In this chapter we set up the finite element matrix systems for the vibration of elastic rods, Euler beams, and flat elastic structures and derive finite element solutions of some examples. We also solve the eigenvalue problems that arise from the transient parabolic and hyperbolic equations and discuss their relationship with the Helmholtz equation.
KeywordsEigenvalue Problem Vibration Analysis Helmholtz Equation Finite Element Solution Euler Beam
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