Archive of Applied Mechanics最新文献

In this paper, we present a series solution for free in-plane vibration of composite plates with arbitrary shape by using the domain segmentation integral method and derive the tangential and normal vibration displacement equations for the plate boundaries. The solution presented is widely applicable to the analysis of free in-plane vibration of plates; it can accurately and effectively solve the in-plane free vibration problem of arbitrarily shaped non-homogeneous orthotropic plates of variable thickness, complex geometry and variable material properties with respect to in-plane coordinate parameters. To verify the effectiveness, accuracy and applicability of the proposed solution, we perform a computational analysis of different orthogonalization intervals, weight functions, penalty stiffness and the truncation number of orthogonal polynomials. Additionally, the effects of the parameters of thickness and nonhomogeneity on the in-plane vibration characteristics of plate are studied. As a result, we present a new series of natural frequencies and mode shapes for arbitrarily shaped non-homogeneous orthotropic plates of variable thickness.

Permanent magnetic bearings (PMBs) hold great potential for various applications such as artificial heart pumps, space equipment, and flywheels. This is due to their notable advantages, including the absence of mechanical contact, no friction, and no control system requirements. However, in many practical scenarios involving PMBs, the bearing installation base is often subject to external excitation, which can interfere with its stability. Currently, the impact of base excitation on the PMB-rotor system and methods for enhancing the stability of the PMB-rotor system under base excitation remain subjects of investigation. Hence, this study focuses on conducting stability analysis of the PMB-rotor system under the influence of base excitation. Firstly, the theoretical model of PMB based on the Halbach array is established, and then the system dynamics model of PMB-rotor under base excitation is established by using the second Lagrange equation. Finally, according to the established dynamic model, the effects of base excitation parameters, structural parameters, and external damping on the stability of the PMB-rotor system under base excitation are analysed through the root locus method. The research results presented in this study provide a theoretical reference for further engineering applications of PMBs.

This paper presents a modified tempered fractional thermal conductivity model aimed at enhancing the analysis of thermal behavior in magnetic thermoelastic solids, particularly in response to time-dependent laser pulse heating. Current literature lacks comprehensive approaches that effectively account for the complex interactions of thermal, mechanical, and magnetic fields within such materials. This gap is critical, as understanding these interactions is essential for optimizing the performance and reliability of advanced materials in engineering applications. Our study addresses this need by introducing a fractional model that employs modified tempered Caputo fractional derivatives in conjunction with a single-parameter Mittag–Leffler function. This innovative adjustment incorporates a parameter specifically designed to capture memory effects, resulting in a more accurate representation of the intricate thermal dynamics at play. We solved the governing equations directly using the Laplace transform method, providing exact formulas for displacement, temperature, and thermal stresses in copper. The graphical representations included in the study illustrate the material's deformation and the development of thermal stresses under thermal loading conditions. The findings demonstrate that the introduction of the memory effect parameter significantly enhances the thermoelastic model's ability to characterize the behavior of materials and structures subjected to thermal loads, thereby contributing valuable insights to the field of magnetic thermoelasticity.

In this study, the scattering of water waves by an undulating bottom in a two-layer fluid with current, surface tension, and interfacial tension is investigated. The perturbation technique followed by the Fourier transform technique are applied to solve the coupled boundary value problem. A Bragg resonance arises between the surface waves and the bottom ripples, which is associated with the reflection of incident wave energy. Hence, the Bragg coefficients namely, Bragg reflection and transmission coefficients, and associated velocity potentials are analysed which are obtained in integral forms. In order to clearly understand the efficacy of the present study, a certain type of undulating bottom, known as sinusoidal bottom undulation, has been examined. It has been shown that when the combined effects of surface tension, interfacial tension, and current are taken into account, the wave reflection is minimal. Moreover, a shift in the Bragg resonant frequency is seen with a change in current speed. In addition, interfacial tension influences both surface and interfacial waves, whereas surface tension primarily impacts surface waves. The results obtained here are expected to be qualitatively helpful in tackling problems of flexural gravity waves in two-layer fluid in the presence of current.

This study presents a finite element model formulated to analyze accurately the bending behavior of functionally graded (FG) plates, employing an improved first-order shear deformation theory (FSDT). In contrast to the conventional Mindlin–Reissner theory, our enhanced FSDT incorporates a parabolic shear strain distribution, providing a more realistic depiction of shear strain throughout the plate’s thickness. Material properties of the FG plates are modeled to undergo continuous variation through the thickness, utilizing power law, exponential, and sigmoid distributions. The investigation focuses on assessing the impact of material composition and geometric parameters under both sinusoidal and uniformly distributed loads, considering various boundary conditions. Comparative analyses with previously published literature underscore the precision and simplicity of our model. The obtained results demonstrate strong agreement with solutions derived from other high-order theories, affirming the accuracy of our proposed model. This research contributes valuable insights into the bending behavior of FG plates and reinforces the reliability of the developed finite element model.

