Vibrations of Elastic Systems: With Applications to MEMS and NEMS (Solid Mechanics and Its Applications Book 184)

"This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures. Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated. A large number of graphs and tables are given to show the impact of various factors on the systems' natural frequencies, mode shapes, and responses"--SpringerLink Annotation This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures. Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated. A large number of graphs and tables are given to show the impact of various factors on the systems natural frequencies, mode shapes, and responses Front Matter....Pages i-xvi Introduction....Pages 1-6 Spring-Mass Systems....Pages 7-82 Thin Beams: Part I....Pages 83-220 Thin Beams: Part II....Pages 221-271 Timoshenko Beams....Pages 273-339 Thin Plates....Pages 341-399 Cylindrical Shells and Carbon Nanotube Approximations....Pages 401-437 Back Matter....Pages 439-489