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The objective of this work is to develop mathematical simulation models for predicting the transient behaviour of strings and beams subjected to impacts. The developed models are applied to study the dynamics of the piano and the sitar. For simulating rigid point impacts on continuous systems, a new method is proposed based on the unit impulse response. The developed method allows one to relate modal velocities before and after impact, without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. The results using the unit-impulse-based coefficient of restitution method are also compared to those obtained with a penalty approach,with good agreement. A new moving boundary formulation is presented to simulate wrapping contacts in continuous systems impacting rigid distributed obstacles. The free vibration response of an ideal string impacting a distributed parabolic obstacle located at its boundary is analyzed to understand and simulate a sitar string. The portion of the string in contact with the obstacle is governed by a different partial differential equation (PDE) from the free portion represented by the classical string equation. These two PDEs and corresponding boundary conditions, along with the transversality condition that governs the dynamics of the moving boundary, are obtained using Hamilton's principle. A Galerkin approximation is used to convert them into a system of nonlinear ordinary differential equations, with time-dependent mode-shapes as basis functions. The advantages and disadvantages of the proposed method are discussed in comparison to the penalty approach for simulating wrapping contacts. Finally, the model is used to investigate the mechanism behind the generation of the buzzing tone in a sitar. An alternate formulation using the penalty approach is also proposed, and the results are contrasted with those obtained using the moving boundary approach. A model for studying the interaction between a flexible beam and a string at a point including friction has also been developed. This model is used to study the interaction between a piano hammer and the string. A realistic model of the piano hammer-string interaction must treat both the action mechanism and the string. An elastic stiff string model is integrated with a dynamic model of a compliant piano action mechanism with a flexible hammer shank. Simulations have been used to compare the mechanism response for impact on an elastic string and a rigid stop. Hammer head scuffing along the string, as well as length of time in contact, were found to increase where an elastic string was used, while hammer shank vibration amplitude and peak contact force decreased. Introducing hammer-string friction decreases the duration of contact and reduces the extent of scuffing. Finally, significant differences in hammer and string motion were predicted for a highly flexible hammer shank. Initial contact time and location, length of contact period, peak contact force, hammer vibration amplitude, scuffing extent, and string spectral content were all influenced.

The objective of this work is to develop mathematical simulation models for predicting the transient behaviour of strings and beams subjected to impacts. The developed models are applied to study the dynamics of the piano and the sitar. For simulating rigid point impacts on continuous systems, a new method is proposed based on the unit impulse response. The developed method allows one to relate modal velocities before and after impact, without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. The results using the unit-impulse-based coefficient of restitution method are also compared to those obtained with a penalty approach,with good agreement. A new moving boundary formulation is presented to simulate wrapping contacts in continuous systems impacting rigid distributed obstacles. The free vibration response of an ideal string impacting a distributed parabolic obstacle located at its boundary is analyzed to understand and simulate a sitar string. The portion of the string in contact with the obstacle is governed by a different partial differential equation (PDE) from the free portion represented by the classical string equation. These two PDEs and corresponding boundary conditions, along with the transversality condition that governs the dynamics of the moving boundary, are obtained using Hamilton's principle. A Galerkin approximation is used to convert them into a system of nonlinear ordinary differential equations, with time-dependent mode-shapes as basis functions. The advantages and disadvantages of the proposed method are discussed in comparison to the penalty approach for simulating wrapping contacts. Finally, the model is used to investigate the mechanism behind the generation of the buzzing tone in a sitar. An alternate formulation using the penalty approach is also proposed, and the results are contrasted with those obtained using the moving boundary approach. A model for studying the interaction between a flexible beam and a string at a point including friction has also been developed. This model is used to study the interaction between a piano hammer and the string. A realistic model of the piano hammer-string interaction must treat both the action mechanism and the string. An elastic stiff string model is integrated with a dynamic model of a compliant piano action mechanism with a flexible hammer shank. Simulations have been used to compare the mechanism response for impact on an elastic string and a rigid stop. Hammer head scuffing along the string, as well as length of time in contact, were found to increase where an elastic string was used, while hammer shank vibration amplitude and peak contact force decreased. Introducing hammer-string friction decreases the duration of contact and reduces the extent of scuffing. Finally, significant differences in hammer and string motion were predicted for a highly flexible hammer shank. Initial contact time and location, length of contact period, peak contact force, hammer vibration amplitude, scuffing extent, and string spectral content were all influenced.

