Structural Vibration : Exact Solutions for Strings, Membranes, Beams, and Plates

This book is a comprehensive survey on multiple exact vibration solutions. It serves as a benchmark for other approximate methods used by industry professionals, researchers, and academics working in structural and mechanical engineering. Specifically, it provides basic governing equations of motion and boundary conditions, as well as exact solutions for the vibration of beams, plates, membranes, and strings. It examines the exact functions for a large range of differential equations, providing a rich source of practical problems when teaching differential equations to engineering science students.

Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates offers an introduction to structural vibration and highlights the importance of the natural frequencies in design. It focuses on free vibrations for analysis and design of structures and machine and presents the exact vibration solutions for strings, membranes, beams, and plates.

This book emphasizes the exact solutions for free transverse vibration of strings, membranes, beams, and plates. It explains the intrinsic, fundamental, and unexpected features of the solutions in terms of known functions as well as solutions determined from exact characteristic equations. The book provides:

• A single-volume resource for exact solutions of vibration problems in strings, membranes, beams, and plates
• A reference for checking vibration frequency values and mode shapes of structural problems
• Governing equations and boundary conditions for vibration of structural elements
• Analogies of vibration problems

provides practicing engineers, academics, and researchers with a reference for data on a specific structural member as well as a benchmark standard for numerical or approximate analytical methods.