Abstract
This study presents a systematic re-examination of zero-frequency component (ZFC) characteristics in nonlinear ultrasonic waves, with particular emphasis on rectangular pulse excitation scenarios. By combining theoretical analysis with finite-element simulations, we reveal that material nonlinearities substantially affect the waveform morphology of ZFC. Our results demonstrate that materials exhibiting bilinear stiffness nonlinearity (BSN) produce a distinct right-triangular ZFC profile, while those with weak quadratic nonlinearity (WQN) generate a flat-topped ZFC configuration. These findings not only provide critical insights for resolving long-standing controversies regarding ZFC waveform characteristics, but also establish ZFC analysis as a robust diagnostic methodology for identifying specific nonlinear constitutive behaviors in materials. The research advances the fundamental understanding of nonlinear wave propagation mechanisms and paves the way for novel applications in quantitative material characterization and precision damage assessment. This work provides critical insights for refining nonlinear ultrasonic measurement interpretation and introduces a promising paradigm for non-destructive evaluation techniques.
Key Words
bilinear stiffness; quasi-static component; structure health monitoring; weak quadratic nonlinearity; zerofrequency component
Address
Xiao-Qiang Sun: Chongqing Industry Polytechnic College, Chongqing, 401120, P.R. China
Fei-Long Li: Centre for Artificial Intelligence and Robotics (CAIR), Hong Kong Institute of Science & Innovation, Chinese Academy of Sciences, Hong Kong Science Park, New Territories, Hong Kong SAR, PR China
Liu Lian: Research and Development Center, Loncin Motor Co., Ltd., Chongqing, 400039, China
Gui-Lin She: College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, Chin
Ning Hu: Interdisciplinary Research Institute of Advanced Intelligent Equipment, Xihua University, Chengdu, 610039, China; School of Mechanical Engineering, Hebei University of Technology, Tianjin, 300401, China
Abstract
Functionally graded (FG) beams are critically important in advanced engineering applications due to their ability to
tailor material properties for improved performance under extreme conditions. This study investigates the static and vibration behaviors of a sandwich beam with a functionally graded material (FGM) core and viscoelastic interfaces based on the twodimensional theory of elasticity. Young's Module and material density of functionally graded material (FGM) core is assumed to vary exponentially in thickness direction and the Poisson's ratio is held constant. In bending analysis, the sandwich beam is subjected to uniform pressure at the top surface whereas the bottom surface is traction-free. State space differential equations are derived using differential equations of motion as well as stress-displacement relations. For simply supported boundary conditions, these equations are solved analytically by using Fourier series expansion along the longitudinal direction, and other boundary conditions are solved semi-analytically using one-dimensional differential quadrature method (DQM) along the axial direction and state space across the transverse direction. Imperfect interfaces are modeled by the Kelvin-Voigt viscoelastic law. Time-dependent behavior is specified by dissolving the first-order differential equation of sliding displacement at the viscoelastic interfaces. Moreover, the influence of solid/elastic/ viscoelastic interfaces, different boundary conditions, length-tothickness ratio, elastic spring coefficient, and time passing on the static and vibration behavior of the beam are investigated. Major insights include the significant impact of imperfect bonding on vibration and bending behavior, discontinuity in transverse displacement for elastic and viscoelastic models, and higher transverse stresses in solid interfaces compared to viscoelastic ones.
