Minimisation of the sound power radiated by a submarine through optimisation of its resonance changer

An important cause of sound radiation from a submarine in the low frequency range is fluctuating forces at the propeller. The forces are transmitted to the hull via the shaft and the fluid. Sound radiation occurs due to hull and propeller vibrations as well as dipole sound radiation caused by the operation of the propeller in a non-uniform wake. In order to minimise sound radiation caused by propeller forces, a hydraulic vibration attenuation device known as a resonance changer can be implemented in the propeller/shafting system. In this work, cost functions that represent the overall radiated sound power are investigated, where the virtual stiffness, damping and mass of the resonance changer were chosen as design parameters. The minima of the cost functions are found by applying gradient based optimisation techniques. The finite element and boundary element methods are used to model the structure and the fluid, respectively. The adjoint operator is employed to calculate the sensitivity of the cost function to the design parameters. The influence of sound radiation due to propeller vibration on the optimisation of the resonance changer as well as the influence of the reduction in amplitude for higher harmonics of the blade-passing frequency on the control performance is investigated.     

Reduction of vibration and noise radiation of an underwater vehicle due to propeller forces using periodically layered isolators

Using periodic structure theory, the suppression of vibration and noise radiation from an underwater vehicle due to excitation from propeller forces is investigated. The underwater vehicle is modelled in two parts (the hull and the propeller/shafting system). A model of the propeller/shafting system is constructed using a modular approach and considers the propeller, shaft, thrust bearing, isolation structure and foundation. Different forms of isolator are considered – a simple spring-damper system, a continuous rod and a periodically layered structure. The dynamic properties of the underwater vehicle and the isolation performances of various isolators are compared and analysed. The stop band properties of the periodic isolator are used to enhance the passive control performance. Furthermore, an integrated isolation device is proposed that consists of the periodic isolator and a dynamic absorber, and its isolation performance is investigated. The effects of the absorber parameters on the performance of the integrated device are also analysed. Finally, the radiated sound pressure is calculated to verify the attenuation. The numerical results show that the vibration and noise radiation are greatly attenuated in the stop bands. By optimising the design of the periodic isolators and its integrated structures, the suppression of the vibration and noise radiation can be improved effectively.     

Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

Non-cavitating propeller noise modeling and inversion

Marine propeller is the dominant exciter of the hull surface above it causing high level of noise and vibration in the ship structure. Recent successful developments have led to non-cavitating propeller designs and thus present focus is the non-cavitating characteristics of propeller such as hydrodynamic noise and its induced hull excitation. In this paper, analytic source model of propeller non-cavitating noise, described by longitudinal quadrupoles and dipoles, is suggested based on the propeller hydrodynamics. To find the source unknown parameters, the multi-parameter inversion technique is adopted using the pressure data obtained from the model scale experiment and pressure field replicas calculated by boundary element method. The inversion results show that the proposed source model is appropriate in modeling non-cavitating propeller noise. The result of this study can be utilized in the prediction of propeller non-cavitating noise and hull excitation at various stages in design and analysis.     

Torsional vibration of crankshaft in an engine–propeller nonlinear dynamical system

Theoretical and experimental studies on torsional vibration of an aircraft engine–propeller system are presented in this paper. Two system models—a rigid body model and a flexible body model, are developed for predicting torsional vibrations of the crankshaft under different engine powers and propeller pitch settings. In the flexible body model, the distributed torsional flexibility and mass moment of inertia of the crankshaft are considered using the finite element method. The nonlinear autonomous equations of motion for the engine–propeller dynamical system are established using the augmented Lagrange equations, and solved using the Runge–Kutta method after a degrees of freedom reduction scheme is applied. Experiments are carried out on a three-cylinder four-stroke engine. Both theoretical and experimental studies reveal that the crankshaft flexibility has significant influence on the system dynamical behavior.     

Structural and acoustic responses of a fluid-loaded cylindrical hull with structural discontinuities

This paper studies the low frequency vibrational behaviour and radiated sound of a submarine hull under axial excitation. The submarine is modelled as a fluid-loaded cylindrical shell with internal bulkheads and ring-stiffeners and closed at each end by circular plates. A smeared approach is used to model the ring stiffeners. The external pressure acting on the hull due to the fluid loading is calculated using an infinite model and is shown to be a good approximation at low frequencies. The radiated sound pressure is obtained by considering the finite cylindrical hull to be extended by two semi-infinite rigid baffles. The sound pressure is then only due to the radial displacement of the cylindrical shell, without taking into account the scattering at the finite ends. The main aim of this paper is to observe the influence of the various complicating effects such as the bulkheads, ring-stiffeners and fluid loading on the structural and acoustic responses of the finite cylindrical shell. Results from the analytical models presented in this paper are compared to the computational results from finite element and boundary element models.     

