Hyun Woo Park

Accurate closed-form descriptions of wave scattering caused by edge cracks in thick beams remain challenging because the scattering process involves coupled axial, propagating bending, and evanescent bending wave motions. While previous studies resolved the incident propagating bending wave case for an edge-cracked Timoshenko beam, the physical roles of modes I and II crack in multimodal wave scattering have not been fully elucidated, particularly for incident axial and evanescent bending waves, owing to the absence of the corresponding closed-form coefficients. Accordingly, the remaining 12 closed-form scattering coefficients were derived within a unified axial–bending–shear–coupling framework, thereby completing the 18-coefficient scattering matrix for the three admissible incident wave types. An analysis of the completed matrix revealed that the contribution of mode II crack to wave scattering was selective. All six scattering responses induced by an incident axial wave were governed exclusively by mode I crack and were independent of mode II crack compliance, whereas incident evanescent bending waves produced coupled scattering involving both modes I and II crack and could contribute substantially to the conversion into propagating bending waves at higher normalized frequencies. The formulation was further examined through the far-field power flux balance, which demonstrated that mode II crack compliance locally redistributed individual scattering amplitudes but did not affect the macroscopic energy balance. The proposed closed-form solutions were validated via comparison with previously reported finite-element analysis results. This framework provides physical insights into multimodal wave scattering and offers an analytical basis for model-based inverse analysis in ultrasonic crack evaluation.

Conventional crack evaluation techniques that utilize the first few narrowband modal frequencies often suffer from limited accuracy and robustness, particularly when assessing multiple incipient cracks in a beam (i.e., crack–depth ratio < 0.2). To overcome these limitations, this study proposes a crack assessment method that leverages broadband modal frequencies measured from surface‐bonded piezoelectric wafers up to the beam’s cut‐off frequency. The proposed approach employs a closed‐form frequency equation derived from the phase‐closure principle, which accurately predicts the fractional reduction in modal frequencies caused by incipient cracks. This equation enables the construction of a large database of fractional reduction in modal frequencies for various multiple incipient crack scenarios with minimal computational cost. Using this database, we constructed a physics‐informed machine learning model to identify the number of incipient cracks. Next, we estimated the locations and depths of the cracks by minimizing the least‐squares error between the measured and calculated fractional reductions using the closed‐form frequency equation. In addition, the optimal grid resolution was determined using a bilinear fitting method to reduce the computation time required to solve the minimization problem. The proposed method is evaluated through blind tests using numerical simulation datasets from finite element analysis and experimental datasets from piezoelectric wafers bonded on beams with various multiple‐crack scenarios. The blind‐test results provide insight into the diagnostic capability and robustness of the proposed approach, demonstrating its practical applicability for reliable crack‐number prediction under experimental measurement uncertainty and supporting its potential use in structural health monitoring of beam‐like structures.

This paper proposes a physics-informed neural network (PINN) for predicting the early-age time-dependent behaviors of prestressed concrete beams. The PINN utilizes deep neural networks to learn the time-dependent coupling among the effective prestress force and the several factors that affect the time-dependent behavior of the beam, such as concrete creep and shrinkage, tendon relaxation, and changes in concrete elastic modulus. Unlike traditional numerical algorithms such as the finite difference method, the PINN directly solves the integro-differential equation without the need for discretization, offering an efficient and accurate solution. Considering the trade-off between solution accuracy and the computing cost, optimal hyperparameter combinations are determined for the PINN. The proposed PINN is verified through the comparison to the numerical results from the finite difference method for two representative cross sections of PSC beams.

이 논문은 곡선보의 모드 진동수를 예측하기 위해 단순화된 진동수 방정식을 제시한다. 특히, 한쌍의 전달 파동과 두쌍의 소멸 파동이 존재하는 곡선보의 진동수 범위에서 단순화된 진동수 방정식을 유도한다. 보의 양쪽 지점으로 입사되는 소멸 파동은 무시할 수 있다고 가정한다. 위상폐합원리를 다양한 지점 조건을 가지는 곡선보에 적용한다. 곡선보에서 파 반사 계수를 먼저 계산한 후 파 반사에 의한 위상변화를 위상폐합원리에 적용하여 진동수 방정식을 유도한다. 진동수 방정식으로부터 모드 진동수를 계산하기 위해 뉴턴-랩슨법을 적용한다. 제안된 주파수 방정식은 다양한 지지 조건 및 스팬 각도에 대한 수치 해석 결과로 검증한다.

This article analytically formulates and investigates the evolution of electromechanical admittance of piezoelectric transducers collocated on a finite beam from wave propagation perspective. First, the analytic wave solutions are obtained based on the linear piezoelectricity and the Timoshenko beam theory. Then, the evolution of wave propagation to vibration on a finite beam has been formulated in terms of a wave unit which appears periodically due to the multiple reflections at beam supports. The formulation has been extended to describe the underlying mechanism how electromechanical signatures evolve from wave units. The support conditions and material damping of a beam have been considered explicitly for both wave units and electromechanical signatures. The validity of the proposed formulation has been demonstrated through proof-of-concept numerical examples providing valuable physical insights into the relevance between wave units and electromechanical signatures.