Article
Polymer Science
Umer Sharif, Xinmei Xiang, Miaochang Zhu, Jun Deng, Jing Sun, Dauda Sh. Ibrahim, Orelaja Oluseyi Adewale
Summary: The current study focuses on the production and experimental examination of sandwich beams consisting of an aluminum face sheet and 3D-printed honeycomb cores filled with magnetorheological elastomer (MRE). The results suggest that the proposed sandwich beam constructions have the ability to alter the damping ratio, damping coefficient, and stiffness through the application of a magnetic field. Significant variations in damping were observed when the magnets were located in the central regions of the structures.
Article
Chemistry, Physical
Zhicheng Huang, Jinbo Pan, Ziheng Yang, Xingguo Wang, Fulei Chu
Summary: The present study investigates the nonlinear vibration behavior of EVES beams using a FE model. The FE model shows better accuracy in predicting the natural frequency of sandwich beams, with the prediction accuracy of damping related to the thickness of each layer. The results provide important reference values for the design and optimization of viscoelastic sandwich structures.
Article
Computer Science, Interdisciplinary Applications
Kamal Krishna Bera, Arnab Banerjee
Summary: A consistent dynamic stiffness matrix is formulated for flutter analysis of bridge decks. The equations of motion for vertical, lateral, and torsional degrees of freedom are considered, and the self-excited lift, drag, and torsional moment are based on the unsteady linear model involving eighteen flutter derivatives. The velocity-dependent and strain rate-dependent viscous damping coefficients, obtained in terms of the corresponding modal damping ratios, are also included in the formulation. The present formulation allows accurate flutter analysis with a minimal number of elements compared to conventional finite element approaches.
COMPUTERS & STRUCTURES
(2023)
Article
Materials Science, Multidisciplinary
Yun-Long Chen, Li Ma
Summary: This article investigates the free vibration and damping characteristics of carbon fiber-reinforced sandwich cylindrical shells with 3D reentrant auxetic cores (3D RSCSs). Finite element analysis and theoretical predictions using the Rayleigh-Ritz method and third-order shear deformation theory are conducted. Experimental tests on all-composite 3D RSCSs specimens manufactured through hot press molding and interlocking assembly validate the predicted modal properties. Furthermore, the influences of fiber ply angles and geometric parameters on the natural frequency and damping loss factor are investigated.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Mechanics
Koutoati Kouami, Mohri Foudil, Daya El Mostafa, Carrera Erasmo
Summary: A beam finite element model is proposed for static and free vibration analyses of FGM sandwich beams with viscoelastic nonlinear material behavior. Different viscoelastic frequency-dependent laws, Timoshenko 1st order, and Reddy's higher order shear models are used. The stiffness matrix is nonlinear and frequency dependent. The study shows that beam behavior is sensitive to the loss factor, and damping properties are nonlinearly dependent on the power law index. Boundary conditions affect vibration modes.
COMPOSITE STRUCTURES
(2021)
Article
Acoustics
Weijun Li, Kun Lin, Kaifa Wang, Baolin Wang
Summary: This study investigates the dynamic performance of a sandwich beam with a shear thickening fluid (STF) core under periodic excitation. The addition of STF allows the beam to have adjustable stiffness and damping capacity during dynamic deformation. The research findings reveal that the resonant frequency of the beam increases with the amplitude of the external excitation in a power law relationship. Furthermore, the initial damping ratio of the STF with shear thinning zone decreases initially and then increases with the increase of the initial excitation amplitude.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Materials Science, Multidisciplinary
Weijun Li, Kun Lin, Kaifa Wang, Baolin Wang
Summary: The dynamic performances of a sandwich beam with a shear thickening fluid (STF) core under random excitation are investigated. The response frequencies and damping ratios of the beam increase with the standard deviation of the external random excitation. The sandwich beam with an STF core provides better damping for larger broadband excitation and produces a response both inside and outside the load frequency domain. An optimal thickness ratio for the structure that maximizes the damping ratio is identified.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Physics, Applied
Adham Naji, Sami Tantawi
Summary: A variational theory is presented for beam loading in microwave cavities, which provides steady-state solutions for the detuning of a cavity's resonant frequency, Q, and optimal coupling coefficient due to beam loading. The derived Lagrangian includes various effects and is applied to predict detuning parameters for maximizing gain in klystron input cavities. The formulation offers advantages for analyzing and designing beam-loaded cavity structures, providing a self-consistent model for beam-field interaction and guiding cavity-shape optimization.