Dynamic behavior and sound transmission analysis of a fluid-structure coupled system using the direct-BEM/FEM

A direct-BEM/Fem method was proposed to analyze the vibration and acoustic radiation characteristics of a submerged structure. Model parameters of the structure and the fluid-structure interaction due to surrounding water were analyzed by using FEM and direct BEM. Vibration velocity of the outer hull surface and underwater sound pressure were computed through modal superposition technique. The direct-BEM/FEM method was first validated by analyzing a submerged cylindrical shell, then was used to analyze the vibro-acoustic behavior of a submarine stern structure. The results have demonstrated the direct-BEM/FEM method is more effective than FEM in computing the underwater sound radiation of the stern structure.     

Active control of sound radiated by a submarine in bending vibration

This paper theoretically investigates the use of inertial actuators to reduce the sound radiated by a submarine hull in bending vibration under harmonic excitation from the propeller. The radial forces from the propeller are tonal at the blade passing frequency and are transmitted to the hull through the stern end cone. The hull is modelled as a fluid loaded cylindrical shell with ring stiffeners and two equally spaced bulkheads. The cylinder is closed by end-plates and conical end caps. The actuators are arranged in circumferential arrays and attached to the prow end cone. Both Active Vibration Control and Active Structural Acoustic Control are analysed. The inertial actuators can provide control forces with a magnitude large enough to reduce the sound radiated by the vibrations of the hull in some frequency ranges.     

Dynamics modelling of a flexible hub-beam system with a tip mass

This paper presents a finite-element model for a flexible hub-beam system with a tip mass. Both viscous damping and air drag force are introduced into this model. The complete coupling between the system rigid and flexible degrees of freedom is allowed since the start of the formulation and developing the system kinematic variables. Based on deformation theory and geometric constraints, a second order approximation for the displacement field is proposed and the dynamic stiffening is accounted for. Hamilton's principle is utilized in deriving the equations of motion. The corresponding dynamics models of the tip mass and damping forces are developed in a consistent manner through formulating their energy expressions and applying Hamilton's principle. The finite element method is employed for spatial discretization due to its versatility, high accuracy and convergence. Numerical simulations show that the second order term in deformation field can have significant effect on dynamics behavior of flexible multibody systems. It is also shown that the traditional linear model cannot account for dynamic stiffening and may lead to erroneous result in some high-speed systems because the deformation field commonly used in structural dynamics is straight employed in this model. In contrast, the developed model (CCM) based on the second order deformation field can predict valid results. The effects of tip mass and damping on dynamics behavior of the hub-beam system are also discussed.     

Propeller sheet cavitation noise source modeling and inversion

Propeller sheet cavitation is the main contributor to high level of noise and vibration in the after body of a ship. Full measurement of the cavitation-induced hull pressure over the entire surface of the affected area is desired but not practical. Therefore, using a few measurements on the outer hull above the propeller in a cavitation tunnel, empirical or semi-empirical techniques based on physical model have been used to predict the hull-induced pressure (or hull-induced force). In this paper, with the analytic source model for sheet cavitation, a multi-parameter inversion scheme to find the positions of noise sources and their strengths is suggested. The inversion is posed as a nonlinear optimization problem, which is solved by the optimization algorithm based on the adaptive simplex simulated annealing algorithm. Then, the resulting hull pressure can be modeled with boundary element method from the inverted cavitation noise sources. The suggested approach is applied to the hull pressure data measured in a cavitation tunnel of the Samsung Heavy Industry. Two monopole sources are adequate to model the propeller sheet cavitation noise. The inverted source information is reasonable with the cavitation dynamics of the propeller and the modeled hull pressure shows good agreement with cavitation tunnel experimental data.     

Comparison between the discrete and finite element methods for modelling an agricultural spray boom—Part 1: Theoretical derivation

The paper develops a systematic procedure for modelling linear flexible multibody structures of which the flexible parts are a composition of beams. The theory of mechanics of solids is fit into a general expression of virtual work, linking rigid-body motions with flexible deformations of the different bodies. A comparison is made with the finite element method for approximating the behaviour of the flexible bodies. It turns out that the discrete element method boils down to a particular selection of shape functions of which the mass matrix is inconsistent with the flexibility matrix. Furthermore, contrary to the finite element method, only point forces can be applied.     

