A study of vibration and vibration control of ship structures

This paper examines the vibration characteristics and vibration control of complex ship structures. It is shown that input mobilities of a ship structure at engine supports, due to out-of-plane force or bending moment excitations, are governed by the flexural stiffness of the engine supports. The frequency averaged input mobilities of the ship structure, due to such excitations, can be represented by those of the corresponding infinite beam. The torsional moment input mobility at the engine support can be estimated from the torsional response of the engine bed section under direct excitation. It is found that the inclusion of ship hull and deck plates in the ship structure model has little effect on the frequency-averaged response of the ship structure. This study also shows that vibration propagation in complex ship structures at low frequencies can be attenuated by imposing irregularities to the ring frame locations in ships. Vibration responses of ship structures due to machinery excitations at higher frequencies can be controlled by structural modifications of the local supporting structures such as engine beds in ships.

The feasibility of vibration analysis as a technique to detect osseointegration of transfemoral implants

One of the main causes of above knee or transfemoral amputation (TFA) in the developed world is trauma to the limb. The number of people undergoing TFA due to limb trauma, particularly due to war injuries, has been increasing. Typically the trauma amputee population, including war-related amputees, are otherwise healthy, active and desire to return to employment and their usual lifestyle. Consequently there is a growing need to restore long-term mobility and limb function to this population. Traditionally transfemoral amputees are provided with an artificial or prosthetic leg that consists of a fabricated socket, knee joint mechanism and a prosthetic foot. Amputees have reported several problems related to the socket of their prosthetic limb. These include pain in the residual limb, poor socket fit, discomfort and poor mobility. Removing the socket from the prosthetic limb could eliminate or reduce these problems. A solution to this is the direct attachment of the prosthesis to the residual bone (femur) inside the residual limb. This technique has been used on a small population of transfemoral amputees since 1990. A threaded titanium implant is screwed in to the shaft of the femur and a second component connects between the implant and the prosthesis. A period of time is required to allow the implant to become fully attached to the bone, called osseointegration (OI), and be able to withstand applied load; then the prosthesis can be attached. The advantages of transfemoral osseointegration (TFOI) over conventional prosthetic sockets include better hip mobility, sitting comfort and prosthetic retention and fewer skin problems on the residual limb. However, due to the length of time required for OI to progress and to complete the rehabilitation exercises, it can take up to twelve months after implant insertion for an amputee to be able to load bear and to walk unaided. The long rehabilitation time is a significant disadvantage of TFOI and may be impeding the wider adoption of the technique. There is a need for a non-invasive method of assessing the degree of osseointegration between the bone and the implant. If such a method was capable of determining the progression of TFOI and assessing when the implant was able to withstand physiological load it could reduce the overall rehabilitation time. Vibration analysis has been suggested as a potential technique: it is a non destructive method of assessing the dynamic properties of a structure. Changes in the physical properties of a structure can be identified from changes in its dynamic properties. Consequently vibration analysis, both experimental and computational, has been used to assess bone fracture healing, prosthetic hip loosening and dental implant OI with varying degrees of success. More recently experimental vibration analysis has been used in TFOI. However further work is needed to assess the potential of the technique and fully characterise the femur-implant system. The overall aim of this study was to develop physical and computational models of the TFOI femur-implant system and use these models to investigate the feasibility of vibration analysis to detect the process of OI. Femur-implant physical models were developed and manufactured using synthetic materials to represent four key stages of OI development (identified from a physiological model), simulated using different interface conditions between the implant and femur. Experimental vibration analysis (modal analysis) was then conducted using the physical models. The femur-implant models, representing stage one to stage four of OI development, were excited and the modal parameters obtained over the range 0-5kHz. The results indicated the technique had limited capability in distinguishing between different interface conditions. The fundamental bending mode did not alter with interfacial changes. However higher modes were able to track chronological changes in interface condition by the change in natural frequency, although no one modal parameter could uniquely distinguish between each interface condition. The importance of the model boundary condition (how the model is constrained) was the key finding; variations in the boundary condition altered the modal parameters obtained. Therefore the boundary conditions need to be held constant between tests in order for the detected modal parameter changes to be attributed to interface condition changes. A three dimensional Finite Element (FE) model of the femur-implant model was then developed and used to explore the sensitivity of the modal parameters to more subtle interfacial and boundary condition changes. The FE model was created using the synthetic femur geometry and an approximation of the implant geometry. The natural frequencies of the FE model were found to match the experimental frequencies within 20% and the FE and experimental mode shapes were similar. Therefore the FE model was shown to successfully capture the dynamic response of the physical system. As was found with the experimental modal analysis, the fundamental bending mode of the FE model did not alter due to changes in interface elastic modulus. Axial and torsional modes were identified by the FE model that were not detected experimentally; the torsional mode exhibited the largest frequency change due to interfacial changes (103% between the lower and upper limits of the interface modulus range). Therefore the FE model provided additional information on the dynamic response of the system and was complementary to the experimental model. The small changes in natural frequency over a large range of interface region elastic moduli indicated the method may only be able to distinguish between early and late OI progression. The boundary conditions applied to the FE model influenced the modal parameters to a far greater extent than the interface condition variations. Therefore the FE model, as well as the experimental modal analysis, indicated that the boundary conditions need to be held constant between tests in order for the detected changes in modal parameters to be attributed to interface condition changes alone. The results of this study suggest that in a clinical setting it is unlikely that the in vivo boundary conditions of the amputated femur could be adequately controlled or replicated over time and consequently it is unlikely that any longitudinal change in frequency detected by the modal analysis technique could be attributed exclusively to changes at the femur-implant interface. Therefore further development of the modal analysis technique would require significant consideration of the clinical boundary conditions and investigation of modes other than the bending modes.

