obtained with both a single layer integral equation on the shell surface and a double layer on an internal surface presenting pressure discontinuity. The modeling takes into account the shell modal behavior, the fluid loading and the radiation in both internal and external medium. The resolution is made by expanding the shell motion in the modes of the simply supported shell in vacuo. The main presented results are dealing with the internal radiation impedances and the influence of the flowing fluid (heavy and/or light) on the acoustic power radiated in both external and internal medium.

An Analytical Solution for the Vibration and Far-Field Sound Radiation Analysis of Finite, Semisubmerged Cylindrical Shells

The vibration response and far-field sound radiation of a semisubmerged, finite cylindrical shell with low-frequency excitation are studied. The solution to this problem can be divided into two steps. The first step is to apply the wave propagation approach to determine the vibration response of the cylindrical shell. In the cylindrical coordinate system, the Flügge shell equations and Laplace equation are used to describe the cylindrical shell and surrounding fluid so that the vibration responses of the shell can be addressed analytically. The fluid free surface effect is taken into account by applying the sine series to force the velocity potential on the free surface to be zero. Furthermore, compared with the FEM (the finite element method), the present method is not only reliable but also effective. In the second step, the far-field sound radiation is solved by the Fourier transform technique and the stationary phase method in accordance with the vibration responses of the shell from the previous step. The boundary element method is applied to validate the reliability of the acoustical radiation calculation. The circumferential directivity of far-field sound pressure is discussed, and it is found that the maximum value of the sound pressure always appears directly under the structure when the driving frequencies are relatively low. Besides, in consideration of simplicity and less computation effort, the present method can be used for the rapid prediction of the vibration and far-field sound pressure of a semisubmerged cylindrical shell with low-frequency excitation.

Near-field target strength of finite cylindrical shell in water

In this study, near-field acoustic scattering from a finite elastic cylindrical shell is investigated based on a previous cylinder method. An analytic expression for scattered pressure is derived in the form of a Kirchhoff–Helmholtz integral with the assumption that the field induced on the cylinder surface is determined by the canonical solution of an infinite elastic cylindrical shell. A useful approximate solution of the integral is obtained in the near-field zone of the receiver and then applied to formulate the near-field target strength. The results of the approximate solution are compared with the full numerical solution and experimental data measured using a linear frequency-modulated continuous-wave pulse at a frequency range of 5 to 25 kHz in a water tank in a laboratory. The results indicate consistency, except for some discrepancies due to experimental restrictions. The approximate solution is validated via finite element modeling using COMSOL Multiphysics. Moreover, the range dependency of the near-field formula and the effect of the end-caps in the finite cylindrical shell are investigated through simulations.

Investigation of Low‐Frequency Sound Radiation Characteristics and Active Control Mechanism of a Finite Cylindrical Shell

In this paper, the radiation characteristics and active structural acoustic control of a submerged cylindrical shell at low frequencies are investigated. First, the coupled vibro‐acoustic equations for a submerged finite cylindrical shell are solved by a modal decomposition method, and the radiation impedance is obtained by the fast Fourier transform. The modal shapes of the first ten acoustic radiation modes and the structure‐dependent radiation modes are presented. The relationships between the vibration modes and the radiation modes as well as the contributions of the radiation modes to the radiated sound power are given at low frequencies. Finally, active structural acoustic control of a submerged finite cylindrical shell is investigated by considering the fluid‐structure coupled interactions. The physical mechanism of the active control is discussed based on the relationship between the vibration and radiation modes. The results showed that, at low frequencies, only the first several radiation modes contributed to the sound power radiated from a submerged finite cylindrical shell excited by a radial point force. By determining the radiation modes that dominate the contribution to the radiated sound, the physical mechanism of the active control is explained, providing a potential tool to allow active control of the vibro‐acoustic responses of submerged structures more effectively.

Estimate of the Impedance of a Finite Cylindrical Shell for the Exponential Mode of Displacement

An algorithm for computing the impedance of a finite cylindrical shell submerged into liquid is developed. The formula obtained allows estimating the maximum and asymptotic values of impedance in dependence on the frequency and wave parameter of the exponential mode of the radial displacement of the shell.

Forced Oscillations of a Finite Cylindrical Shell Excited by Discrete Forces

In this paper, we propose a numerical-analytical method for calculating forced oscillations of a shell structure composed of a set of finite elastic cylindrical shells and elastic rings, to which discrete disturbing forces are applied. Examples of calculating the amplitude–frequency characteristics and vibration modes of the shell structure are given.

