title: Free vibration analysis of plates and shells by using the Superposition Method

authors: Mochida, Yusuke

subjects: Superposition Method

abstract: This thesis is devoted to investigate the capability of the Superposition Method for obtaining the transient response of plates and the natural frequencies of thin doubly curved shallow shells. The Superposition Method gives accurate results with only a few terms and has proved to be efficient for both cases. To investigate the transient response, all supports of a thin simply supported rectangular plate under self weight are suddenly removed. The resulting motion comprises a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response. The modes and natural frequencies of the plate are obtained using the Superposition Method and the Rayleigh-Ritz method with the ordinary and degenerated free-free beam functions. The W–W algorithm is then used to delimit the natural frequencies from the frequency equation derived in a determinantal form. There is an excellent agreement between the results from both approaches but the modes based on the Superposition Method result in more accurate values with fewer terms, and have shown faster convergence. The results from the Superposition Method may serve as benchmarks for the transient response of completely free plates. The transient response is found to be dominated by the lower modes. The centre of vibration is shifted parallel from the original xy plane by the distance of the first mode of the plate (a rigid body translation) multiplied by the first transient coefficient. In the investigation of doubly curved shells, the natural frequency parameters of thin shallow shells with three different sets of boundary conditions were obtained for several different curvature ratios and two aspect ratios. The solutions to the building blocks, which are subject to simply-supported out-of-plane conditions and shear diaphragm in-plane conditions at all four edges, are represented by series of sine and cosine functions, generated using Galerkin’s method since an exact solution is not available for the doubly curved shells. Once displacement functions for the building blocks are obtained, the prescribed boundary conditions of the actual shell under investigation are then satisfied using the Superposition Method. The rate of convergence is found to be excellent and the results agree well with published results obtained using the Ritz method and those obtained using a Finite Element package, Abaqus. The computations show that it is possible to obtain the first 12 natural frequency parameters of the shallow shells on the rectangular planform with a rapid convergence rate.

text: Free vibration analysis of plates and shells by using the Superposition Method This thesis is devoted to investigate the capability of the Superposition Method for obtaining the transient response of plates and the natural frequencies of thin doubly curved shallow shells. The Superposition Method gives accurate results with only a few terms and has proved to be efficient for both cases. To investigate the transient response, all supports of a thin simply supported rectangular plate under self weight are suddenly removed. The resulting motion comprises a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response. The modes and natural frequencies of the plate are obtained using the Superposition Method and the Rayleigh-Ritz method with the ordinary and degenerated free-free beam functions. The W–W algorithm is then used to delimit the natural frequencies from the frequency equation derived in a determinantal form. There is an excellent agreement between the results from both approaches but the modes based on the Superposition Method result in more accurate values with fewer terms, and have shown faster convergence. The results from the Superposition Method may serve as benchmarks for the transient response of completely free plates. The transient response is found to be dominated by the lower modes. The centre of vibration is shifted parallel from the original xy plane by the distance of the first mode of the plate (a rigid body translation) multiplied by the first transient coefficient. In the investigation of doubly curved shells, the natural frequency parameters of thin shallow shells with three different sets of boundary conditions were obtained for several different curvature ratios and two aspect ratios. The solutions to the building blocks, which are subject to simply-supported out-of-plane conditions and shear diaphragm in-plane conditions at all four edges, are represented by series of sine and cosine functions, generated using Galerkin’s method since an exact solution is not available for the doubly curved shells. Once displacement functions for the building blocks are obtained, the prescribed boundary conditions of the actual shell under investigation are then satisfied using the Superposition Method. The rate of convergence is found to be excellent and the results agree well with published results obtained using the Ritz method and those obtained using a Finite Element package, Abaqus. The computations show that it is possible to obtain the first 12 natural frequency parameters of the shallow shells on the rectangular planform with a rapid convergence rate.

year: 2010

title: Facilitating Elemental Composition in an Orff Classroom

authors: Stewart, Celia Ann

subjects: Orff Schulwerk

abstract: This study sought to gain an understanding of how the programming and pedagogical decisions of an Orff teacher impact on the success of a group of children in composing in an elemental style. Orff-Schulwerk is a child-centred approach to music education, which uses songs, dances, rhymes, clapping games, poetry and stories from the child’s world as the basis of music and movement activities. Carl Orff, originator of the approach, called this music and movement activity “elemental” – basic, unsophisticated, concerned with the fundamental building blocks of music and movement. 

