Continuum Mechanics and Thermodynamics最新文献

In the present paper, we study the problem of reflection of homogeneous plane waves from a free surface of generalized magneto micropolar thermoelastic using modified Ohm’s law and generalized Fourier law. There exist five coupled elastic waves propagating in such materials which are longitudinal, transverse, micropolar, thermal, and magnetically influenced waves. We have examined the analysis for an incident longitudinal wave at the free surface. The phase velocities of these waves are obtained analytically and numerically. Using appropriate boundary conditions, the amplitude and energy ratios corresponding to the reflected waves are obtained analytically and numerically. Magnetic and thermal effects on the reflected waves are examined, and we also confirmed the conservation law of energy in all cases.

The last decades have seen growing interest in connecting principles of thermodynamics with methods from analytical mechanics. The thermodynamic formalism has become an inspiring framework in the study of smooth dynamical systems, and pioneering works of Helmholtz, Clausius, and Boltzmann have been reinstated as possible dynamical foundations of the (first part of the) Heat Theorem. The present paper follows the work of Wald et al., where black hole entropy was identified as a Noether charge. The adiabatic invariance of the thermodynamic entropy indeed invites a connection with Noether’s theorem, and has been the subject of various papers. Here we add the case of GENERIC, a macroscopic dynamics whose acronym stands for “General Equation for Non-Equilibrium Reversible-Irreversible Coupling”. Its evolution has two contributions: a dissipative part, which is of a generalized gradient descent form, and a Hamiltonian flow. We consider a quasistatic protocol for external parameters, and we embed GENERIC as the zero-cost flow for a Lagrangian governing the dynamical fluctuations. We find a continuous symmetry of the corresponding path-space action with the thermodynamic entropy as Noether charge, both in the Lagrangian and Hamiltonian formalisms. We make the calculations explicit through the example of an inertial probe with nonlinear friction.

Functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAM) have attracted much attention due to their excellent negative Poisson’s ratio properties. Research on the vibration characteristics of FG-GOEAM cylindrical shells remains insufficient. To fill this gap, this work systematically investigates the free vibration behavior of FG-GOEAM cylindrical shells under different temperature profiles using first-order shear deformation shell theory. There are three common types of temperature profiles: uniform temperature rise, linear temperature rise, and sinusoidal temperature rise. Temperature correction functions for LTP and STP conditions are established by taking the geometrically neutral surface temperature of each layer of the shell as a proxy for the overall temperature of that layer. To accurately characterize the effects of thermal effects, a thermal strain energy analysis model is introduced in this work. The material parameters were determined based on a micromechanical model assisted by genetic programming. The governing equations are derived by Hamilton’s principle and solved by Navier’s method. After validating the model, this work investigates the effects of key parameters on the vibration characteristics of the FG-GOEAM cylindrical shell. The numerical results of this work are expected to provide a theoretical basis for the structural optimization and innovative design of FG-GOEAM cylindrical shells.

This paper is concerned with modeling inertia effects in materials. We propose elasticity-inertia models incorporating a novel element called inerter, which exhibits the property of equivalent inertia. Different from the existing works that capture inertia effects by strain gradients, the proposed models directly model general inertia effects by inerters. The stress-strain relationships of the proposed models are represented by spring-inerter networks, which resemble viscoelastic models represented by spring-dashpot networks. It shows that in the constitutive equations and dynamic equations of the proposed models, strain acceleration terms or micro-inertia terms can be easily and directly obtained without adding terms or using operator transformations. The dispersion and vibration properties of the proposed models are derived analytically. The discretization methods are presented as well for obtaining numerical solutions of the proposed models. The proposed elasticity-inertia models provide a very natural way in capturing inertia effects, offering an alternative perspective for modeling inertia effects in materials.

This study proposes Chebyshev polynomials-based different shear deformation theories to analyse the buckling, bending, and free vibration behaviours of axially loaded functionally graded (FG) curved beams for the first time. The Chebyshev-third-order shear deformation theory satisfies the condition of eliminating shear stress at the bottom and top surfaces of the FG curved beam without requiring a shear correction factor. Furthermore, this theory can be simplified to the first-order shear deformation and classical beam theories. The material characteristics of the FG curved beam exhibit variability through its thickness by a power law distribution. The governing equations are derived from Lagrange’s equations. The Ritz method, utilising polynomial shape functions based on the Fibonacci sequence, has been developed to solve the problem. FG curved beams with four boundary conditions are examined, including simply-supported, clamped-free, clamped-simply supported, and clamped-clamped. Numerical examples are carried out to assess the accuracy and efficacy of the present theory. Additionally, the study elucidates the behavioural patterns of FG curved beams regarding various parameters such as boundary condition, slenderness ratio, curvature, and power-law index. The findings of this study serve as a benchmark for future research endeavours. Moreover, they have the potential to enhance the design and optimisation of FG curved beams across a diverse array of engineering applications.

