Forced vibration analysis of inhomogeneous rods with non-uniform cross-section



Forced vibration analysis of cantilever rods is presented that have material properties and crosssection
areas that arbitrarily vary in the axial direction, solved using Laplace transform in time
domain and complementary functions method (CFM) in the spatial domain. Under the Laplace
transformation, the partial differential equation is transformed into time-independent boundary
value problem in the axial direction, which is solved by CFM. Then, inverse transform is taken
by modified Durbin’s method into the time domain. In the end, the non-dimensional displacement
results are compared with both benchmark and finite element method (FEM) solutions available in
the literature. In addition to satisfying a fair amount of accuracy with small computational costs,
the approach presented in this study is well-structured, simple, and efficient.


Inhomogeneous; non-uniform; complementary functions method; Laplace transform.

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