PHYSICAL REVIEW APPLIED
(2021)
Article
Computer Science, Interdisciplinary Applications
Michael F. Herbst, Antoine Levitt
Summary: In this study, a novel adaptive damping algorithm for self-consistent field (SCF) iterations in Kohn-Sham density-functional theory is proposed. The algorithm adjusts the damping in each SCF step using a backtracking line search based on a theoretically sound and accurate energy model. Unlike traditional SCF schemes, this algorithm is fully automatic and does not require user input for selecting the damping parameter. The algorithm is successfully applied to various challenging systems, including elongated supercells, surfaces, and transition-metal alloys.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Subash Acharya, Vipin J. Allien, N. P. Puneet, Hemantha Kumar
Summary: Magnetorheological fluid (MRF) sandwich beams, composed of MRF sandwiched between face layers, show potential for semi-active vibration control. Optimal particle size and weight fraction of carbonyl iron powder in MRF were determined based on maximizing damping ratio and minimizing MRF weight, with larger particles and higher weight fractions showing better vibration suppression capabilities.
INTERNATIONAL JOURNAL OF SMART AND NANO MATERIALS
(2021)
Article
Instruments & Instrumentation
Umer Sharif, Lin Chen, Beibei Sun, Dauda Sh Ibrahim, Orelaja Oluseyi Adewale, Noman Tariq
Summary: Sandwich beams with an aluminium face sheet and a magnetorheological elastomer (MRE) filled in a honeycomb core of Nylon and Resin8000 were manufactured and experimentally analysed in this study. The dynamic properties of the beams were evaluated by subjecting them to sine sweep and classic shock tests, both with and without the application of magnetic field. The experimental results showed that the sandwich beams exhibited good vibration level attenuation, particularly in the primary vibration mode. The induced magnetic field was capable of changing the natural frequencies, vibration amplitudes, and damping ratios of the sandwich beams with MRE honeycomb core.
SMART MATERIALS AND STRUCTURES
(2022)
Article
Engineering, Civil
Mao Cristian Pinto Cruz
Summary: In this paper, a novel continuous beam method is proposed for the structural analysis of tall buildings with long shear walls. The proposed method considers the rotation kinematic field due to the shear deformation of the walls and is derived from the coupling of a classic sandwich beam and a shear beam. The equilibrium equations, constitutive laws, and boundary conditions of the continuous model are obtained using a variational approach. Closed-form analytical methods are proposed for uniform-height buildings and a numerical method is proposed for buildings with variable properties along their height.
THIN-WALLED STRUCTURES
(2023)
Article
Acoustics
Sungjin Han, Woong-Ryeol Yu
Summary: In this study, the interface between steel and polymer layers was investigated, and it was found that the interfacial adhesion strength between the two materials does not significantly affect the loss factor of the sandwich composites. However, the adhesive layer itself has a significant influence on the vibration-damping performance of the composite. Therefore, a five-layered sandwich model considering two adhesive layers was proposed to accurately predict the loss factor.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Optics
Aqsa Ehsan, Muhammad Qasim Mehmood, Kashif Riaz, Yee Sin Ang, Muhammad Zubair
Summary: The exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates, known as the vector space-fractional Bessel beam (SFBB), has been introduced in this study. Scalar and vector wave analysis focused on electromagnetics applications, particularly in cases where beam dimensions are comparable to wavelength. The SFBBs, with continuous order orbital angular momentum dependence, serve as a bridge between ordinary integer Bessel beams and fractional Bessel beams, providing better control over beam characteristics and applications in optical devices.