This paper presents an effective approach for dynamic analysis of liquid-filled clamp pipe (LFCP) systems based on the spectral element method (SEM). In this regard, six stiffness components are used to represent the elastic supporting effect of a clamp on the pipe structure, and analytical parameters are derived to realize the Rayleigh damping model in the SEM. This determines an SEM-based approach for dynamic analysis of the LFCP system. Numerical verification of the SEM is implemented for natural frequency analysis of the LFCP in conjunction with the straight, the L-shape, and parallel pipe systems. Compared to the finite-element or the transfer-matrix method in the literature, simulation results have confirmed the high accuracy and efficiency of utilizing the SEM for numerical modelling of the LFCP system. Various realizations of the pipe diameter, the fluid density and pressure, and the clamp coefficients are also considered to investigate their combined effects on structural characteristics. It has confirmed that the SEM based approach provides an effective routine for dynamic analysis of the LFCP system.

Contact mechanics is a complex and advanced field of engineering, with continuous research dedicated to modeling and examining contact problems in multilayered and multibody systems. Given that fatigue and fracture failures often result from contact loads, precise determination of subsurface stresses is crucial for the design of mechanical components. This study provides an exact analytical solution for the frictionless indentation of a functionally graded (FG) orthotropic layer by a rigid cylindrical punch. The FG orthotropic layer, which rests on a rigid, non-adhesive substrate, is treated as a nonhomogeneous medium with an orthotropic stress–strain relationship. Part of its top surface experiences normal tractions, while the rest remains traction-free. The analysis also incorporates the gravitational force affecting the FG orthotropic layer. Five distinct real orthotropic materials are used, each with individually graded stiffness constants in their principal directions, to define the FG orthotropic behavior of the material. The governing equations are formulated using the singular integral equation method and transformed into algebraic systems via the Gauss–Chebyshev integration technique. A comprehensive parametric study examines how variations in dimensionless punch radius, compressive force, inhomogeneity parameters, and body force influence contact widths, contact pressures, normal and shear stresses, critical load factor, and the initial point of interface separation.

As the key structure of aero-engine, the predictionand analysis of the dynamic characteristics of the casing is ofgreat significance for evaluating the safety of the structure andpreventing resonance. Based on Love shell theory, Donnell shelltheory and Soedel shell theory, the prediction model ofthree-layered thin-walled cylindrical shell is established by energymethod and solved and analyzed by Rayleigh Ritz method. This paperinvestigates nine classical boundary conditions including simplesupport–simple support (S–S), fixed support–fixed support(C–C), free–free (F–F), sliding–sliding (SL–SL), fixedsupport–simple support (C-S), fixed support–free (C–F), fixedsupport–sliding (C–SL), free–simple support (F–S),free–simple support (text{(F-)}) and free–sliding (F-SL). In this paper,the natural frequency values of the three models are solved underdifferent length–diameter ratio, thickness–diameter ratio andcircumferential wave number. The accuracy of the models establishedin this paper is verified by comparison with published papers, andthe differences and application ranges of the solution results ofdifferent models are given. The research of this paper providesuseful references for the design and optimization of aero-enginecylindrical shell.

The aim of this work is to obtain an alternative of the Phragmén-Lindelöf type for homogeneous elastic materials when the elastic tensor is not positive definite. Indeed, it is necessary to impose some conditions to this tensor in order to prove the estimates. We propose several examples of elastic tensors which are not positive definite but satisfying the above conditions. Finally, the extensions to the three-dimensional and thermoelastic cases are also considered.

In this paper, for the first time, the static bending and free vibration of bi-directional functionally graded (2D-FG) nanobeams partially resting on an elastic foundation are investigated. The nanobeams are composed of four material components and exhibit mechanical characteristics that vary smoothly and continuously along the thickness and length of the beam according to a power law. For the purpose of analysis, a finite element model is established using a two-node beam element, with each node having five degrees of freedom, combining Lagrangian and Hermitian shape functions. Based on a higher-order shear deformation theory and nonlocal theory, the governing equations of the 2D-FG nanobeams are derived using Hamilton's principle. Through the comparisons of the results obtained from the model with published results in the open literature, the accuracy and reliability of the present model are confirmed. Therefore, the proposed algorithm is compatible for predicting mechanical behaviors of nanobeams with arbitrary material distribution, various boundary conditions and complex loads. New numerical results are conducted to assess the influence of parameters such as volume fraction indexes, nonlocal parameters, foundation coefficients, length-to-height ratio and boundary conditions on the bending static and free vibration behaviors of the 2D-FG nanobeams. Especially, the role of the partial elastic foundations on the bending and vibration of the 2D-FG nanobeams is extensively investigated.