This self-study project focused on two questions: 1. What pedagogical decision-making facilitated student achievement of the music programme learning objectives? 2. What activity design factors facilitated student achievement of the music programme learning objectives? To answer these questions, a programme of work was planned and implemented with a group of sixteen Year 5 and 6 students. The students worked sequentially with a range of Orff processes and media before embarking on their own compositions. Data were collected through four methods: a personal reflective journal, video recordings of two sessions, the observations of two critical friends and a focus group made up of five students, randomly selected from the participants who were interviewed at the mid- and end-point of the programme. An inductive, thematic approach was used to analyse the data. Themes emerging from an analysis of journal reflections were compared and contrasted with themes emerging from an analysis of critical friend observations and focus group interviews.

This study found that the most successful pedagogical strategies that facilitated successful outcomes for this group of students were: creating a safe and supportive environment; facilitation of collaborative learning; encouraging and empowering the children to make connections to, and draw on, their previous learning; facilitating opportunities for in-depth reflection by the peer group and the students themselves; providing constructive feedback and feed-forward; the provision of sufficient time and opportunity; the use of humour; teacher modelling: ensuring the aims and expectations are clear and managing classroom behaviour.

In investigating the general nature of activities, this study found that the most successful were those that: explored Orff media and utilised Orff pedagogy; energised and focussed the participants; involved the children in practical music making where they were using their whole bodies to sing, move and play; were scaffolded and allowed children to enter at a level that was comfortable for them; had clear links to both the short and long-term goals; and made links to children’s lives and experiences. The specific activities that the students found most successful were those that explored the pentatonic scale and provided opportunities for improvisation and the playing activities, with both body and untuned percussion. 

The study was limited to a small group of children in a high-decile school that was well resourced. All students except one had a strong musical background with some instrumental skills. Results may have been different with a cohort of students from a lower decile school, who may not have had the musical background that this group had.

text: Facilitating Elemental Composition in an Orff Classroom This study sought to gain an understanding of how the programming and pedagogical decisions of an Orff teacher impact on the success of a group of children in composing in an elemental style. Orff-Schulwerk is a child-centred approach to music education, which uses songs, dances, rhymes, clapping games, poetry and stories from the child’s world as the basis of music and movement activities. Carl Orff, originator of the approach, called this music and movement activity “elemental” – basic, unsophisticated, concerned with the fundamental building blocks of music and movement. 

This self-study project focused on two questions: 1. What pedagogical decision-making facilitated student achievement of the music programme learning objectives? 2. What activity design factors facilitated student achievement of the music programme learning objectives? To answer these questions, a programme of work was planned and implemented with a group of sixteen Year 5 and 6 students. The students worked sequentially with a range of Orff processes and media before embarking on their own compositions. Data were collected through four methods: a personal reflective journal, video recordings of two sessions, the observations of two critical friends and a focus group made up of five students, randomly selected from the participants who were interviewed at the mid- and end-point of the programme. An inductive, thematic approach was used to analyse the data. Themes emerging from an analysis of journal reflections were compared and contrasted with themes emerging from an analysis of critical friend observations and focus group interviews.

This study found that the most successful pedagogical strategies that facilitated successful outcomes for this group of students were: creating a safe and supportive environment; facilitation of collaborative learning; encouraging and empowering the children to make connections to, and draw on, their previous learning; facilitating opportunities for in-depth reflection by the peer group and the students themselves; providing constructive feedback and feed-forward; the provision of sufficient time and opportunity; the use of humour; teacher modelling: ensuring the aims and expectations are clear and managing classroom behaviour.

In investigating the general nature of activities, this study found that the most successful were those that: explored Orff media and utilised Orff pedagogy; energised and focussed the participants; involved the children in practical music making where they were using their whole bodies to sing, move and play; were scaffolded and allowed children to enter at a level that was comfortable for them; had clear links to both the short and long-term goals; and made links to children’s lives and experiences. The specific activities that the students found most successful were those that explored the pentatonic scale and provided opportunities for improvisation and the playing activities, with both body and untuned percussion. 

The study was limited to a small group of children in a high-decile school that was well resourced. All students except one had a strong musical background with some instrumental skills. Results may have been different with a cohort of students from a lower decile school, who may not have had the musical background that this group had.

year: 2013

title: Health information research privacy standards should include Māori perspectives on privacy

authors: Ragupathy, Rajan

subjects: computer science

abstract: Secondary research using health records and other personal health data (henceforth referred to as health information research) is a valuable tool for tackling New Zealand’s health and social challenges. It requires however suitable privacy standards to maintain public confi dence and social license. The privacy protocols used by New Zealand district health boards have been described in this journal, as have additional safeguards that could be adopted to prevent privacy breaches.¹,²

text: Health information research privacy standards should include Māori perspectives on privacy Secondary research using health records and other personal health data (henceforth referred to as health information research) is a valuable tool for tackling New Zealand’s health and social challenges. It requires however suitable privacy standards to maintain public confi dence and social license. The privacy protocols used by New Zealand district health boards have been described in this journal, as have additional safeguards that could be adopted to prevent privacy breaches.¹,²

year: 2019