1. Vibration of beams
2. Vibration of rectangular(classic) Kirchhoff plates
The DSC algorithm is a wavelet collocation scheme. It is also calledlocal spectral method for its flexibility in handling boundary conditionsand spectral accuracy. It is essentially non dispersive (END) andis used to study the vibration of plates with a variety of edge and internalsupports. Among these exploitations, the vibration of plate at highfrequency modes is a challenge task for most other existing methods. Webasically achieve near 2 point per wavelength (PPW) in approximating highorder vibration modes (or thousands of vibration modes with a matrix sizeof 10 thousand).Another challenge work is the analysis of plates with random,dense internal support. Other existing methods suffer from either slowconvergence or numerical instability.
3. Vibration of Mindlin plateswith rectangular and triangular shapes and various edge supports
We developed a new method, the DSC-Ritz method, based ona combination of DSC wavelet basis functions and the pb-2-Ritz approach.The DSC-Ritz method is used to study both Kirchhoff and Mindlin plateswith a variety of boundaries and geometries.