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The dynamic response of the nuclear power plants (NPPs) with pile foundation reinforcement have not yet been systemically investigated in detail. Thus, there is an urgent need to improve evaluation methods for nonlithological foundation reinforcements, as this issue is bound to become an unavoidable task.

A nonlinear seismic wave input method is adopted to consider both a nonlinear viscoelastic artificial boundary and the nonlinear properties of the overburden layer soil. Subsequently, the effects of certain vital parameters on the structural response are analyzed.

A suitable range for the size of the overburden foundation is suggested. Then, when piles are used to reinforce the overburden foundation, the peak frequencies in the floor response spectra (FRS) in the horizontal direction becomes higher (38%). Finally, the Poisson ratio of the foundation soil has a significant influence on the FRS peak frequency in the vertical direction (reduce 35%–48%).

The quantifiable results are performed to demonstrate the seismic responses with respect to key design parameters, including foundational dimensions, the Poisson Ratio of the soil and the depth of the foundation. The results can help guide the development of seismic safety requirements for NPPs.

The purpose of this paper is to investigate the free vibration response of a laminated honeycomb sandwich panels (LHSP) for aerospace applications. Higher order shear deformation theory (HSDT) was simplified for the dynamic analysis of LHSP. Furthermore, the effects of honeycomb parameters on the value of natural frequency (NF) of vibration were explored.

This paper applies HSDT to the analysis of composite LHSP to derive four vibration differential equations of motion and solve it to find the NF of vibration. Two analytical models (Nayak and Meunier models) were selected from literature for comparison of the NF of vibration. In addition, a numerical model was built by using ABAQUS and the results were compared. Furthermore, parametric studies were conducted to explore the effect of honeycomb parameters on the value of the NF of vibration.

The present model is successful in simplifying HSDT for the analysis of LHSP. The first five natural frequencies of vibration were calculated analytically and numerically. In the parametric study, increasing core height or young’s modulus or changing laminate layup will increase the value of NF of vibration. Furthermore, increasing plate constraint (using clamped edge boundary condition) will increase the value of NF of vibrations.

The current analysis is suitable for all-composite symmetric LHSP. However, for isotropic or non-symmetric materials, minor modifications might be adopted.

The application of simplified HSDT to the analysis of LHSP is one of the important values of this research. The other is the successful and complete dynamic analysis of all-composite LHSP.

This study aims at investigating the heat transfer characteristics of a nonsquare enclosure when hydrodynamic resistance is altered discontinuously along its inner surface. Particularly, it focuses on investigating how several essential factors collaboratively influence the natural convection, including the Rayleigh number (Ra), the aspect ratio (AR), the nanoparticle volume fraction (ϕ) and the locations of changing hydrodynamic resistance.

To achieve these objectives, an L-shaped enclosure of various AR is adopted, while zero local shear resistance is applied and modeled by stress-free (SF) patches of four distinct arrangements (corresponding to Cases 1–4). The nanofluid is modeled by Buongiorno’s two-phase model. The effects are explored using an in-house numerical framework based on a hybrid lattice Boltzmann-finite difference method with the total variation minimization scheme.

The results show that when Ra is sufficiently large, i.e. Ra = 10⁵, SF patches can generally enhance the heat transfer performance regardless of other factors. However, the ways of achieving those enhancements are different, which mainly depend on the arrangement of the SF patches and AR but are nearly independent of ϕ. The maximum improvement of heat transfer can be achieved in Case 3 with AR = 0.6, Ra = 10⁵ and ϕ = 0.04, where the averaged Nusselt number is enhanced by 8.89%.

This study presents a new scenario where the SF patches of various arrangements are applied to enhance the nanofluid natural convection of a nonsquared enclosure, and it reveals how the improvement is achieved and cooperatively affected by several important factors.

The induction of geological disasters is predominantly influenced by the dynamic evolution of the stress and plastic zones of the multilayer rock formations surrounding deep-rock roadways, and the behaviours and mechanisms of high in situ stress are key scientific issues related to deep-resource exploitation. The stress environment of deep resources is more complex owing to the influence of several geological factors, such as tectonic movements and landforms. Therefore, in practical engineering, the in situ stress field is in a complex anisotropic three-dimensional state, which may change the deformation and failure law of the surrounding rock. The purpose of this study is to investigate the tunnelling-induced stress and plastic evolution causing instability of multilayered surrounding rock by varying three-dimensional in situ stresses.

