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This paper focuses on the development of a three-dimensional panel method in time and frequency domains combined with the finite element method for analyzing the hydroelastic responses of rotating marine propellers in the wake of ships. A fully non-penetration boundary condition imposed on the deformed blade surface is conducted, in which the corrections of both the incoming flow velocities and the normal vectors imposed on the deformed and undeformed blade surface are taken into account. The added-mass and -damping matrices due to strongly coupled fluid-structure interaction are considered. Results of the present method are compared with experimental data available in the literature. It is observed that the fully non-penetration boundary condition applied on the deformed blade surface should be imposed to predict the unsteady performance of elastic propellers, which is due to the change of the added damping predicted by considering different non-penetration boundary conditions. [ABSTRACT FROM AUTHOR]

The hydroelastic analysis of the propeller-shafting system in the non-uniform wake is a key step for designing a modern propeller-shafting system. The hydroelastic responses of the propeller-shafting system in the wake of ships are predicted by applying a three-dimensional time-frequency combined panel approach in conjunction with the finite element method. A fully non-penetration boundary condition applied on the deformed blade surface is conducted. The correction of both the incoming flow velocities and the normal vectors imposed on the blade surface of the transient vibration and the equilibrium positions is considered. The added-mass and -damping matrices due to strongly coupled fluid-structure interaction are derived. By comparing the present findings to numerical solutions calculated using the commercial tool Ansys Mechanical, the accuracy of the suggested technique is verified. It is observed that the added damping is higher, and the amplitudes of bearing forces are smaller, by applying the fully non-penetration boundary condition compared with the results obtained by imposing the other two simplified non-penetration conditions. This indicates that the designers need to imply the fully non-penetration condition on the deformed surfaces to predict the hydroelastic dynamics of the propeller-shafting system, especially in the case of high skew propellers. In addition, the amplitudes of the exciting forces after considering the fluid and propeller-shaft system interaction can be larger or smaller than those ignoring the interaction. The results depend on the phase difference and the mode shape. • A fluid-propeller-shafting system using a fully non-penetration condition was studied. • The correction of both the incoming flow velocity and normal vector was considered. • The fully non-penetration condition applied on deformed surfaces should be imposed. • The correction of the incoming flow velocities and the normal vectors is considered. [ABSTRACT FROM AUTHOR]