Article
Mathematics, Applied
Baowei Feng, Ahmet Ozkan Ozer
Summary: In this paper, a three-layer Rao-Nakra sandwich beam with viscoelastic core is investigated. The existence and uniqueness of local and global weak solutions are proven by utilizing nonlinear semigroup theory and the theory of monotone operators. Under certain assumptions, the global existence of potential well solutions and the uniform energy decay rates are shown to be solutions to a specific nonlinear ODE. Additionally, the existence of a smooth global attractor with finite fractal dimension and exponential attractors for the associated dynamical system are also established. This paper extends the existing linear analysis to nonlinear analysis of the stability of the Rao-Nakra sandwich beam.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Mathematics
Sergey A. Lurie, Dmitrii B. Volkov-Bogorodskii, Petr A. Belov
Summary: A mathematical statement for coupled stationary thermoelasticity is presented based on a variational approach, addressing inhomogeneous materials in contact boundary problems. The analysis of potential energy density and model parameters influences the solution structure, discussing the characteristics of gradient theories in coupled thermoelasticity and stationary thermal conductivity. The study explores the effects of higher order coupling between temperature and deformation fields, leading to changes in characteristic equations and solution structures.
Article
Mechanics
S. Lurie, D. Volkov-Bogorodskii, H. Altenbach, P. Belov, L. Nazarenko
Summary: This paper considers a linear model describing a reversible thermomechanical process with coupled gradient thermoelasticity and stationary thermal conductivity. The mathematical statements and analytical solutions of the model are presented, and the influence of couple effects and scale effects on periodic inhomogeneous structures is studied.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Thermodynamics
Kyaw Ye Ko, Yury Solyaev, Sergey Lurie, Arseniy Babaytsev, Lev Rabinskiy, Ivan Kondakov
Summary: This paper investigates the compliance minimization problems in rib-stiffened plates under transverse loading using the variable-thickness approach. The optimization problems in such cases are usually ill-posed and their solutions depend heavily on the mesh. To address this issue, an additional regularization constraint is introduced on the thickness gradient, and the convergence and efficiency of the method are evaluated. Variable thickness is defined using a topology optimization approach, introducing additional design variables in the nodes of shell-type elements. Numerical solutions are obtained through finite element simulations using Mindlin-Reissner theory and the method of moving asymptotes. The study shows that well-converged optimal solutions can be achieved for benchmark problems with rib-stiffened panels loaded by concentrated forces. Parametric studies are conducted to analyze the effects of shape function order, penalty factor values, and initial conditions for plate thickness. Recommendations for optimal settings of the method are established, and theoretical and experimental assessments on the advantages and accuracy of the variable-thickness approach are provided based on comparisons with standard designs.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Mechanics
V. V. Vasiliev, S. A. Lurie
Summary: The paper proposes a modified form of differential equations for describing physical processes in applied mathematics and mechanics. It is noted that classical equations may exhibit discontinuities of the first and second kind at singular points, which are not physically meaningful and not observed in experiments. The new equations consider finite dimensions instead of infinitely small elements and include nonlocal functions averaged over the element volume. The Helmholtz equations are used to relate these nonlocal functions to actual physical variables without singular points. The paper also discusses singular problems in mathematical physics and elasticity theory and compares the obtained solutions with experimental results.
JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Yury Solyaev
Summary: In this paper, a variant of the second gradient continuum model is introduced to describe the spatial dispersion effects of high-frequency waves in anisotropic crystals. The model considers strain and inertia gradient effects, as well as classical electro-mechanical coupling. The simplified constitutive equations of the model contain seven and four length scale parameters for piezoelectric hexagonal crystals and elastic cubic crystals, respectively. It is shown that these parameters can be identified based on the fitting of the continuum model to lattice dynamics calculations.
