.... By using the addition theorems of Bessel functions, a complex scattering wave field of multiple damage is investigated. Measurements agreed well between theoretical results and FE simulations. Numerical results of a plate with two damage are graphically presented by considering S 0 and A 0 modes...

... ( 3 − ε + 2 ε 2 ω ¯ 2 − ε 2 2 ω ¯ 2 z 2 ) The homogeneous solution of Eq. 2 is a linear combination of two Bessel functions that can be written as A3 v ¯ h ( z ) = C 1 J 0 ( z ) + C 2 Y 0 ( z ) where...

... matrix algebra Bessel functions A broad range of engineering problems involves longitudinal vibration analysis of uniform and nonuniform bars. A great deal of research on longitudinal vibration of structural components has taken place over the last decade, as reviewed by Timoshenko et al. 1...

... to Bessel’s equations or ordinary differential equations with constant coefficients for several cases, and the corresponding exact analytical solutions are thus obtained. All the exact solutions derived here are expressed in terms of Bessel functions or trigonometric functions. The numerical example shows...