Active isolation of a flexible structure from base vibration

This paper presents a theoretical and experimental investigation into an active vibration isolation system. Electromagnetic actuators are installed in parallel with each of four passive mounts, which are placed between a flexible equipment structure and a base structure which is either flexible or rigid. Isolation of low-frequency vibration is studied, so that the passive mounts can be modelled as lumped parameter springs and dampers. Decentralized velocity feedback control is employed, where each actuator is operated independently by feeding back the absolute equipment velocity at the same location. Good control and robust stability have been obtained both theoretically and experimentally for the multichannel control systems. This is to be expected if the base structure is rigid, in which case the actuator and sensor are, in principle, collocated and the control system implements a skyhook damper. With a flexible base structure, however, collocation is lost due to the reactive actuator force acting on the base structure, but the control system is still found to be robustly stable and to perform well. Attenuations of 20 dB are obtained in the sum of squared velocities on the equipment structure at the rigid-body mounted resonance frequencies. In addition, attenuations of up to 15 dB are obtained at the resonance frequencies of both the low order flexible modes of the base structure and the equipment structure.     

Simulation and assessment of stray light effects in infrared cameras using non-sequential ray tracing

In this article, we have evaluated the stray light effects in infrared cameras operating in the 3–5 μm waveband having cooled focal plane array detectors. A non-sequential ray tracing method is used to model the multiple reflections from polished lens surfaces as well as diffused scattering from rough mechanical surfaces inside the camera housing. The flux signature on the detector surface due to the self-emission of in-band radiation from the lenses and camera housing is calculated. The flux signature due to sources beyond the nominal field-of-view of the camera is also calculated. Light splitting into multiple diffraction orders from diffractive lens surfaces is taken into account both in the transmission and the reflection paths. The wavelength and angle dependent reflection coefficient of the anti-reflection coatings on the polished lens surfaces is taken into account. The effect of local heating of camera mounts on the stray light signature on the detector surface is also evaluated. The results show that using the non-sequential ray tracing method, useful predictions can be made for the stray light signature in the infrared cameras. Such calculations can be used to identify areas in the camera housing which need to be temperature stabilized to reduce their detrimental stray-light signature.     

Coupled dynamic analysis of a single gimbal control moment gyro cluster integrated with an isolation system

Control moment gyros (CMGs) are widely used as actuators for attitude control in spacecraft. However, micro-vibrations produced by CMGs will degrade the pointing performance of high-sensitivity instruments on-board the spacecraft. This paper addresses dynamic modelling and performs an analysis on the micro-vibration isolation for a single gimbal CMG (SGCMG) cluster. First, an analytical model was developed to describe both the coupled SGCMG cluster and the multi-axis isolation system that can express the dynamic outputs. This analytical model accurately reflects the mass and inertia properties, the gyroscopic effects and flexible modes of the coupled system, which can be generalized for isolation applications of SGCMG clusters. Second, the analytical model was validated using MSC.NASTRAN software based on the finite element technique. The dynamic characteristics of the coupled system are affected by the mass distribution and the gyroscopic effects of the SGCMGs. The gyroscopic effects produced by the rotary flywheel will stiffen or soften several of the structural modes of the coupled system. In addition, the gyroscopic effect of each SGCMG can interact with or counteract that of others, which induce vibration modes coupled together. Finally, the performance of the passive isolation was analysed. It was demonstrated that the gyroscopic effects should be considered in isolation studies on SGCMG clusters; otherwise, the isolation performance will be underestimated if they are ignored.     

A HYBRID FINITE SEGMENT/FINITE ELEMENT MODELLING AND EXPERIMENT ON A FLEXIBLE DEPLOYMENT SYSTEM

This paper focuses on the dynamic responses of a flexible deployment system that has a central rigid body and four articulated flexible beams and undergoes locking impact. A hybrid finite segment/finite element model and an experiment are presented for the deploy-ment system. The flexible beam components in the system are modelled with the finite segments connected by massless beam elements, wherein the finite segments describe the inertia of the large rotation flexible beam and the massless elastic elements describe the elas-ticity of the flexible beam by taking the advantage of small deformation in the relative co-ordinate system. To model the internal impacts in the articulate joints due to clearances, a continuous contact force model of locking joint is also proposed. The governing differential-algebraic equations of the system are established by the Newton-Euler method with Lagrange multipliers and are solved with the method of generalized co-ordinate partitioning. To accelerate the numerical integration, a “longitudinal constraint” is suggested to alleviate the stiff problem of the dynamic equations. In addition, a physical model of the deployment system is constructed. The deployment is released by the compressed springs in the joints. A position measuring system of linear CCD cameras is used to measure the large displacement of the system. Correlations between the mathematical model and the experiments are also presented. Reasonable results are obtained.     

