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In the high frequency analysis of vibrating systems, averaged energies are of interest to describe the response level. However, energetic parameters do not include modal information and thus exhibit smooth characteristics. In this book, the development of an efficient tool considering primary response variables in a discrete manner is mainly proposed. In this regard, two approaches are developed based on Discrete Singular Convolution. The accuracy of these approaches is validated by comparing with available analytical solutions. As a secondary study, this book introduces two different application procedures for the DSC method. The first one is an algorithm for free vibration analysis of symmetrically laminated composite plates. The second one is an implementation for free vibrations of thick beams and plates. This book is derived from the authors theses and research studies. It is provided that basic theoretical foundations of Discrete Singular Convolution for low and high frequency free and forced vibration analysis. In the book, reader can also find some basic Matlab® codes of the DSC method for free vibration analysis.