STUDY ON MESHFREE HERMITE RADIAL POINT INTERPOLATION METHOD FOR FLEXURAL WAVE PROPAGATION MODELING AND DAMAGE QUANTIFICATION

Abstract

THIS PAPER STUDIES ON THE NUMERICAL MODELING OF THE FLEXURAL WAVE PROPAGATION IN EULER-BERNOULLI BEAMS USING THE HERMITE-TYPE RADIAL POINT INTERPOLATION METHOD (HRPIM) UNDER THE DAMAGE QUANTIFICATION APPROACH. HRPIM EMPLOYS RADIAL BASIS FUNCTIONS (RBFS) AND THEIR DERIVATIVES FOR SHAPE FUNCTION CONSTRUCTION AS A MESHFREE TECHNIQUE. THIS STUDY EVALUATES THE PERFORMANCE OF MULTIQUADRIC (MQ) RBF TO THE ASSESSMENT OF THE REFLECTION RATIO AND HRPIM SIGNALS COMPARED WITH THE THEORETICAL AND FINITE ELEMENT RESPONSES. THE RESULTS REPRESENT THAT MQ IS A SUITABLE RBF FOR HRPIM AND WAVE PROPAGATION; HOWEVER, THE RANGE OF THE PROPER SHAPE PARAMETERS IS IMPRESSIVE. FURTHERMORE, IT CAN BE FOUND THE NUMBER OF FIELD NODES IS THE MAIN PARAMETER FOR ACCURATE WAVE PROPAGATION MODELING USING HRPIM. THE SIZE OF SUPPORT DOMAIN SHOULD BE LESS THAN AN UPPER BOUND TO PREVENT HIGH ERROR. WITH REGARD TO THE NUMBER OF QUADRATURE POINTS, PROVIDING THE MINIMUM NUMBERS OF POINTS ARE ADEQUATE FOR THE STABLE SOLUTION BUT THE EXISTENCE OF MORE POINTS IN DAMAGE REGION DOES NOT LEADS TO NECESSARILY THE ACCURATE RESULTS. IT IS CONCLUDED THE PURE HRPIM WITHOUT ANY POLYNOMIAL TERMS IS ACCEPTABLE BUT CONSIDERING A FEW TERMS WILL IMPROVE THE ACCURACY EVEN THOUGH MORE TERMS MAKES THE PROBLEM UNSTABLE AND INACCURATE.