210 v. Kostopoulos et al Accelerometer 0.5 Spectrum Analysis Initial Velocity ditioning Amplifier A/D Gripping System Signal from stress measuring device sinusoid load Gate for selected measures Waveform Emission SPARTAN AT 8000 Acoustic Preamplif Emission 40dB System Analysing System Gripping system of the Universal testing machine Fig. 2.(a) Representation of the experimental set up for the dynamic response measurements;(b) Representation of the experi- mental set up for the acoustic emission The general solution of eqn(3)exhibits the form Wn(x, t)=Cmen+C2ne-kn+CS,en+ C4, e-inAI [D=正E=下成(1+r where the following relation has been used where Ex is the real part of Exe, Ere is the mea sure of El, e and ne is the effective loss factor which is defined as Assuming the wave number kep then the vibration frequency is a complex quantity of the form nex= Rx(Ee is the imaginary part of Exe)(8) Finally the application of the boundary conditions and for physical reasons Imposing for De"the for the case of a cantilever beam concludes to the form that contains the effective complex bending following expression for the eigenfrequencies of the modulus of elasticity then problem4The general solution of eqn (3) exhibits the form Wn…x;t†ˆ Cc 1nenx‡Cc 2neÿnx‡Cc 3neinx‡Cc 4neÿinx  …4† where the following relation has been used k4 n ˆ !c2 n a2 c …5† Assuming the wave number k" then the vibration frequency is a complex quantity of the form !c n ˆ !n ÿ idn …6† and for physical reasons Imposing for Dc xx ÿ1 the form that contains the e€ective complex bending modulus of elasticity then Dc xx ÿ1 ˆ 12 h3 : 1 Ec;e xx ˆ 12 h3 1 ER;e xx 1 ‡ ne xx ÿ
ˆ 12 h3 : 1 jEc;e xx jei: arctan ne ‰ Š xx …7† where ER;e xx is the real part of Ec;e xx ; jEc;e xx j is the mea￾sure of Ec;e xx and ne xx is the e€ective loss factor which is de®ned as ne xx ˆ EI;e xx ER;e xx …EI;e xx is the imaginary part of Ec;e xx † …8† Finally the application of the boundary conditions for the case of a cantilever beam concludes to the following expression for the eigenfrequencies of the problem14 Fig. 2. (a) Representation of the experimental set up for the dynamic response measurements; (b) Representation of the experi￾mental set up for the acoustic emission measurements. 210 V. Kostopoulos et al.