Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Derivation of Equations
Equilibrium Approach
The equations of motion of a vibrating system can be derived by using the dynamic equilibrium approach, the variational method, or the integral equation formulation. This chapter considers the dynamic equilibrium approach that can be implemented by using either Newton's second law of motion or D'Alembert's principle. The assumptions made in deriving the differential equation of motion of a transversely vibrating plate are: the thickness of the plate is small compared to its other dimensions; the middle plane of the plate does not undergo in‐plane deformation; the transverse deflection is small compared to the thickness of the plate; and the influence of transverse shear deformation is neglected. In the equilibrium approach, the boundary conditions are developed by considering the physics of the problem. Although the equilibrium and variational approaches can give the same equations of motion, the variational methods have the advantage of yielding the exact form of the boundary conditions automatically.
Derivation of Equations
Equilibrium Approach
The equations of motion of a vibrating system can be derived by using the dynamic equilibrium approach, the variational method, or the integral equation formulation. This chapter considers the dynamic equilibrium approach that can be implemented by using either Newton's second law of motion or D'Alembert's principle. The assumptions made in deriving the differential equation of motion of a transversely vibrating plate are: the thickness of the plate is small compared to its other dimensions; the middle plane of the plate does not undergo in‐plane deformation; the transverse deflection is small compared to the thickness of the plate; and the influence of transverse shear deformation is neglected. In the equilibrium approach, the boundary conditions are developed by considering the physics of the problem. Although the equilibrium and variational approaches can give the same equations of motion, the variational methods have the advantage of yielding the exact form of the boundary conditions automatically.
Derivation of Equations
Equilibrium Approach
Rao, Singiresu S. (Autor:in)
Vibration of Continuous Systems ; 69-85
06.03.2019
17 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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