This paper presents a comparison of optimization algorithms for constrained damping (CLD) patches’ layout to minimize the maximum vibration response of the odd modes, which constitutes the dominant acoustic radiation, of a simply-supported beam excited by a harmonic transverse force. An analytical model based on Euler-Bernoulli beam assumptions is derived first to relate the displacement response of the beam with bonded CLD patches and their layout. Four different nonlinear optimization methods/algorithms are then respectively used to optimize the CLD patches’ locations and lengths with aim of minimum displacement amplitude at middle of the beam. The considered methods include subproblem approximation method, the first-order method, sequential quadratic programming (SQP) and genetic algorithm (GA). The efficiency of each considered optimization method is evaluated and also compared in terms of obtained optimal beam displacement. The results show that GA is most efficient in obtaining the best optimum for this optimization problem in spite of highest computation efforts required to improve its stability. / Singapore-MIT Alliance (SMA)

This paper presents the layout optimization of passive constrained layer damping (PCLD) treatment for vibration control of cylindrical shells under a broadband force excitation. The equations governing the vibration responses are derived using the energy approach and assumed-mode method. These equations provided relationship between the integrated displacement response over the whole structural volume, i.e. the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, Genetic algorithms (GAs) based penalty function method is employed to find the optimal layout of rectangular PCLD patches with minimize the maximum displacement response of PCLD-treated cylindrical shells. Optimization solutions of PCLD patches’ locations and shape are obtained under the constraint of total amount of PCLD in terms of percentage added weight to the base structure. Examination of the optimal layouts reveals that the patches tend to increase their coverage in the axial direction and distribute over the whole surface of the cylindrical shell for optimal control of the structural volume displacement. / Singapore-MIT Alliance (SMA)

During aircraft development, the impact of vibrations is examined and how this affects the aircraft structure under different conditions. Those vibrations can damage electronic equipment that are installed within the fuselage and can even lead to material fatigue within the structure. To reduce vibrations there are two approaches that are preferred to use, installing vibration insulators attached between the structure and the electrical component or change the design of the structure to a stiffer one. Those methods are easiest to implement in an early stage of the development but in later stages, when vibration problems usually are detected, it is too difficult and expensive to do major changes of the structure and there is lack of space to implement vibration insulators. A third method is then to apply passive damping in form of damper mats to surfaces on structures where critical vibrations occurs.    The effects on the structural behavior when damper mats are applied to a certain structure are studied in this thesis work. The purpose is to get deeper knowledge about how damper mats can be used to reduce vibrations in aircraft structures. The type of damper mat that is studied is known as Constrained Layer Damping, CLD, which is a sandwich of a visco-elastic material layer and a stiffer constraining material layer. Modelling and simulation methods that are based on commercial FE-software have been developed. The analysis method is based on doing a modal analysis with structural damping taken into account. This makes it possible to predict the overall global damping at each structural mode. The models for damper mats have in this project been verified with experimental testing using typical damper mats. The methodology can be used to predict the behavior of damped structures in order to obtain an effective and lightweight passive damping solution. / Under utvecklingen av flygplan undersöks hur vibrationer påverkar flygplansstrukturen under olika förutsättningar. Dessa vibrationer kan skada elektronisk utrustning som är monterad i flygplanskroppen och kan även göra så att materialutmattning uppstår i flygplansstrukturen. För att motverka vibrationer finns det två metoder som är att föredra, antingen att montera vibrationsisolatorer mellan de elektroniska utrustningarna och strukturen eller att ändra designen på strukturer till en styvare. Dessa metoder är enkla att implementera i ett tidigt steg i utvecklingsprocessen men i senare steg, då vibrationsproblem ofta upptäcks, så är det för komplicerat och för dyrt att göra större ändringar på strukturen och så är det ont om plats för att kunna installera vibrations isolatorer. En tredje metod är istället att implementera passiv dämpning i form av dämpningsmattor på ytor av strukturen där kritiska vibrationer uppstår. Effekterna av det strukturella uppförandet när dämpningsmattor är applicerade på en viss struktur har studerats i det här examensarbetet. Syftet är att få en fördjupad kunskap om hur dämpningsmattor kan användas för att reducera vibrationer i flygplan strukturer. Den typ av dämpningsmatta som har studerats är känd som Constrained Layer Damping, CLD, vilken är en sandwich av ett visko-elastiskt lager samt ett styvare lager.  Modellerings och simuleringsmetoder som är baserade på kommersiella FE-mjukvaror har utvecklats. Analysmetoderna är baserade på att utföra modalanalys tillsammans med strukturell dämpning. Detta möjliggör att förutse den övergripande dämpningen vid varje strukturell mod. Modellerna för dämpningsmattorna har i det här projektet verifierats med experimental testning av typiska dämpningsmattor. Metodiken kan användas till att prediktera beteendet av dämpade strukturer för att uppnå en effektiv och lättviktig passiv dämpningslösning.

