The fourier spectral element method for vibration analysis of general dynamic structures

The Fourier Spectral Element Method (FSEM) was proposed by Wen Li on the vibration of simple beams (Li, 1999), and was extended to the vibration of rectangular plates (Li, 2004). This dissertation proposes a revised formulation on the vibration of rectangular plates with general boundary conditions, and extends the FSEM on the vibration of general triangular plates with elastic boundary supports. 3-D coupling formulation among the plates and beams is further developed. A general dynamic structure is then analyzed by dividing the structure into coupled triangular plates, rectangular plates, and beams. The accuracy and fast convergence of FSEM method is repeatedly benchmarked by analytical, experimental, and numerical results from the literature, Laboratory test, and commercial software. The Key feature of FSEM method is that the approximation solution satisfies both the governing equation and the boundary conditions of the beam (plates) vibration in an exact sense. The displacement function composes a standard Fourier cosine series plus several supplementary functions to ensure the convergence to the exact solution including displacement, bending moment, and shear forces, etc. All the formulation is transformed into standard form and a set of stored matrices ensure fast assembly of the studied structure matrix. Since the matrix size of the FSEM method is substantially smaller than the FEA method, FSEM method has the potential to reduce the calculation time, and tackle the unsolved Mid-frequency problem

Textile hybrid kinetic adaptive structures: a case study

Dissertação de mestrado integrado em Engenharia CivilThis thesis has the main objective to study three distinct typologies of structures. These structures are, form-active structures, in particular membrane structures, bending-active structures and the integration of both concepts with a kinetic principle, therefore adaptive hybrid structures. Both membrane and bending-active are structures that require form finding, since the form of these structures is dependent on the loading and boundary conditions, thus only known a posteriori. These structures are subject to large deformations and thus, geometric nonlinearities must be considered during the calculation. Additionally, the flexibility of membrane structures conjugated with the elastic behaviour of bending-active structures creates the perfect conditions for the development of hybrid kinetic structures that adapt according to the external loading conditions present. This study intends to elaborate an exploratory approach on these concepts, thus bringing forward the main problems that originate when analysing a structure of this type. Therefore, firstly a study on membrane, bending-active, hybrid and kinetic structures is presented, containing the most relevant knowledge that currently exists regarding these topics. Then, the structural aspects that are inherent to these structures are exposed. Three routines are developed in Sofistik® in order form find and calculate the above-mentioned structures. Validations are made on these routines and software analysis. The structural feasibility of an architectural concept proposed by Costa (2017) of a hybrid adaptive concept is studied by applying these routines, and the kinetic hybrid concept is simulated in Sofistik®. The adaptive principle is also extended to function structurally, by taking advantage of the bending prestress implied by the bending-active elements. Finally, external wind loads are applied to this structure, in order to test the effectiveness of the structural adaptive concept. It was concluded that there is significant importance of the bending adaptive movement in the loadbearing capacity of the overall system. Additionally, the choice of the initial shape of the structure defines a crucial step on the definition of the structure, since it affects the process of form finding, that latter affects the structural performance.A presente dissertação tem como objetivo principal estudar três tipologias distintas de estruturas. Estas estruturas são as estruturas de forma ativa, particularmente as estruturas em membrana, as estruturas de flexão ativa e a integração de ambos os conceitos com um princípio cinético, ou seja, estruturas hibridas adaptativas. Tanto as estruturas de membranas como as estruturas de flexão ativa são estruturas que requerem determinação da forma pois, como a forma destas estruturas é dependente das condições de tensão e de fronteira, apenas é conhecida a posteriori. Estas estruturas estão sujeitas a grandes deformações e, portanto, as não linearidades geométricas devem ser consideradas durante o cálculo. Para além disto, a flexibilidade das estruturas de membrana conjugada com o comportamento elástico das estruturas de flexão ativa geram condições perfeitas para o desenvolvimento de estruturas cinéticas hibridas que se adaptam de acordo com as condições de carregamento presentes. Este estudo pretende elaborar uma aproximação exploratória a estes conceitos, trazendo para primeiro plano os principais problemas originários da análise deste tipo de estruturas. Desta forma, primeiramente é apresentado um estudo sobre estruturas de membrana, flexão ativa, hibridas e cinéticas, contendo a informação mais relevante que existe atualmente sobre estes assuntos. De seguida, os aspetos estruturais inerentes a estas estruturas são expostos. Três rotinas são desenvolvidas no Sofistik® de forma a determinar a forma e calcular as estruturas anteriormente mencionadas. São realizadas validações destas rotinas e da análise preconizada pelo software. A viabilidade estrutural de um conceito de arquitetura proposto por Costa (2017) sobre uma estrutura hibrida adaptativa é estudada através da aplicação destas rotinas, e o princípio cinético hibrido é simulado através do Sofistik®. O princípio adaptativo é alargado de modo a funcionar estruturalmente, tirando partido da pretensão implícita pelos elementos de flexão ativa. Finalmente, são aplicadas cargas externas de vento à estrutura, de forma a testar a eficácia do principio adaptativo estrutural. Foi concluído que o movimento adaptativo de flexão tem uma importante significância ao nível da carga admissível na estrutura. Adicionalmente, a escolha da geometria inicial da estrutura define uma etapa fundamental na definição da estrutura, pois afeta o processo de form finding, que mais tarde afeta o desempenho estrutural