Key Words
beam; differential quadrature; FGM; static; vibration; viscoelastic
Address
Hesamaldin Saghafi and Akbar Alibeigloo: Mechanical Engineering Department, Faculty of Engineering, Tarbiat Modares University, Tehran 14115-143, Iran
Abstract
Fundamental Natural Frequency (FNF) is the lowest natural frequency at which a structural and mechanical system
vibrates. For those systems, knowing FNF is crucial to avoid resonance, which can lead to excessive vibrations and potential failure. Therefore, the main objective of this paper is to determine FNF of Integral Bridge (IB) system considering Soil-Structure Interaction (SSI) effects. To achieve this aim, FNFs of the studied system are obtained by developing Finite Element Models (FEMs) in the ANSYS program. The results which uncover in the following, help designer to know effective factors on stiffness of the IB. The results show FNFs of the IB decrease significant with increasing spans of the studied models (for all cases: onespan bridge, two-spans bridge and three-spans bridge) from 10 m to 15 m and 20 m, by an average of 20.75% and 52.85%, respectively. Also, FNFs of the studied models reduce with increasing number of spans from one span to two and three spans, by an average of 13.6% and 20.2%, respectively. In addition, FNFs of the studied models decrease with increasing width of the IB from 7.05 m to 10.7 m and 14.35 m, by an average of 6.7% and 11.1%, respectively. Furthermore, FNFs of the IB change with
changing thickness of abutment, deck and wing walls, only by maximum 8.18%. In the end, FNFs of one-span bridge, twospans
bridge, and three-spans bridge show increase with considering SSI effects, by 48.9%, 34.7%, and 20.4%, respectively.
Key Words
finite element method; fundamental natural frequency; integral bridge; soil structure interaction
Address
Farhad Abbas Gandomkar and Negar Samimifard: Department of Structure, Faculty of Civil Engineering, Jundi-Shapur University of Technology, Dezful, Iran
Abstract
This study investigates the time-dependent response of a thin plate subjected to thermal waves and variable-time
pressure loads. Specifically, we analyze how the thermal wave time lag influences the plate's elastic response when combined with variable pressure loading. A finite difference approach is employed to determine the elastic behavior of the plate under these conditions, utilizing a three-dimensional (spatial and temporal) implicit technique to compute deformation. Our findings reveal that as the duration of the variable pressure load approaches the material's phase lag, the influence of the thermal load
becomes more pronounced, leading to fluctuations in plate deflection (ranging from -0.00038 to -0.00023) and resulting in multiple local maxima at 0.376 and 0.8 non-dimensional time units—one associated with the thermal load and the other with the mechanical load. Additionally, changing the plate material from a highly thermally conductive material such as Aluminum (o=1.459x10-12) to a material with a lower thermal wave speed and higher phase lag (o=0.1) results in a 0.024-time shift for the maximum deformation due to thermal expansion and approximately 0.656-time shift for the combined thermal and pressure loading. Furthermore, we found that the time lags between the plate's minimum and maximum deformation and between the applied loads and the response exhibit different trends depending on variations in mechanical load duration (td) and material phase lag (o). Synchronizing the thermal wave with the applied pressure minimizes the time lag, whereas staggering them may result in a time lag of up to 1.9 non-dimensional time units.
Key Words
combined thermal and mechanical loading; hyperbolic heat conduction model; non-Fourier heat conduction model; plate deflection; thermal stresses
Address
Momen M. Qasaimeh: Mechanical Engineering Department, The Hashemite University, Damascus Hwy, Zarqa, Jordan
Feras H. Darwish: Department of Mechanical Engineering, Higher Colleges of Technology, Muroor Road, AlSaada Street, AlNahyan, Abu Dhabi, UAE
Abstract
This research presents a comprehensive analysis of the dynamic behavior of bidirectional functionally graded (BDFG) Reissner-Mindlin plates subjected to moving loads, with a particular focus on material gradation effects and structural optimization. The study assumes a symmetric bidirectional variation of material properties along both the length and thickness directions, governed by a nonlinear power-law distribution. By strategically tailoring this material gradation, significant improvements in structural performance and dynamic stability are achieved. A finite element model is meticulously developed and rigorously validated against established benchmarks to ensure accuracy in predicting the mechanical response under varying boundary conditions and moving load velocities. The results highlight that symmetric bidirectional material gradation plays a
critical role in enhancing vibration resistance, reducing deflections, and improving overall mechanical performance. Surprisingly, contrary to conventional assumptions, increasing material gradation nonlinearity does not always yield enhanced dynamic stability, instead, certain configurations exhibit unexpected resonance phenomena at specific velocity thresholds, challenging traditional design paradigms. Additionally, the study uncovers a counterintuitive dependency of dynamic responses on boundary conditions, where certain soft-clamped configurations outperform fully clamped ones in mitigating peak deflections under high-speed loads. These findings offer novel design insights for optimizing advanced structural components across multiple engineering applications, including civil, mechanical, and aerospace structures, where high-performance functionally graded materials (FGMs) are crucial for sustaining dynamic loads efficiently.