Based on data from the Yangquan Coal Mine, China, a finite difference model was established, and the elastic-plastic constitutive model and element deletion technology designed in the study were analysed. Gradual tunnelling along the roof and floor of the coal seam was used in the model, which predicted the impact tendency, and compared the results with the impact tendency report to verify the validity of the model. The evolutions of the stress field and plastic zone of the coal roadway in different stress fields were studied by modifying the maximum horizontal in situ stress, minimum horizontal in situ stress and lateral pressure coefficient.

The results shown that the in situ stress influenced the stress distribution and plastic zone of the surrounding rock. With an increase in the minimum horizontal in situ stress, the vertical in situ stress release area of the roof surrounding rock slowly decreased; the area of vertical in situ stress concentration area of the deep surrounding rock on roadway sides decreased, increased and decreased by turn; the area of roof now-shear failure area first increased and then decreased. With an increase in the lateral pressure coefficient, the area of the horizontal in situ stress release area of the surrounding rock increased; the area of vertical in situ stress release area of the roof and floor surrounding rock first decreased and then increased; the area of deep stress concentration area of roadway sides decreased; and the plastic area of the surrounding rock and the area of now-shear failure first decreased and then increased.

The results obtained in this study are based on actual cases and reveal the evolution law of the disturbing stress and plastic zone of multilayer surrounding rock caused by three-dimensional in situ stress during the excavation of deep rock roadways, which can provide a practical reference for the extraction of deep resources.

This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method.

A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case.

The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented.

A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

A unified framework for solving the bending, buckling and vibration problems of rectangular thin plates (RTPs) with four free edges (FFFF), including isotropic RTPs, orthotropic rectangular thin plates (ORTPs) and nano-rectangular plates, is established by using the symplectic superposition method (SSM).

The original fourth-order partial differential equation is first rewritten into Hamiltonian system. The class of boundary value problems of the original equation is decomposed into three subproblems, and each subproblem is given the corresponding symplectic eigenvalues and symplectic eigenvectors by using the separation variable method in Hamiltonian system. The symplectic orthogonality and completeness of symplectic eigen-vectors are proved. Then, the symplectic eigenvector expansion method is applied to solve the each subproblem. Then, the symplectic superposition solution of the boundary value problem of the original fourth-order partial differential equation is given through superposing analytical solutions of three foundation plates.

The bending, vibration and buckling problems of the rectangular nano-plate/isotropic rectangular thin plate/orthotropic rectangular thin plate with FFFF can be solved by the unified symplectic superposition solution respectively.

The symplectic superposition solution obtained is a reference solution to verify the feasibility of other methods. At the same time, it can be used for parameter analysis to deeply understand the mechanical behavior of related RTPs. The advantages of this method are as follows: (1) It provides a systematic framework for solving the boundary value problem of a class of fourth-order partial differential equations. It is expected to solve more complicated boundary value problems of partial differential equations. (2) SSM uses series expansion of symplectic eigenvectors to accurately describe the solution. Moreover, symplectic eigenvectors are orthogonal and directly reflect the orthogonal relationship of vibration modes. (3) The SSM can be carried to bending, buckling and free vibration problems of the same plate with other boundary conditions.

The purpose is to explore the free vibration behaviour of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The goal of this study is to gain a better knowledge of the dynamic response of nanoscale structures made of functionally graded materials and porous features. The Rayleigh-Ritz approach is used in this study to generate realistic mathematical models that take elastic foundation support into account. This research can contribute to the design and optimization of advanced nanomaterials with potential applications in engineering and technology by providing insights into the influence of material composition, porosity and foundation support on the vibrational properties of nanoplates.

A systematic methodology is proposed to evaluate the free vibration characteristics of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The study began by developing the mathematical model, adding material properties and establishing governing equations using the Rayleigh-Ritz approach. Numerical approaches to solve the problem are used, using finite element methods. The results are compared to current solutions or experimental data to validate the process. The results are also analysed, keeping the influence of factors on vibration characteristics in mind. The findings are summarized and avenues for future research are suggested, ensuring a robust investigation within the constraints.

