Identification of elastic properties utilizing non-destructive vibrational evaluation methods with emphasis on definitio
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REVIEW PAPER
Identification of elastic properties utilizing non-destructive vibrational evaluation methods with emphasis on definition of objective functions: a review Jun Hui Tam 1 Received: 4 July 2019 / Revised: 9 October 2019 / Accepted: 14 October 2019 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Defining a suitable objective function is important as it affects the solution search process and the solution quality. In vibrational material identification, a number of objective functions have been employed since the last decades. It is the intent of the present study to provide a comprehensive review of the previous and current trends of non-destructive vibrational material identification with emphasis on the definition of objective function. Prior to defining an objective function, several aspects should be given utmost attention, including selection of responses, design variables and goals. Along with the critical review of past research, potential areas that could be worth for future investigation are as well explicated. Keywords Elastic properties . Material identification . Non-destructive . Objective function . Vibration
Nomenclature Dij Flexural rigidities E1 or Ex Elastic modulus in 1-direction or x-direction E2 or Ey Elastic modulus in 2-direction or y-direction E3 or Ez Elastic modulus in 3-direction or z-direction FD Damage penalization term G12 or In-plane shear modulus (1-2 plane or x-y plane) Gxy Out-of-plane shear modulus (1-3 plane or x-z G13 or Gxz plane) G23 or Out-of-plane shear modulus (2-3 plane or y-z Gyz plane) K 213 Shear correction factors (1-2 plane) K 223 Shear correction factors (2-3 plane) L Surface that is parallel to y-axis MAC Modal assurance criteria MACi MAC value between experimental and evaluated mode shape of mode i. N Total number of design parameters
Responsible Editor: Raphael Haftka * Jun Hui Tam [email protected]; [email protected] 1
Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
R Wf Wfi Wi Wφ Wφi fri fMAC, 0 ff, 0 f(x) ff(x) fri fφ(x) gi(x) h n v12 or vxy v21 or vyx v13 or vxz x x0j βi
Surface that is parallel to x-axis Scaling factors or weighting factors for natural frequency Scaling factor or weighting factor for natural frequency of mode i Scaling factor or weighting factor for mode i Scaling factors or weighting factors for mode shape Scaling factor or weighting factor for mode shape of mode i Experimental natural frequency of mode i Initial values of fMAC(x) Initial values of ff(x) Objective function Natural frequency objective function Evaluated natural frequency of mode i Mode shape objective function Constraint Thickness of plate Total number of modes used Major Poisson’s ratio Minor Poisson’s ratio Minor Poisson’s ratio Design variables (expressed in terms of elastic properties or dimensionless parameters) Initial estimate of jth parameter xj Elemental stiffness reduction factor
J.H. Tam
λi λi φi φi γ
Evaluated eigenvalues λi ¼ ω2i ¼ ð2πfri Þ2 Exp
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