Modelling of continuous and discontinuous floating slab tracks in a tunnel using a periodic approach

This paper presents a periodic approach to couple a track and a tunnel-soil system of different periodicity. The periodicity of the track and the tunnel-soil system is exploited using the Floquet transform to efficiently formulate the problem in the frequency-wavenumber domain as well as to limit the discretization effort to a reference cell. The track and the tunnel-soil system are modelled as two separate systems of different periodicity and are coupled in the frequency-wavenumber domain. A coupled periodic finite element-boundary element method is used to model the tunnel-soil system, while a periodic finite element model or an analytical approach is used to model the track.A general analytical formulation to compute the response of three-dimensional periodic media that are excited by moving loads is discussed. It is shown that the response due to moving loads on the track can be calculated from the transfer function of the track-tunnel-soil system and the axle loads.A methodology for computing the transfer functions of the coupled track-tunnel-soil system as well as the computation of dynamic forces accounting for the interaction between the moving vehicle and the periodic track are described. The model accounts for quasi-static forces as well as dynamic forces due to parametric excitation and unevenness excitation.The methodology has been used to assess the vibration isolation efficiency of continuous and discontinuous floating slab tracks. It is concluded that both continuous and discontinuous floating slab tracks have a similar efficiency in the frequency range well above the isolation frequency of the slabs, which is usually higher than the slab passage frequency. In case of discontinuous slab tracks, the parametric excitation is found to be important, which results in a poorer performance of the track at low frequencies.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium

The effect of the induced vibrations in the carbon nanotubes (CNTs) arising from the internal fluid flow is a critical issue in the design of CNT-based fluidic devices. In this study, in-plane vibration analysis of curved CNTs conveying fluid embedded in viscoelastic medium is investigated. The CNT is modeled as a linear elastic cylindrical tube where the internal moving fluid is characterized by steady flow velocity and mass density of fluid. A modified-inextensible theory is used in formulation and the steady-state initial forces due to the centrifugal and pressure forces of the internal fluid are also taken into account. The finite element method is used to discretize the equation of motion and the frequencies are obtained by solving a quadratic eigenvalue problem. The effects of CNT opening angle, the elastic modulus and the damping factor of the viscoelastic surrounded medium and fluid velocity on the resonance frequencies are elucidated. It is shown that curved CNTs are unconditionally stable even for a system with sufficiently high flow velocity. The most results presented in this investigation have been absent from the literature for fluid-induced vibration of curved CNTs embedded in viscoelastic foundations.     

Visualization of the inflow ahead of a rotating propeller attached to a container ship model

The inflow ahead of a rotating propeller attached to a container ship model was visualized using a two-frame particle image velocimetry (PIV) technique. For illuminating the inflow region, a transparent window was installed at the stern of the ship model. Ensemble-averaged mean velocity fields were measured at four different blade phases under the design loading condition. The characteristics of the inflow in the upper plane above the propeller axis are quite different from those below the propeller axis. In the far upstream region above the propeller axis, most of the inflow comes from the hull wake and the axial velocity is very small. As the inflow moves toward the propeller plane, its axial velocity component increases rapidly. In addition, the variation of the inflow characteristics with respect to phase angle becomes apparent. The thick hull boundary layer and out-of-plane motion resulting from the propeller rotation produce a large turbulent kinetic energy around the tip of the propeller blade in the upper inflow region. The axial velocity distribution of the propeller inflow is asymmetric with respect to the vertical center axis, exhibiting different axial velocities on the port and starboard sides.     

Numerical Investigation on Vibration Performance of Flexible Plates Actuated by Pneumatic Artificial Muscle

This paper theoretically introduced the feasibility of changing the vibration characteristics of flexible plates by using bio-inspired, extremely light, and powerful Pneumatic Artificial Muscle (PAM) actuators. Many structural plates or shells are typically flexible and show high vibration sensitivity. For this reason, this paper provides a way to achieve active vibration control for suppressing the oscillations of these structures to meet strict stability, safety, and comfort requirements. The dynamic behaviors of the designed plates are modeled by using the finite element (FE) method. As is known, the output force vs. contraction curve of PAM is nonlinear generally. In this present finite element model, the maximum forces provided by PAM in different air pressure are adopted as controlling forces for applying for the plate. The non-linearity between the output force and displacement of PAM is avoided in this study. The dynamic behaviors of plates with several independent groups of controlling forces are observed and studied. The results show that the natural frequencies of the plate can be varying and the max amplitude decreases significantly if the controlling forces are applied. The present work also demonstrates the potential of the PAM actuators as valid means for damping out the vibration of flexible systems.