... characteristic of a cracked cantilever beam is approximated by a truncated polynomial series and response amplitudes of various harmonics are investigated for both qualitative and quantitative characterization. A new procedure is suggested whereby the presence of a breathing crack in a structure can be first...

...Muhammad Tanveer; Anand V. Singh A numerical approach is presented for linear and geometrically nonlinear forced vibrations of laminated composite plates with piezoelectric materials. The displacement fields are defined generally by high degree polynomials and the convergence of the results...

... characteristic orthogonal polynomials generated by using Gram-Schmidt orthogonalization procedure in Rayleigh-Ritz method. 19 12 2005 25 07 2006 vibrations structural acoustics Rayleigh-Ritz methods Young's modulus shear modulus polynomials elliptic orthotropic nonhomogeneous...

...J. L. Liu Piecewise interpolation polynomials are employed to approximate an arbitrary dynamic load. By extending the Duhamel integral, we can offer a numerical solution technique of the differential equation of motion in various kinds of material and damping cases in every branch of force...

...-invariant systems are represented by linear differential equations, which reduce to polynomial equations through Laplace transformation. These studies have resulted in important findings leading to computationally tractable methods based on the type...

... components u s , u z , and u θ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ϕ and z directions. Potential (strain) and kinetic energies of the circular ring are formulated, and upper bound values...