Vibration characteristics of slender structures under human induced loads

This paper presents the outcome of investigations and studies of the vibratioon characteristics and response of low frequency structural systems for a composite concrete steel floor plate and a reverse profiled cable tensioned foot bridge. These highly dynamic and slender structure are the engineering response to planning, aesthetic and environmental influences, but are prone to excessive and complex vibration. A number of design codes and practice guides provided information to engineers for vibration mitigation However, they are limited to very simple load function applied to a few uncoupled translational modes of excitation. Motivated by the need to address the knowledge gaps in this area, the investigations described in this paper focused on synchronous multi-modal and coupled excitation of the floor plate and footbridge with considerations for torsinal effects. The results showed the potential for adverse dynamic response from multi-modal and coupled excitation influenced by patterned loading, structure geometry, stiffness distribution, directional effects, forcing functions based on activity frequency and duration of foot contact, and modal participation. It was also shown that higher harmonics of the load frequency can excite higher modes in the composite floor structure. Such responsive behaviour is prevalent mainly in slender and lightweight construction and not in stiffer and heavier structural systems. The analytical techniques and methods used in these investigations can supplement the current limited code and best practice provisions for mitigating the impact of human induced vibrations in slender structural systems.

Vibration characteristics of concrete-steel composite floor structures

This paper discusses the vibration characteristics of a concrete-steel composite multi-panel floor structure; the use of these structures is becoming more common. These structures have many desirable properties but are prone to excessive and complex vibration, which is not currently well understood. Existing design codes and practice guides provide generic advice or simple techniques that cannot address the complex vibration in these types of low-frequency structures. The results of this study show the potential for an adverse dynamic response from higher and multi-modal excitation influenced by human-induced pattern loading, structural geometry, and activity frequency. Higher harmonics of the load frequency are able to excite higher modes in the composite floor structure in addition to its fundamental mode. The analytical techniques used in this paper can supplement the current limited code and practice guide provisions for mitigating the impact of human-induced vibrations in these floor structures.

