Monitoring prestress in plates by sideband peak count-index (SPC-I) and nonlinear higher harmonics techniques

Abstract

Abstract Propagating guided waves in a homogeneous, isotropic, prestressed, hyperelastic plate show nonlinear characteristics that depend on the state of initial prestress. These nonlinear phenomena include higher harmonic generation, occurring when Lamb wave modes of different frequencies ( $$\omega _a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:math> and $$\omega _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> ) are allowed to mix within the material generating secondary waves at frequencies $$2\omega _a,2\omega _b\, \text {and}\,\omega _a\pm \omega _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mspace/> <mml:mtext>and</mml:mtext> <mml:mspace/> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>±</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:mrow> </mml:math> . Further, if prescribed internal-resonance conditions are satisfied, the amplitude of secondary waves increases in space, providing a response quantity which is dependent on prestress and easy to be observed. Using the finite element method, in this paper we investigate the time and space evolution of higher harmonics arising in one-way wave mixing. The influence of prestress on the response is elucidated, observing the nonlinear parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> . It is further shown that the nonlinear ultrasonic technique called sideband peak count-index (SPC-I) can provide an effective monitoring tool for prestress.

Topics & Concepts