The Fourier Spectrum Element Method For Vibration And Power Flow Analysis Of Complex Dynamic Systems

A general numerical method, the so-called Fourier-Space Element Method (FSEM), is proposed for the vibration and power flow analyses of complex built-up structures. In a FSEM model, a complex structure is considered as a number of interconnected basic structural elements such as beams and plates. The essence of this method is to invariably express each of displacement functions as an improved Fourier series which consists of a standard Fourier cosine series plus several supplementary series/functions used to ensure and improve the uniform convergence of the series representation. Thus, the series expansions of the displacement functions and their relevant derivatives are guaranteed to uniformly and absolutely converge for any boundary conditions and coupling configurations. Additionally, and the secondary variables of interest such as interaction forces, bending moments, shear forces, strain/kinetic energies, and power flows between substructures can be calculated analytically. Unlike most existing techniques, FSEM essentially represents a powerful mathematical means for solving general boundary value problems and offers a unified solution to the vibration problems and power flow analyses for 2- and 3-D frames, plate assemblies, and beam-plate coupling systems, regardless of their boundary conditions and coupling configurations. The accuracy and reliability of FSEM are repeatedly demonstrated through benchmarking against other numerical techniques and experimental results. FSEM, because of its exceptional computational efficacy, can be efficiently combined with the Monte Carlo Simulation (MCS) to predict the statistical characteristics of the dynamic responses of built-up structures in the presence of model uncertainties. Several examples are presented to demonstrate the mean behaviors of complex built-up structures in the critical mid-frequency range in which the responses of the systems are typically very sensitive to the variances of model variables