For a propeller vibrating in a fluid, the added mass and damping coefficients characterize the hydrodynamic forces and moments acting on the propeller, which are of great importance for evaluation of the vibration behaviors of submerged propellers. The present paper is concerned with the development of a numerical method for predicting the added mass and damping coefficients of a rotating marine propeller immersed in water. The three-dimensional panel method in frequency-domain is employed to establish the strongly coupled fluid-structure interaction models of the propellers to compute the added mass and damping coefficients. The relationship between the added mass and damping matrices due to the whole vibration of a rotating propeller and the local vibrations of the propeller blades is considered. Results of the present method are compared with those experimental and numerical data available in the literature. Very good agreement is achieved. The differences of the added mass and damping coefficients due to propeller vibrations of two types are analyzed. The results show that the added mass and damping coefficients of a submerged rotating propeller are functions of the ratio of oscillation frequency of rigid propeller f v to the blade frequency f b , and the advance ratio. In addition, the non-penetration boundary conditions should be imposed on the deformed blade surface for predicting the added mass and damping coefficients m 32 , m 62 , c 32 and c 62 , where m 32 ( c 32 ) and m 62 ( c 62 ) denote mass (damping) coefficients related to the lateral force and bending moment in the z direction induced by the transversal vibration in the y direction. Absolute values of all coefficients in the added mass matrix decrease as the ratio f v / f b is increased, and the absolute values of the coefficients in the added damping matrix increases with an increase in the advance ratio. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytical method for the vibro-acoustic analysis of a functionally graded shell of revolution immersed in an infinite light or heavy fluid. The structural model of the shell is formulated on the basis of a modified variational method combined with a multi-segment technique, whereas a spectral Kirchhoff–Helmholtz integral formulation is employed to model the exterior fluid field. The material properties of the shell are estimated by using the Voigt׳s rule of mixture and the Mori–Tanaka׳s homogenization scheme. Displacement and sound pressure variables of each segment are expanded in the form of a mixed series using Fourier series and Chebyshev orthogonal polynomials. A set of collocation nodes distributed over the roots of Chebyshev polynomials are employed to establish the algebraic system of the acoustic integral equations, and the non-uniqueness solution is eliminated using a combined Helmholtz integral equation formulation. Loosely and strongly coupled schemes are implemented for the structure-acoustic interaction problem of a functionally graded shell immersed in a light and heavy fluid, respectively. The present method provides a flexible way to account for the individual contributions of circumferential wave modes to the vibration and acoustic responses of functionally graded shells of revolution in an analytical manner. Numerical tests are presented for sound radiation problems of spherical, cylindrical, conical and coupled shells. The individual contributions of the circumferential modes to the radiated sound pressure and sound power of functionally graded shells are observed. Effects of the material profile on the sound radiation of the shells are also investigated. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytical approach for predicting the vibration and acoustic responses of an arbitrarily shaped, multilayered shell of revolution immersed in a light or heavy unbounded fluid. A higher-order shear deformable zig-zag shell theory with general shape functions is proposed to describe the displacement field of a multilayered shell with arbitrary curvatures, which provides a theoretical unification of most thin and shear deformable shell theories in the literature. Based on the higher-order zig-zag theory, the structure model of the multilayered shell is formulated by using a modified variational method combined with a multi-segment technique, whereas a Chebyshev spectral Kirchhoff–Helmholtz integral formulation is employed to model the exterior acoustic fluid. The displacement field of the shell and the sound pressure of the fluid are expanded by Fourier series and Chebyshev orthogonal polynomials. Such a treatment reduces the size of the problem and permits a semi-analytical solution for the displacement and acoustic variables. A set of collocation nodes distributed over the roots of Chebyshev polynomials are used to establish the algebraic system of the acoustic integral equations, and the non-uniqueness solution is eliminated by means of interior CHIEF points. Numerical examples are given for vibration and acoustic radiation analyses of multilayered spherical, cylindrical and conical shells. Comparison studies are performed to evaluate the accuracy of various shell theories. The validity of the present method for acoustic analyses of multilayered shells is demonstrated by comparing the results with exact solutions and those obtained from the coupled finite element/boundary element method. Individual contributions of circumferential modes to the radiated sound of multilayered shells are examined. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a semi-analytical procedure for solving linear vibration problems of composite laminated and sandwich hollow bodies of revolution with arbitrary combinations of boundary constraints in the framework of the three-dimensional theory of elasticity. Multilevel partitioning hierarchy, viz., multilayered body of revolution, individual layer and layer segment, is adopted in the theoretical analysis. The appropriate continuity constraints on common interfaces are imposed by means of a modified variational principle combined with the least-squares weighted residual method. The displacement field of each layer segment is characterized by a mixed series of basis functions, i.e., Fourier series and orthogonal polynomials. Numerical examples concerning the free vibrations of composite laminated and sandwich hollow cylinders, cones, and spheres, are presented to show the performance of the method, and comparisons of the present results are made with solutions available in the literature and those obtained from finite element analyses. With regard to the forced vibration problems, steady-state vibration responses of a sandwich hollow cylinder under a uniformly distributed normal harmonic pressure are analyzed, and time-domain solutions of composite laminated and sandwich hollow spheres subjected to various impulsive loads, including a rectangular pulse, a triangular pulse, a half-sine pulse and an exponential pulse, are also examined. Numerical experiments show that the present method is accurate, efficient and reliable for predicting the full spectrum of vibration behaviors of multilayered hollow bodies of revolution. [Copyright &y& Elsevier]

Abstract: This is the first of two companion papers which collectively present a novel semi-analytical method and its associated applications for linear vibration analyses of functionally graded bodies (either hollow or solid) of revolution with arbitrary boundary conditions. A modified variational principle combined with a multi-segment partitioning procedure is employed to formulate the theoretical model in the context of three-dimensional theory of elasticity. Displacement variations of each body segment are represented by Fourier series for the circumferential variable and orthogonal polynomials for the meridional and normal variables. The effective material properties of functionally graded bodies are assumed to vary continuously in the normal direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents, and are estimated by Voigt's rule of mixture and Mori–Tanaka's homogenization scheme. The proposed method is capable of handling various combinations of boundary constraints in a unified fashion, including free, simply-supported, clamped and elastic-supported boundary conditions, and allows the use of different polynomials as displacement functions for meridional and normal variables, such as Chebyshev and Legendre orthogonal polynomials as well as hybrid polynomials. Moreover, it permits to deal with the lower- and high-order vibration problems of functionally graded bodies of revolution subjected to dynamic loads of arbitrary type. In Part I, attention is principally focused on the theoretical development and solution methodology of the method. Comprehensive studies on the convergence, accuracy, stability and efficiency of the method are addressed in Part II, where parametric studies concerning the influences of the geometrical parameters, material distributions as well as boundary conditions on free, steady-state and transient vibrations of functionally graded cylinders, cones and spheres are also investigated in detail. [Copyright &y& Elsevier]