Key Words
bidirectional FG materials; finite element method; mechanical behavior; moving force; Reissner-Mindlin plate; symmetrically FG plates
Address
Mohamed Ashry: Mechanical Design & Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt; University of Girona, AMADE, Polytechnic School, Girona, Spain
Alaa A. Abdelrahman: Mechanical Design & Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt; Industrial Engineering Department, Jeddah International College (JIC), P.O. Box 23831, Jeddah, Saudi Arabia
Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia; Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
Ahmed Amin Daikh: Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, University Centre of Naama, Naama, Algeria; Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P. 29000, Mascara, Algérie
Abdallah M. Kabeel: Mechanical Design & Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
Abdelghani Baltach, Ali Benhamena, Mohamed Ikhlef Chaouch, Mohammed El-Sallah Zagane, Murat Yaylaci, Şevval Öztürk, Mehmet Emin Özdemir and Ecren Uzun Yaylaci
Abstract
This study examines how contact pressure and shear stress act on contact areas subjected to fretting loading. The
research utilizes a non-linear finite element method, which calculates both normal and shear stresses, to assess the fracture behavior of flat surfaces. The study particularly emphasizes the influence of shear forces on the distribution of these stresses. A multiaxial fatigue criterion is used to identify potential crack initiation points within the contact zone. The critical point for crack initiation along the contact line is determined by evaluating the maximum values of hydrostatic and deviatoric stresses. The size
of the regions experiencing sticking and slipping behavior is directly related to the levels of contact pressure and shear force. Importantly, the study found a strong agreement between the finite element method simulations and the analytical results.
Key Words
contact mechanics; crack nucleation; finite element analysis; fretting; friction
Address
Abdelghani Baltach: Department of Mechanical Engineering, University of Ibn Khaldoun, 14000, Tiaret, Algeria; Laboratory of Quantum Physics of Matter and Mathematical Modeling (LPQ3M), University Mostapha Stambouli-Mascara, 29000, Mascara, Algeria
Ali Benhamena: Laboratory of Quantum Physics of Matter and Mathematical Modeling (LPQ3M), University Mostapha Stambouli-Mascara, 29000, Mascara, Algeria
Mohamed Ikhlef Chaouch: Laboratory of Quantum Physics of Matter and Mathematical Modeling (LPQ3M), University Mostapha Stambouli-Mascara, 29000, Mascara, Algeria
Mohammed El-Sallah Zagane: Department of Mechanical Engineering, University of Ibn Khaldoun, 14000, Tiaret, Algeria; Laboratory of Quantum Physics of Matter and Mathematical Modeling (LPQ3M), University Mostapha Stambouli-Mascara, 29000, Mascara, Algeria
Murat Yaylaci: Department of Civil Engineering, Recep Tayyip Erdogan University, 53100, Rize, Turkey; Turgut Kiran Maritime Faculty, Recep Tayyip Erdogan University, 53900, Rize, Turkey
Şevval Öztürk: Department of Civil Engineering, Recep Tayyip Erdogan University, 53100, Rize, Turkey
Mehmet Emin Özdemir: Department of Civil Engineering, Cankiri Karatekin University, 18100, Çankiri, Turkey
Ecren Uzun Yaylaci: Faculty of Fisheries, Recep Tayyip Erdogan University, 53100, Rize, Turkey