The Rayleigh-Ritz technique is used to investigate the free vibration properties of elastic foundation-supported porous functionally graded nanoplates. The findings show that differences in material composition, porosity and foundation support have a significant impact on the vibrational behaviour of nanoplates. The Rayleigh-Ritz approach is good at modelling and predicting these properties. Furthermore, the study emphasizes the possibility of customizing nanoplate qualities to optimize certain vibrational responses, providing useful insights for engineering applications. These findings expand understanding of dynamic behaviours in nanoscale structures, making it easier to build innovative materials with specific features for a wide range of industrial applications.

The novel aspect of this research is the incorporation of elastic foundation support, porous structures and functionally graded materials into the setting of nanoplate free vibrations, utilizing the Rayleigh-Ritz technique. Few research have looked into this complex combo. By tackling complicated interactions, the research pushes boundaries, providing a unique insight into the dynamic behaviour of nanoscale objects. This novel approach allows for a better understanding of the interconnected effects of material composition, porosity and foundation support on free vibrations, paving the way for the development of tailored nanomaterials with specific vibrational properties for advanced engineering and technology applications.

This paper aims to investigate analytical solutions of natural frequencies and mode shapes of Euler-Bernoulli beams with step changes in the stiffness.

In this work, analytical solutions for a beam with a single discontinuity was performed. Subsequently, based on an effective matrix formulation, the closed-form expressions of the single discontinuity beam could be conveniently extended to stepped beams with multiple stiffness discontinuities.

The results of the study show that the natural frequency of the beam can be adjusted by the local stiffness variation, and step location plays a significant role in free vibration responses.

The effects of the stiffness of the segment and step location on the natural frequencies of the stepped beams under different boundary conditions were examined using the proposed analytical scheme. This study provides insights into the design of variable-stiffness beam structures with the capability to adjust natural frequencies.

This paper aims to derive a reduced-order model for the heat transfer across the interface between a millimetric thermocapillary liquid bridge from silicone oil and the surrounding ambient gas.

Numerical solutions for the two-fluid model are computed covering a wide parametric space, making a total of 2,800 numerical flow simulations. Based on the computed data, a reduced single-fluid model for the liquid phase is devised, in which the heat transfer between the liquid and the gas is modeled by Newton’s heat transfer law, albeit with a space-dependent Biot function Bi(z), instead of a constant Biot number Bi.

An explicit robust fit of Bi(z) is obtained covering the whole range of parameters considered. The single-fluid model together with the Biot function derived yields very accurate results at much lesser computational cost than the corresponding two-phase fully-coupled simulation required for the two-fluid model.

Using this novel Biot function approach instead of a constant Biot number, the critical Reynolds number can be predicted much more accurately within single-phase linear stability solvers.

The Biot function for thermocapillary liquid bridges is derived from the full multiphase problem by a robust multi-stage fit procedure. The derived Biot function reproduces very well the theoretical boundary layer scalings.

The purpose of this article is to investigate the propagation characteristics (such as particle motion, attenuation and phase velocity) of a Rayleigh wave in a nonlocal generalized thermoelastic media.

The bulk waves are represented with Helmholtz potentials. The stress-free insulated and isothermal plane surfaces are taken into account. Rayleigh wave dispersion relation has been established and is found to be complex. Due to the presence of radicals, the dispersion equation is continuously computed as a complicated irrational expression. The dispersion equation is then converted into a polynomial equation that can be solved numerically for precise complex roots. The extra zeros in this polynomial equation are eliminated to yield the dispersion equation’s roots. These routes are then filtered for inhomogeneous wave propagation that decays with depth. To perform numerical computations, MATLAB software is used.

In this medium, only one mode of Rayleigh wave exists at both isothermal and insulated boundaries. The thermal factors of nonlocal generalized thermoelastic materials significantly influence the particle motion, attenuation and phase velocity of the Rayleigh wave.

Numerical examples are taken to examine how the thermal characteristics of materials affect the existing Rayleigh wave’s propagation characteristics. Graphical analysis is used to evaluate the behavior of particle motion (such as elliptical) both inside and at the isothermal (or insulated) flat surface of the medium under consideration.