MECHANICAL ENERGY HARVESTER FOR POWERING RFID SYSTEMS COMPONENTS: MODELING, ANALYSIS, OPTIMIZATION AND DESIGN

Finding alternative power sources has been an important topic of study worldwide. It is vital to find substitutes for finite fossil fuels. Such substitutes may be termed renewable energy sources and infinite supplies. Such limitless sources are derived from ambient energy like wind energy, solar energy, sea waves energy; on the other hand, smart cities megaprojects have been receiving enormous amounts of funding to transition our lives into smart lives. Smart cities heavily rely on smart devices and electronics, which utilize small amounts of energy to run. Using batteries as the power source for such smart devices imposes environmental and labor cost issues. Moreover, in many cases, smart devices are in hard-to-access places, making accessibility for disposal and replacement difficult. Finally, battery waste harms the environment. To overcome these issues, vibration-based energy harvesters have been proposed and implemented. Vibration-based energy harvesters convert the dynamic or kinetic energy which is generated due to the motion of an object into electric energy. Energy transduction mechanisms can be delivered based on piezoelectric, electromagnetic, or electrostatic methods; the piezoelectric method is generally preferred to the other methods, particularly if the frequency fluctuations are considerable. In response, piezoelectric vibration-based energy harvesters (PVEHs), have been modeled and analyzed widely. However, there are two challenges with PVEH: the maximum amount of extractable voltage and the effective (operational) frequency bandwidth are often insufficient. In this dissertation, a new type of integrated multiple system comprised of a cantilever and spring-oscillator is proposed to improve and develop the performance of the energy harvester in terms of extractable voltage and effective frequency bandwidth. The new energy harvester model is proposed to supply sufficient energy to power low-power electronic devices like RFID components. Due to the temperature fluctuations, the thermal effect over the performance of the harvester is initially studied. To alter the resonance frequency of the harvester structure, a rotating element system is considered and analyzed. In the analytical-numerical analysis, Hamilton’s principle along with Galerkin’s decomposition approach are adopted to derive the governing equations of the harvester motion and corresponding electric circuit. It is observed that integration of the spring-oscillator subsystem alters the boundary condition of the cantilever and subsequently reforms the resulting characteristic equation into a more complicated nonlinear transcendental equation. To find the resonance frequencies, this equation is solved numerically in MATLAB. It is observed that the inertial effects of the oscillator rendered to the cantilever via the restoring force effects of the spring significantly alter vibrational features of the harvester. Finally, the voltage frequency response function is analytically and numerically derived in a closed-from expression. Variations in parameter values enable the designer to mutate resonance frequencies and mode shape functions as desired. This is particularly important, since the generated energy from a PVEH is significant only if the excitation frequency coming from an external source matches the resonance (natural) frequency of the harvester structure. In subsequent sections of this work, the oscillator mass and spring stiffness are considered as the design parameters to maximize the harvestable voltage and effective frequency bandwidth, respectively. For the optimization, a genetic algorithm is adopted to find the optimal values. Since the voltage frequency response function cannot be implemented in a computer algorithm script, a suitable function approximator (regressor) is designed using fuzzy logic and neural networks. The voltage function requires manual assistance to find the resonance frequency and cannot be done automatically using computer algorithms. Specifically, to apply the numerical root-solver, one needs to manually provide the solver with an initial guess. Such an estimation is accomplished using a plot of the characteristic equation along with human visual inference. Thus, the entire process cannot be automated. Moreover, the voltage function encompasses several coefficients making the process computationally expensive. Thus, training a supervised machine learning regressor is essential. The trained regressor using adaptive-neuro-fuzzy-inference-system (ANFIS) is utilized in the genetic optimization procedure. The optimization problem is implemented, first to find the maximum voltage and second to find the maximum widened effective frequency bandwidth, which yields the optimal oscillator mass value along with the optimal spring stiffness value. As there is often no control over the external excitation frequency, it is helpful to design an adaptive energy harvester. This means that, considering a specific given value of the excitation frequency, energy harvester system parameters (oscillator mass and spring stiffness) need to be adjusted so that the resulting natural (resonance) frequency of the system aligns with the given excitation frequency. To do so, the given excitation frequency value is considered as the input and the system parameters are assumed as outputs which are estimated via the neural network fuzzy logic regressor. Finally, an experimental setup is implemented for a simple pure cantilever energy harvester triggered by impact excitations. Unlike the theoretical section, the experimental excitation is considered to be an impact excitation, which is a random process. The rationale for this is that, in the real world, the external source is a random trigger. Harmonic base excitations used in the theoretical chapters are to assess the performance of the energy harvester per standard criteria. To evaluate the performance of a proposed energy harvester model, the input excitation type consists of harmonic base triggers. In summary, this dissertation discusses several case studies and addresses key issues in the design of optimized piezoelectric vibration-based energy harvesters (PVEHs). First, an advanced model of the integrated systems is presented with equation derivations. Second, the proposed model is decomposed and analyzed in terms of mechanical and electrical frequency response functions. To do so, analytic-numeric methods are adopted. Later, influential parameters of the integrated system are detected. Then the proposed model is optimized with respect to the two vital criteria of maximum amount of extractable voltage and widened effective (operational) frequency bandwidth. Corresponding design (influential) parameters are found using neural network fuzzy logic along with genetic optimization algorithms, i.e., a soft computing method. The accuracy of the trained integrated algorithms is verified using the analytical-numerical closed-form expression of the voltage function. Then, an adaptive piezoelectric vibration-based energy harvester (PVEH) is designed. This final design pertains to the cases where the excitation (driving) frequency is given and constant, so the desired goal is to match the natural frequency of the system with the given driving frequency. In this response, a regressor using neural network fuzzy logic is designed to find the proper design parameters. Finally, the experimental setup is implemented and tested to report the maximum voltage harvested in each test execution

