报告人一：Dušan Zorica教授，塞尔维亚诺维萨德大学理学院
报告题目一：Stored energy and dissipated power for one-dimensional viscoelastic body
报告题目二：Compresive and shear wave propagation in three-dimensional fractional viscoelastic infinite solid media
报告人二：Nevena Rosić博士，塞尔维亚贝尔格莱德大学机械工程学院
报告题目三：Wave propagation in periodic and quasiperiodic metastructures: modeling, dispersion analysis, and applications
报告时间：2025年6月10日（周二）15:00开始（北京时间）
报告地点：线上Zoom会议（会议号: 852 4818 9667）
主办单位：伟德国际1949始于英国
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报告一摘要：
Considering the linear constitutive model containing fractional integrals and Riemann-Liouville fractional derivatives, the power per unit volume is expressed in time domain in terms of stored energy and dissipated power per unit volume depending on the relaxation modulus and creep compliance. Considering the fractional anti-Zener and Zener models, restrictions on model parameters narrowing thermodynamical constraints ensure relaxation modulus and creep compliance to be completely monotone and Bernstein function respectively, that a priori guarantee the positivity of stored energy and dissipated power per unit volume. Assuming strain as a sine function, the time evolution of power per unit volume is investigated when expressed through the relaxation modulus and creep compliance. Further, two forms of energy and two forms of dissipated power per unit volume are examined in order to see whether they coincide.
报告二摘要：
In order to analyze the wave propagation in three-dimensional isotropic and viscoelastic body, the Cauchy initial value problem on unbounded domain is considered for the wave equation written as a system of fractional partial differential equations consisting of equation of motion of three-dimensional solid body, equation of strain, as well as of the constitutive equation, obtained by generalizing the classical Hooke’s law of three-dimensional isotropic and elastic body by replacing Lamé coefficients with the relaxation moduli to account for different memory kernels corresponding to the propagation of compressive and shear waves. The displacement field is obtained by the action of the resolvent tensor on the initial conditions.
报告三摘要：
This research explores the propagation of mechanical waves through periodic structures composed of elastic beams connected by rigid segments, springs, dashpots, mass resonators, and inerters. Their unique wave propagation features, particularly their frequency band structure, classify them as metamaterials or metastructures. By tessellating modified unit cells, quasiperiodic structures are created to investigate controlled disorder and its effects on wave behavior, such as mode localization. Additionally, slender phononic structures with time-varying viscoelastic interlayers are studied, leading to non-reciprocal wave propagation. Mathematical models based on the transfer matrix method, Timoshenko and Euler-Bernoulli beam theories, and dynamic system modeling are developed. Dispersion characteristics are analyzed using the Bloch-Floquet theorem, and numerical methods are implemented in MATLAB and validated through finite element simulations in COMSOL Multiphysics. The study offers insight into wave attenuation mechanisms like Bragg scattering and local resonance, and provides tools for engineering structures with tailored wave propagation properties for applications in vibration isolation, acoustic filtering, and seismic protection.
