Abstract
Paper describes a simulation of an elastic wave in homogenous isotropic waveguide with generic cross-section using semi-analytical finite element (SAFE) formulation. The wave is considered a travelling displacement field in the waveguide as a result to forcing excitation and is expressed via modes’ superposition. The solutions for modes are obtained solving SAFE governing eigen problem. Attenuation of the medium in SAFE framework differently from prior researchers is simulated via Rayleigh damping. It is shown, that severe damping is not properly supported by the SAFE formulation and revision for properly accepting linear viscosity is needed.
Highlights
The guided elastic waves are widely used in non-destructive long-range inspection for the elongated structures
By the computational experiments presented here we investigate how the dispersion curves of different wave modes depend on values and
The analysis of propagating waves in waveguides by semi-analytical finite element (SAFE) method enables to obtain the travelling-wave responses in infinite or almost-infinite waveguide structures
Summary
The guided elastic waves are widely used in non-destructive long-range inspection for the elongated structures (waveguides). The dispersion curves provide information about phase and group velocities of the waves at particular frequency. The first theoretical approach to guided waves dates back to Pochhammer and Chree who were the first researchers, who obtained the solution in the form of dispersion curves of the rod waveguides [5, 6]. Along with obtaining the dispersion curves, the extensions of SAFE approach may simulate the forced response of the waveguide excited by the piezoelectric transducer at one end [2]. In most investigations SAFE provided the dispersive solutions of waves in undamped waveguides of arbitrary cross-sections. We analyzed the free and forced propagating wave response of the waveguide subjected to Rayleigh damping by employing SAFE method. The forced response was presented as the superposition of the modes obtained SAFEM
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