Analytical and experimental study of the vibro-acoustic behavior of a semi-submerged finite cylindrical shell

The vibro-acoustic behavior of a semi-submerged finite cylindrical shell is studied theoretically and experimentally. An analytical form of the vibro-acoustic coupling equation is developed using the wavenumber transformation and separation of variables for the sound pressure and the mode expansion for the shell's motion. The far-field radiation sound pressure is derived by utilizing the stationary-phase approximation. The radial velocity, radiated sound power, and sound pressure directivities (including the circumferential and axial directivities) from analytical models are compared with numerical and experimental results to verify the method. The assumption that the shell is terminated by semi-infinite rigid baffles is the main reason for the deviations between the analytical and experimental results. Below the ring frequency, acoustic radiation from a semi-submerged finite cylindrical shell occurs primarily because the air–liquid demarcation points on the shell surface act as radiation sources. Therefore, the circumferential and axial directivity patterns of a semi-submerged finite cylindrical shell can be approximated as a superposition of two in-phase dipoles formed by the air–liquid demarcation points and as a superposition of two in-phase dipole line sources, respectively. Simple formulas are derived to predict the circumferential and axial directivity patterns. This is a new and simplified approach for predicting the directivity patterns of a semi-submerged finite cylindrical shell. The vibro-acoustic behavior of a semi-submerged finite cylindrical shell differs from that of a submerged shell, especially the circumferential directivity pattern due to the reflection from the free surface.

Influence of the Position of Artificial Boundary on Computation Accuracy of Conjugated Infinite Element for a Finite Length Cylindrical Shell

Structural finite element coupled with the conjugated infinite element method is an efficient numerical technique for solving the acoustic radiation problem due to the vibration of underwater objects. However, for large complex structures, the total acoustic mesh would become very large if the artificial boundary is too far away from the structural wetted surface. Thus, the calculation time can become too long to confine the application of the conjugated infinite element method. On the other hand, if the artificial boundary is close to the structural wetted surface, it will lead to computation accuracy losing due to the near-field effects. Consequently, it is essential to present some guidelines based on the physical mechanism of structural acoustics to choose a suitable artificial boundary that optimizes calculation accuracy and efficiency. In present work, the evanescent wave theory of an infinite length cylindrical shell is adopted to theoretically analyze the decay characteristic of evanescent waves in near field. Then, the effect of the position of artificial boundary on computation accuracy of conjugated infinite element for a finite length ring-stiffened cylindrical shell is numerically investigated. Results suggested that for the cylindrical shell mentioned in this study, the artificial boundary can be placed at least 0.4 times the acoustic wavelength away from the structural wetted surface. What’s more, for high frequencies or large-scale structures, the required non-dimensional distance between the artificial boundary and the structural wetted surface increases.

Forced Vibrations of a Cylindrical Shell Immersed in Liquid

A numerical-analytical method is proposed for calculating the forced vibrations of a shell structure immersed in liquid. The structure is a set of finite elastic cylindrical shells and elastic rings to which concentrated discrete forces are applied. Examples of a comparative calculation of the frequency response and vibration modes of the shell structure in a vacuum and in liquid are given.

Acoustic performance prediction of a multilayered finite cylinder equipped with porous foam media

This paper presents an analytical model to embed porous materials in a finite cylindrical shell in order to obtain the sound transmission loss coefficient. Although the circumferential modes are considered only for calculating the amount of the transmitted noise through an infinitely long cylinder, the present study employs the longitudinal modes in addition to circumferential ones to analyze the vibroacoustic performance of a simply supported cylinder subjected to the porous core based on the first order shear deformation theory. To achieve this goal, the structure is immersed in a fluid and excited by an acoustic wave. In addition, the acoustic pressures and the displacements are developed in the form of double Fourier series. Since these series consist of infinite modes, it is essential to terminate this process by considering adequate modes. Hence, the convergence checking algorithm is employed in the form of some three-dimensional configurations with respect to length, frequency and radius. Afterwards, some figures are plotted to confirm the accuracy of the present formulation. In these configurations, the obtained sound transmission loss from the present study is compared with that of the infinite one. It is shown that by increasing the length of the structure, the results are approached to sound transmission loss of the infinite shells. Moreover, a new approach is proposed to show the transverse displacement of a finite poroelastic cylinder at different frequencies. Based on the outcomes, it is found that by enhancing the length of the poroelastic cylinder, the amount of the transmitted sound into the structure is reduced at the high frequency domain. However, the sound insulation property of the structure is improved at the low frequency region when the radius of the shell is decreased.

Dispersion Relation for a Finite Cylindrical Shell Immersed in a Liquid

The dispersion relation is obtained for a free finite cylindrical shell immersed in a liquid. An example of calculating the roots of the dispersion relation is given.