Structural damage identification with noise polluted Frequency Response Functions (FRFs)

Damage detection in structures has become increasingly important in recent years. While a number of damage detection and localization methods have been proposed, very few attempts have been made to explore the structure damage with noise polluted data which is unavoidable effect in real world. The measurement data are contaminated by noise because of test environment as well as electronic devices and this noise tend to give error results with structural damage identification methods. Therefore it is important to investigate a method which can perform better with noise polluted data. This paper introduces a new damage index using principal component analysis (PCA) for damage detection of building structures being able to accept noise polluted frequency response functions (FRFs) as input. The FRF data are obtained from the function datagen of MATLAB program which is available on the web site of the IASC-ASCE (International Association for Structural Control– American Society of Civil Engineers) Structural Health Monitoring (SHM) Task Group. The proposed method involves a five-stage process: calculation of FRFs, calculation of damage index values using proposed algorithm, development of the artificial neural networks and introducing damage indices as input parameters and damage detection of the structure. This paper briefly describes the methodology and the results obtained in detecting damage in all six cases of the benchmark study with different noise levels. The proposed method is applied to a benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring, which was developed in order to facilitate the comparison of various damage identification methods. The illustrated results show that the PCA-based algorithm is effective for structural health monitoring with noise polluted FRFs which is of common occurrence when dealing with industrial structures.

Human activity-induced vibration in slender structural systems

Human activity-induced vibrations in slender structural sys tems become apparent in many different excitation modes and consequent action effects that cause discomfort to occupants, crowd panic and damage to public infrastructure. Resulting loss of public confidence in safety of structures, economic losses, cost of retrofit and repairs can be significant. Advanced computational and visualisation techniques enable engineers and architects to evolve bold and innovative structural forms, very often without precedence. New composite and hybrid materials that are making their presence in structural systems lack historical evidence of satisfactory performance over anticipated design life. These structural systems are susceptible to multi-modal and coupled excitation that are very complex and have inadequate design guidance in the present codes and good practice guides. Many incidents of amplified resonant response have been reported in buildings, footbridges, stadia a nd other crowded structures with adverse consequences. As a result, attenuation of human-induced vibration of innovative and slender structural systems very ofte n requires special studies during the design process. Dynamic activities possess variable characteristics and thereby induce complex responses in structures that are sensitive to parametric variations. Rigorous analytical techniques are available for investigation of such complex actions and responses to produce acceptable performance in structural systems. This paper presents an overview and a critique of existing code provisions for human-induced vibration followed by studies on the performance of three contrasting structural systems that exhibit complex vibration. The dynamic responses of these systems under human-induced vibrations have been carried out using experimentally validated computer simulation techniques. The outcomes of these studies will have engineering applications for safe and sustainable structures and a basis for developing design guidance.

Damage identification and condition assessment of building structures using frequency response functions and neural networks

This thesis investigated the viability of using Frequency Response Functions in combination with Artificial Neural Network technique in damage assessment of building structures. The proposed approach can help overcome some of limitations associated with previously developed vibration based methods and assist in delivering more accurate and robust damage identification results. Excellent results are obtained for damage identification of the case studies proving that the proposed approach has been developed successfully.

Response And Stability Of A Stochastic Beam-Column Using Stochastic Fem

A beam-column resting on continuous Winkler foundation and discrete elastic supports is considered. The beam-column is of variable cross-section and the variation of sectional properties along the axis of the beam-column is deterministic. Young's modulus, mass per unit length and distributed axial loadings of the beam-column have a stochastic distribution. The foundation stiffness coefficient of the Winkler model, the stiffnesses of discrete elastic supports, stiffnesses of end springs and the end thrust, are all considered as random parameters. The material property fluctuations and distributed axial loadings are considered to constitute independent, one-dimension uni-variate homogeneous real stochastic fields in space. The foundation stiffness coefficient, stiffnesses of the discrete elastic supports, stiffnesses of end springs and the end thrust are considered to constitute independent random variables. Static response, free vibration and stability behaviour of the beam-column are studied. Hamilton's principle is used to formulate the problem using stochastic FEM. Sensitivity vectors of the response and stability parameters are evaluated. Using these statistics of free vibration frequencies, mode shapes, buckling parameters, etc., are evaluated. A numerical example is given.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.