The aim with this master thesis was to set up a FE-simulation of an impact test of a bike helmet in LS-DYNA that correlates well with the peak acceleration score of a real life impact test. Furthermore, a parametric study has been performed in LS DYNA to investigate the robustness of the model, as well as to see which parameters have a great influence on the peak acceleration score. To investigate the acceleration of the helmet, helmet drop tests have been performed at the Borås RISE lab. Building an FE-model of the helmet drop test required multiple iterations to ensure stability and accuracy of the model. The steps of the modelling process included investigating previous simulations of helmet impacts in LS-DYNA, preprocessing of CAD, defining material models and establishing contact and boundary conditions. The parameters that have proven to have a great impact on the peak acceleration value are the tensile stress cutoff, the PC shell thickness, the strain rate dependency, and the EPS thickness. A conclusion of this work is that FE modelling is a way to approximate the peak acceleration value for linear impact tests, and a useful tool for investigating design parameters. The density of the EPS foam is shown to have a large influence on the peak acceleration value in both the experimental tests and the FE simulation. From the FE simulationns, the thickness of the EPS, as well as the thickness of the PC shell have shown to have a great impact on the peak acceleration score. / Syftet med denna masteruppsats var att sätta upp en FE-simulering av ett islagstest för en cykelhjälm i LS-DYNA som korrelerar bra med experimentella islagstest. Vidare har en parametrisk studie utförts i LS DYNA för att undersöka modellens robusthet, samt för att se vilka parametrar som har en stor påverkan på maxaccelerationen. För att undersöka hjälmens acceleration, har islagstester av cykelhjälmar utförts på RISE lab i Borås. För att bygga en FE-modell av ett islagstest krävdes flera iterationer för att säkerställa modellens stabilitet och noggrannhet. Stegen i modelleringsprocessen inkluderade undersökning av tidigare simuleringar av hjälmar i LS-DYNA, förbearbetning av CAD-filer, definiering av materialmodeller och upprättande av kontakt och gränsvillkor. De parametrar som har visat sig har en stor inverkan på det maximala accelerationsvärdet är dragspänningsgränsen, skaltjockleken på PC:n, töjningshastighetsberoendet och EPS-tjockleken. En slutsats av detta arbete är att FE-modellering är ett sätt att approximera värdet på maxaccelerationen för linjära islagstester och ett användbart verktyg för att undersöka designparametrar. Densiteten av EPS-skum har visat sig ha en stor inverkan på maxaccelerationsvärdet i både experimentella tester och FE-simuleringen.

This paper is concerned with general issues related to social impact modelling and assessment of AI-enabled web-based learning platforms (AILPs) fnanced through public funds. The approach described here sheds new light on the assessment of open-access knowledge repositories, overcoming the difculties associated with the estimation of their fnancial characteristics that limit the usefulness of the well-known social return on investment (SROI) method (Pathak, & Dattani, 2014). Another group of methods, namely those based on innovation difusion models (Li et al., 2020), turned out to be inadequate as they do not fully grasp the network-dependent characteristics of online information difusion and immediate social recommendation propagation n the Internet. A promising research case is the successful implementation of the e-science platform within the recent Horizon 2020 project MOVING. Among the contractual goals of this platform is to leverage knowledge provision for efcient training and research in academia, corporations, and public administration. Thus, social impact goals can be achieved with efcient user community building, which assumes the wide use of existing cooperation networks between potential users, and explores the opportunities provided by social media. [Aus: Problem statement]