MATHEMATICS AND MECHANICS OF SOLIDS
(2023)
Article
Chemistry, Multidisciplinary
Yury Solyaev
Summary: The stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, considering the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks.
APPLIED SCIENCES-BASEL
(2023)
Article
Acoustics
Yury Solyaev
Summary: In this paper, the Lamb-type problem of the dynamic response of an isotropic half-space subjected to a time-harmonic vertical point load is studied within the simplified strain gradient elasticity theory (SGET). The high-order motion equations of SGET are solved using the technique of Lame potentials and Hankel transform, and an explicit solution considering traction and double traction boundary conditions is obtained in the transformed domain. The obtained results show that the SGET solution is bounded at the epicenter of the load and takes into account the spatial dispersion effects for the propagated waves, which are important for the analysis of high-frequency processes in structured materials.
Article
Mathematics, Applied
Sergey Lurie, Yury Solyaev
Summary: In this paper, we present a particular variant of the isotropic Mindlin-Toupin gradient theories, which simplifies the traction boundary value problems. This incomplete gradient theory is positive semi-definite and obeys the strong ellipticity conditions of the general Mindlin-Toupin first strain gradient elasticity. Based on the variational approach, we demonstrate that the equilibrium equations and surface traction definition can be formulated solely in terms of total stresses, similar to classical elasticity. The theory is useful for deriving closed form solutions for problems with traction-type boundary conditions, as shown in the examples of cylindrical bending and inplane crack tip fields. The theory allows for a regularized solution for crack problems without predicting a non-physical infinite increase in material rigidity under bending.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Mathematics
Valery V. V. Vasiliev, Sergey A. A. Lurie
Summary: This paper addresses the issue of discontinuities in mathematical physics solutions which describe actual processes but are not observed in experiments. The author suggests that the presence of discontinuities is linked to classical differential calculus that analyzes infinitesimal quantities. To overcome this, the paper introduces nonlocal functions and nonlocal derivatives, which are obtained by averaging over small finite intervals of the independent variable instead of using the traditional point approach. By incorporating these nonlocal functions into classical equations and introducing additional equations to connect them with traditional functions, continuous solutions to classical singular problems in mathematical physics are obtained. The approach is demonstrated and supported by experimental data using the problems of a loaded string and circular membrane.
Article
Mathematics
Y. O. Solyaev, V. A. Korolenko
Summary: In this paper, the authors use the Papkovich-Neuber potentials to derive a variant of the general solution for plain problems in strain gradient elasticity theory (SGET) in bounded domains. The general solution consists of complete sets of functions satisfying 2D Laplace equations and modified Helmholtz equations, including polynomial and modified Bessel functions of integer and fractional orders with angular periodicity. The proposed form of the general solution allows for the derivation of known SGET asymptotic solutions for crack-tip fields.
LOBACHEVSKII JOURNAL OF MATHEMATICS
(2023)
Article
Nanoscience & Nanotechnology
Sergey A. Lurie, Petr A. Belov, Yury O. Solyaev
Summary: The symmetry conditions of gradient distortion models were investigated in this study. The variational significance of order-of-differentiation symmetry conditions of strain gradient elasticity was studied. Ignoring this symmetry can lead to ill-posedness in boundary value problems and erroneous results in modeling. This problem is relevant to all applied models of higher order elasticity theory in micro and nanomechanics.
NANOSCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL
(2023)
Article
Metallurgy & Metallurgical Engineering
N. Ya Golovina, P. A. Belov, S. A. Lur'e, O. Egorova
Summary: This paper compares three lifetime models for materials within the framework of the hypothesis of accumulation of residual strains. The models are based on the Ramberg-Osgood law, an alternative empirical law, and a theoretical law constructed from the solutions of various differential equations in linear and nonlinear sections in a stress-strain curve. It is shown that postulating a linear section in a stress-strain curve leads to the fact that the endurance limit is determined by the point of proportionality limit.
RUSSIAN METALLURGY
(2022)
