2017/04/01 by Alan E. Lindsay, Lindsay, Alan E., Bryan Quaife +3 · 1 citation
Engineering · #Acoustic Wave Phenomena Research #Composite Structure Analysis and Optimization #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1704.00160
openalex publication_date 2017/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the bi-Laplacian eigenvalue problem for the modes of vibration of\na thin elastic plate with a discrete set of clamped points. A high-order\nboundary integral equation method is developed for efficient numerical\ndetermination of these modes in the presence of multiple localized defects for\na wide range of two-dimensional geometries. The defects result in\neigenfunctions with a weak singularity that is resolved by decomposing the\nsolution as a superposition of Green's functions plus a smooth regular part.\nThis method is applied to a variety of regular and irregular domains and two\nkey phenomena are observed. First, careful placement of clamping points can\nentirely eliminate particular eigenvalues and suggests a strategy for\nmanipulating the vibrational characteristics of rigid bodies so that\nundesirable frequencies are removed. Second, clamping of the plate can result\nin partitioning of the domain so that vibrational modes are largely confined to\ncertain spatial regions. This numerical method gives a precision tool for\ntuning the vibrational characteristics of thin elastic plates.\n