Abstract: A three-dimensional elasticity solution is proposed for determining the free and transient vibrations of composite rectangular parallelepipeds with arbitrary combinations of boundary constraints. The theoretical model is formulated by means of a modified variational principle in conjunction with a multi-segment partitioning procedure based on the three-dimensional linear elasticity theory. The displacement components of each parallelepiped segment are expanded by a triplicate series of orthogonally polynomial functions i.e., the Chebyshev orthogonal polynomials of first and second kind and the Legendre orthogonal polynomials of first kind. To demonstrate the reliability and accuracy of the present methodology, a considerable number of free vibration solutions are given for isotropic and composite rectangular parallelepipeds (including beams, plates, and solids) with different combinations of free, simply-supported, clamped and elastic-supported boundary conditions. The present results are compared with existing experimental and analytical results published in the literature as well as those solutions obtained from finite element analyses. New benchmark solutions are also obtained for composite parallelepipeds. With regard to the transient vibration analyses, composite rectangular parallelepipeds subjected to several time-dependent impulsive loads, including a rectangular pulse, a triangular pulse, a half-sine pulse and an exponential pulse, are investigated. The effects of the fiber orientation, boundary condition as well as the type of impulsive load on the transient responses of composite parallelepipeds are also discussed in detail. [Copyright &y& Elsevier]

The understanding of the fluid-propeller-shafting system's hydroelastic behavior is critical for underwater vehicle vibration and noise reduction. A three-dimensional panel method coupled with a three-dimensional finite element method for analyzing the hydroelastic dynamics of fully coupled propeller and shafting systems in the non-uniform flows is developed. The fully coupled fluid-propeller-shafting model is utilized to assess the applicability of the traditional uncoupled fluid-propeller (elastic vibration)/fluid-propeller (six degrees rigid body oscillation)-shafting models, which consider the elasticities of the blades and shaft separately. It is found that the designers need to consider the elastic coupling effect between the shaft and the propeller, especially in the case of high skew propellers. In addition, the uncoupled model underestimates the fluid-induced damping. • The hydroelastic performance of elastic propeller-shafting system was studied. • A panel method combined with the finite element method were employed. • The coupling effect between the shaft and high skew propellers should be considered. • Fluid induced damping may be underestimated when the coupling effect is ignored. [ABSTRACT FROM AUTHOR]

This paper presents a modified variational method for the dynamic analysis of functionally graded piezoelectric (FGPM) deep curved beams with porosity (FGPP beam) resting on an arbitrary number of discrete elastic foundations (EFs). The material properties including the electrical and porous property are assumed to continuously vary in the thickness direction. A modified principle is developed to impose the continuity constrains on the internal and boundaries of the beam in both mechanical and electric field, which allows any linearly independent, complete basis functions to achieve satisfactory solutions. The shear, inertial and curvature effects of the moderately thick deep curved beams are also introduced in the energy functionals. The superior convergence, accuracy and efficiency of the proposed method are validated by comparing the proposed results with those available in literature. Series of numerical examples are presented for the free and transient vibration of the FGPP beams with different material properties. The influences of the power-law index, porosity, applied electric voltage and the EFs on the natural frequencies and transient dynamic responses of the FGPP beams are examined. Especially, the combined effects of porosity properties with other material properties on the dynamic characteristics of the FGPP beams are firstly presented, which are of significance for optimal design of corresponding smart structures. • A modified variational method is developed for the vibration analysis of FGPP deep curved beams. • The method allows flexible choices of admissible functions for the displacement and electric potential. • The radial-tangential-rotational deformation coupling and electro-mechanical coupling are considered. • An arbitrary number of EFs in radial, tangential and rotational directions can be readily taken into account. • Effects of the power-law index, porosity and the EFs on vibration behaviors of the FGPP beams are presented. [ABSTRACT FROM AUTHOR]

• The hydroelastic response of propeller-shafting system in water was examined. • A coupled 3-D panel method/finite element method was proposed. • Propulsion system includes propeller, shaft, coupling, stern and thrust bearings. • The coupling of the fluid, propeller, and the shaft must be considered. The control of unsteady bearing forces generated by propellers is of great importance for the reduction of vibration and noise of underwater vehicles. This paper is concerned with the development of a numerical method for analyzing the hydroelastic behaviors of fully coupled marine propeller and shafting system immersed in water. A three-dimensional panel method for fluid modeling combined with a finite element method for modeling of the shafting system is developed. The two sets of equations of the structural system and the fluid are strongly coupled by considering the non-penetration boundary condition on the wet surface of the propeller. A modal reduction technique is employed to determine the hydroelastic responses of the coupled fluid-propeller-shafting system, which overcomes the low numerical efficiency of the method due to the asymmetric added matrices of the propeller. The validity of the proposed method is confirmed by comparing the present results with those solutions obtained from finite element analysis. It is found that for the case of the driving force frequency close to the umbrella mode frequencies of the propeller and longitudinal mode frequenices of the shaft, the coupling of the fluid, propeller, and the shaft must be taken into account for predicting the dynamic response of the system. A 3-D panel method coupled with a 3-D finite element method is developed for hydroelastic analysis of elastic propeller-shafting system in water. When the driving force frequency is close to the umbrella mode frequencies of the propeller and longitudinal mode frequencies of the shaft, the coupling of the fluid, propeller, and the shaft must be taken into account for predicting the dynamic response of the system. [Display omitted] [ABSTRACT FROM AUTHOR]