Vibration control is inevitable in many fields, including mechanical and civil engineering. This matter becomes more crucial for lightweight systems, like those made of magnesium. One of the most commonly practiced methods in vibration control is to apply constrained layer damping (CLD) patches to the surface of a structure. In order to consider the weight efficiency of the structure, the best shape and locations of the patches should be determined to achieve the optimum vibration suppression with the lowest amount of damping patch. In most research work done so far, the shape of patches are assumed to be known and only their optimum locations are found. However, the shape of the patches plays an important role in vibration suppression that should be included in the overall optimization procedure. In this research, a novel topology optimization approach is proposed. This approach is capable of finding the optimum shape and locations of the patches simultaneously for a given surface area. In other words, the damping optimization will be formulated in the context of the level set technique, which is a numerical method used to track shapes and locations concurrently. Although level set technique offers several key benefits, its application especially in time-varying problems is somewhat cumbersome. To overcome this issue, a unique programming technique is suggested that utilizes MATLAB© and COMSOL© simultaneously. Different 2D structures will be considered and CLD patches will be optimally located on them to achieve the highest modal loss factor. Optimization will be performed while having different amount of damping patches to check the effectiveness of the technique. In all cases, certain constraints are imposed in order to make sure that the amount of damping material remains constant and equal to the starting value. Furthermore, different natural frequencies will be targeted in the damping optimization, and their effects will also be explained. The level set optimization technique will then be expanded to 3D structures, and a novel approach will be presented for defining an efficient 4D level set function to initialize the optimization process. Vibrations of a satellite dish will be optimally suppressed using CLD patches. Dependency of the optimum shape and location of patches to different parameters of the models such as natural frequencies and initial starting point will be examined. In another practical example, excessive vibrations of an automotive dash panel will be minimized by adding damping materials and their optimal distribution will be found. Finally, the accuracy of the proposed method will be experimentally confirmed through lab tests on a rectangular plate with nonsymmetrical boundary conditions. Different damping configurations, including the optimum one, will be tested. It will be shown that the optimum damping configuration found via level set technique possesses the highest loss factor and reveals the best vibration attenuation. The proposed level set topology optimization method shows high capability of determining the optimum damping set in structures. The effective coding method presented in this research will make it possible to easily extend this method to other physical problems such as image processing, heat transfer, magnetic fields, etc. Being interconnected, the physical part will be modeled in a finite element package like COMSOL and the optimization advances by means of Hamilton-Jacobi partial differential equation. Thus, the application of the proposed method is not confined to damping optimization and can be expanded to many engineering problems. In summary, this research: - offers general solution to 2D and 3D CLD applications and simultaneously finds the best shape and location of the patches for a given surface area (damping material); - extends the level set technique to concurrent shape and location optimization; - proposes a new numerical implementation to handle level set optimization problems in any complicated structure; - makes it possible to perform level set optimization in time dependent problems; - extends level set approach to higher order problems.

Vibration control is inevitable in many fields, including mechanical and civil engineering. This matter becomes more crucial for lightweight systems, like those made of magnesium. One of the most commonly practiced methods in vibration control is to apply constrained layer damping (CLD) patches to the surface of a structure. In order to consider the weight efficiency of the structure, the best shape and locations of the patches should be determined to achieve the optimum vibration suppression with the lowest amount of damping patch. In most research work done so far, the shape of patches are assumed to be known and only their optimum locations are found. However, the shape of the patches plays an important role in vibration suppression that should be included in the overall optimization procedure. In this research, a novel topology optimization approach is proposed. This approach is capable of finding the optimum shape and locations of the patches simultaneously for a given surface area. In other words, the damping optimization will be formulated in the context of the level set technique, which is a numerical method used to track shapes and locations concurrently. Although level set technique offers several key benefits, its application especially in time-varying problems is somewhat cumbersome. To overcome this issue, a unique programming technique is suggested that utilizes MATLAB© and COMSOL© simultaneously. Different 2D structures will be considered and CLD patches will be optimally located on them to achieve the highest modal loss factor. Optimization will be performed while having different amount of damping patches to check the effectiveness of the technique. In all cases, certain constraints are imposed in order to make sure that the amount of damping material remains constant and equal to the starting value. Furthermore, different natural frequencies will be targeted in the damping optimization, and their effects will also be explained. The level set optimization technique will then be expanded to 3D structures, and a novel approach will be presented for defining an efficient 4D level set function to initialize the optimization process. Vibrations of a satellite dish will be optimally suppressed using CLD patches. Dependency of the optimum shape and location of patches to different parameters of the models such as natural frequencies and initial starting point will be examined. In another practical example, excessive vibrations of an automotive dash panel will be minimized by adding damping materials and their optimal distribution will be found. Finally, the accuracy of the proposed method will be experimentally confirmed through lab tests on a rectangular plate with nonsymmetrical boundary conditions. Different damping configurations, including the optimum one, will be tested. It will be shown that the optimum damping configuration found via level set technique possesses the highest loss factor and reveals the best vibration attenuation. The proposed level set topology optimization method shows high capability of determining the optimum damping set in structures. The effective coding method presented in this research will make it possible to easily extend this method to other physical problems such as image processing, heat transfer, magnetic fields, etc. Being interconnected, the physical part will be modeled in a finite element package like COMSOL and the optimization advances by means of Hamilton-Jacobi partial differential equation. Thus, the application of the proposed method is not confined to damping optimization and can be expanded to many engineering problems. In summary, this research: - offers general solution to 2D and 3D CLD applications and simultaneously finds the best shape and location of the patches for a given surface area (damping material); - extends the level set technique to concurrent shape and location optimization; - proposes a new numerical implementation to handle level set optimization problems in any complicated structure; - makes it possible to perform level set optimization in time dependent problems; - extends level set approach to higher order problems.