Rotorcraft aeroelastic stability

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low-frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability in hover and forward flight, and analysis of tilt-rotor dynamic stability are considered. Results of parametric investigations of system behavior are presented, and correlation between theoretical results and experimental data from small and large scale wind tunnel and flight testing are discussed

Survey of Army/NASA rotorcraft aeroelastic stability research

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability are considered. Results of parametric investigations of system behavior are presented, and correlations between theoretical results and experimental data from small- and large-scale wind tunnel and flight testing are discussed

Rotary-Wing Aeroelasticity: Current Status and Future Trends

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76177/1/AIAA-9022-592.pd

Conceptual Investigation of Partially Buckling Restrained Braces

Although in its infancy, leveraging high strength fiber reinforced polymer (FRP) materials for retrofit of steel structures has been the focus of recent investigations. Studies include the application of FRP to steel for flexural and fatigue or fracture retrofit as well as improving steel member stability. The research presented in this thesis attempts to introduce the concept of an FRP-stabilized steel member through a retrofit application creating a Partially Buckling Restrained Brace (PBRB). A PBRB seeks to increase steel brace stability and hysteretic energy dissipation during a seismic event through the strategic application of bonded FRP materials along its length. Six 65 ½" long A992 Gr. 50 WT6x7 steel braces were tested under cyclic compressive loading to failure. Two braces were retrofitted with carbon FRP (CFRP) and two braces were retrofitted with glass FRP (GFRP). One brace was encased in an HSS 7 x 0.125" steel tube and filled with grout to create a conventional Buckling Restrained Brace (BRB). The final brace was an unretrofit control specimen. Two arrangements of FRP materials were used for both the CFRP and GFRP retrofit braces: (1) 2" wide strip was applied to each side of the stem of the WT, and (2) 1" wide strips were applied to each side of the stem in an effort to optimize the retrofit application. The GFRP specimens increased the axial capacity of the brace by 6% and 9%, whereas the CFRP specimens had no effect. The observed variability in axial capacity was largely a result of initial loading eccentricities. The GFRP specimens did however show greater control over residual deflections suggesting that the retrofit can delay the formation of a plastic hinge within the brace and maintain compressive capacity through several cyclic loading loops. All of the FRP-retrofit specimens reduced weak-axis lateral displacement of the braces and showed increased control of local behavior. However, the brace is not dominated by local behavior due to its length, and this application may be better suited to shorter braces, similar to those found as cross frames between bridge girders, or to control local buckling in steel I-shaped beams

A Review of Friction Dissipative Beam-to-Column Connections for the Seismic Design of MRFs

The use of friction-based beam-to-column connections (BCCs) for earthquake-resistant moment-resistant frames (MRFs), aimed at eliminating damage to beam end sections due to the development of plastic hinges, has been prevalent since the early 1980s. Different technical solutions have been proposed for steel structures, and some have been designed for timber structures, while a few recent studies concern friction joints employed in reinforced concrete structures. Research aimed at characterizing the behavior of joints has focused on the evaluation of the tribological properties of the friction materials, coefficient of friction, shape and stability of the hysteresis cycles, influence of the temperature, speed of load application, effects of the application method, stability of preload, the influence of seismic excitation characteristics on the structural response, statistical characterization of amplitude, and frequency of the slip excursion during seismic excitation. Studies aimed at identifying the design parameters capable of optimizing performance have focused attention mainly on the slip threshold, device stiffness, and deformation capacity. This review compiles the main and most recent solutions developed for MRFs. Furthermore, the pros and cons for each solution are highlighted, focusing on the dissipative capacity, shape, and stability of hysteresis loops. In addition, the common issues affecting all friction connections, namely the characteristics of friction shims and the role of bolt preload, are discussed. Based on the above considerations, guidelines can be outlined that can be used to help to choose the most appropriate solutions for BCCs for MRFs