We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully Eulerian approach is adopted. We specialize the model to viscoelastic (barotropic) fluids and prove existence and a certain regularity of global weak solutions by a Faedo-Galerkin semi-discretization technique. Then, an extension to multi-component chemically reacting viscoelastic fluids based on a phenomenological approach by Eckart and Prigogine, is advanced and studied. The model is inspired by planetary geophysics. In particular, it describes gravitational differentiation of inhomogeneous planets and moons, possibly undergoing volumetric phase transitions.

The main relations of the two-dimensional of asymmetric elasticity theory are considered. The matrix for the fundamental solutions of these equations is constructed. In the context of two-dimensional asymmetric elasticity, the volume potential, also called logarithmic potential, is obtained, which is the analog of the volume potential, from the abstract theory of singular integral equations. In the same context, the single-layer and double-layer surface potentials are obtained, which are also analogous to the surface potentials from the classical theory of equations of integral type. For the first and the second inside problems with values to the limit are deduced the specific system of integral equations of singular type. Similar for the two outside problems with values to the limit. It is demonstrated that the index of the equations of the integral type, previously defined, is null, for all four systems of singular integral equations.

This study utilizes the nonlocal strain gradient theory (NSGT) to establish a generalized, size-dependent thermoelastic framework for transversely isotropic piezo-thermoelastic (PTE) microbeam under the Euler-Bernoulli beam theory. The model incorporates two different length-scale parameters, viz. nonlocal elasticity and strain gradient effects to characterize microscale structural behavior. To address thermal lagging phenomena, the heat conduction equation is derived based on the Moore-Gibson-Thompson (MGT) framework, which introduces memory-dependent derivatives over a variable time interval. By employing coupled Laplace transform and finite Fourier sine integral methods, analytical solutions for thermoelastic distributions (e.g., deflection, bending moment, thermal moment) are derived for a simply supported microbeam. The Laplace-domain solutions are obtained via Fourier inversion, and their time-domain counterparts are reconstructed using the Zakian’s algorithm. Numerical simulations based on PZT-5A material investigate the influence of kernel functions on heat transport behavior and evaluate the performance of the proposed nonlocal strain gradient model against classical formulations. The results demonstrate a strong sensitivity of physical responses, such as thermal moment and deflection to time delay parameter, revealing the potential for controllable vibration damping. Overall, the study offers valuable design insights for microscale beams in MEMS/NEMS applications, bridging advanced theoretical modeling with practical optimization strategies.

This paper presents a comprehensive study of exact wave solutions within the framework of coupled theory (CT) thermoelasticity, incorporating temperature dependence. We employ tauthorhe method of improved modified extended tanh-function (IMETF) to derive analytical solutions for the governing equations that account for the interaction between thermal and mechanical fields in materials. The temperature-dependent characteristics of materials are considered, which significantly influence the thermoelastic behavior under various loading conditions. The proposed method enhances the conventional tanh-function approach by allowing for more complex wave structures, thereby we obtained of a broader range of exact solutions featuring distinct free parameters, involving hyperbolic,exponential, Jacobi elliptic, dark soliton, compice dark-singular soliton, rational, and polynomial solutions. The results reveal valuable insights into the propagation of waves in thermoelastic materials. In addition, some of the results for stress tensor components, displacement components, and temperature are shown as graphical visualizations.

Magnetic Pulse Welding (MPW) is an innovative solid-state welding technology that uses high-speed electromagnetic forces to achieve defect-free joints without melting the base materials. This paper presents a comprehensive numerical investigation into MPW for industrial applications, focusing on plates and tubular components. By leveraging coupled electromagnetic and mechanical models developed in COMSOL MULTIPHYSICS, this research explores critical parameters affecting weld quality, such as material properties, geometries, air gaps, and energy levels. The simulations demonstrate that Al/Al plate welding achieves complete joint formation within (10 mu s) at a discharge current density of (3.2 times 10^{11} A/m^3), while dissimilar joints such as Cu/Al and Ti/Al require up to (12.5 mu s) and (47 mu s) respectively. In tube welding scenarios, similar material combinations (Al/Al) showed successful bonding within (20 mu s), while dissimilar pairs (Mg/Al and Cu/Al) required significantly more time and higher energy input. Weldability maps and deformation analysis confirm that air gap and coil geometry substantially impact welding time and joint quality. These results underline MPW’s potential for cost-effective, high-speed, and sustainable manufacturing in aerospace and automotive sectors.