Vacuum-assisted toilets make use of a large pressure difference between the ambient pressure and a vacuum tank to transport waste from the toilet bowl to the septic tank. This process requires 98% less water per flush making it an attractive product for transport vehicles such as airplanes, cruise ships, and trains. Unfortunately, the water savings come at the cost of high noise levels. This thesis investigates the acoustic characteristics of a vacuum-assisted toilet flush and several methods to reduce the radiated noise. Some methods include changing rinse parameters such as rinse pressure, rinse length, and rinse timing, adding structural damping of the bowl to reduce re-radiation, inserting a tube between the bowl and valve that utilizes a larger bend radius and longer tube length than what is currently installed, and modifying the valve. The most effective solution without requiring more water per flush was to insert a tube. The initial peak level was reduced by 16 dB and the steady-vacuum noise was reduced by 5 dB. Evidence of evanescent decay and reduced flow velocity as possible mechanisms for the noise reduction are presented and discussed. Rinse variations show a strong impact of the rinse-tube interaction on the noise reduction. In addition to these techniques, a modified flush plate opening and closing velocity profile is suggested which optimizes the sound generated by the opening and closing of the valve. Finally, a promising dual-valve solution that may take extra coordination of vacuum-assisted toilet manufacturers and airplane/cruise ship/train manufacturers is presented. By placing a secondary valve near the septic tank, the main noise from the valve is significantly reduced.

Noise and vibration suppression is an important aspect in the design process of structures and machines. Undesirable vibrations can cause fatigue in a structure and are, therefore, a risk to the safety of a structure. One of the most effective and widely used methods of mitigating these unwanted vibrations from a system is passive damping, by using a viscoelastic material. This dissertation will primarily focus on constrained layer passive damping treatments in structures and the investigation of associated complex modes. The key idea behind constrained damping treatment is to increase damping as affected by the presence of a highly damped core layer vibrating mainly in shear. Our main goal was to incorporate viscoelastic material in a thick stiffened panel with plate-strip stiffeners, to enhance the damping characteristics of the structure. First, we investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the principle of virtual work, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the viscoelastic material was modeled using the complex modulus approach. We used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, by including complex modulus in the base and constraining layers. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically damped and non-proportionally damped structures. Secondly, we studied the free vibration response of an integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners, unlike the rib stiffeners often investigated by researchers. Both plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used here can also be applied to fully clamped, free and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh-Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to the recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite-element software ABAQUS. Some parametric studies were carried out to show the influence of certain important parameters on the overall natural frequencies of the stiffened plate. Finally, we investigated the damped response of an adhesively bonded plate employing plate-strip stiffeners, using FSDT for both the plate and stiffeners. The problem was analyzed using the principle of virtual work. At first, we did not consider damping in the adhesive in order to validate our code, by comparing our results with those available in the literature as well as with the results obtained using ABAQUS 3D model. The results were found to be highly satisfactory. We also considered the effect of changing the stiffness of the adhesive layer on the vibration of the bonded system. As a second step, we included damping in the stiffened structure using complex modulus approach, a widely used technique to represent the rheology of the viscoelastic material. We observed an overall increase in the natural frequencies of the system, due to the damping provided by the viscoelastic material. Moreover, it was noticed that when the thickness of the adhesive layer is increased, the natural frequencies and loss factor of the stiffened structure decrease. A viscoelastic material with high loss factor and small thickness will be a perfect design variable to obtain overall high damping in the structure. / Ph. D.