Archive of Applied Mechanics最新文献

This study examines the perturbed photogravitational Circular Restricted Three-Body Problem (CR3BP) under the combined effects of radiation pressure, albedo, continued fractional perturbations, and a gravitational disc. For the Sun–Earth system with the asteroid belt and the Sun–Jupiter system with the Kuiper belt, we analyze how the modified potential influences equilibrium points, Zero-Velocity Curves (ZVCs), and stability. Numerical results show that as the continued fractional parameter (epsilon ) increases, new collinear ((L_1', L_2')) and non-collinear ((L_4', L_5')) points emerge, while disc mass and other perturbations merely shift their locations. The Jacobi constant decreases with increasing (epsilon ), enlarging the allowed motion regions. Stability analysis indicates that (L_1, L_3, L_4', L_5') are unstable, whereas (L_4, L_5) remain stable within certain ranges of the critical mass ratio (mu _c). The new point (L_1') can be stable for specific (epsilon ) values in both systems. Overall, continued fractional perturbations, disc effects, and surface properties reshape equilibrium configurations and modify classical stability boundaries, enriching celestial dynamics and space mission design.

Bending collapse is a failure mechanism in thin-walled shapes that often appear in structures under impact and high bending loads. It is characterized by the formation of a localized zone of large plastic strains, referred to as a plastic hinge, which is typically described in engineering applications by moment–rotation curves. The importance of this topic primarily lies in the estimation of the crashworthiness of vehicle structures, where tubes with rectangular hollow sections are commonly used in structures for rollover protection. In this field, both the strength and the energy absorption of the shape need to be adequately quantified. Although this topic has been covered in past and recent research, the existing studies are based on empirical deformation mechanisms and energy methods that provide limited insight into the mechanical principles governing bending collapse. In this investigation, numerical simulations are employed to analyze the influence of geometric parameters and strain hardening on the bending properties of rectangular hollow tubes. The finite element models are verified with experimental results reported in the literature. The results show that bending collapse is governed by the occurrence of local buckling in the compressed flange and sidewalls. Moreover, the moment–angle curves are correlated with stress and plastic deformation responses in the plastic hinge. This study gives a comprehensive understanding of the mechanical quantities governing the different stages of bending collapse, offering crucial insights for developing theoretical models for novel thin-walled energy absorbers.

Studies have substantiated that extremely small structural elements exhibit thermomechanical characteristics tied to their size. In addition, experimental tests and analytical simulations highlight thermoelastic damping (TED) as a fundamental reason for energy loss in small-scale vibrating structures. The paper at hand strives to propose an innovative size-sensitive formulation for TED prediction in rotating rectangular cross-sectional nanorings. Size dependence is embedded in the structural and thermal fields by applying the nonlocal theory (NT) and the Moore–Gibson–Thompson (MGT) heat conduction model, respectively. By means of the NT, the equation of motion for the rotating ring is formulated, reflecting the nonlocal influences. Furthermore, solution of the MGT-based coupled heat equation yields the complete temperature profile across the ring structure. Implementation of the solved temperature field in the motion equation produces the real and imaginary components of the ring’s frequency. Applying the frequency-definition method ultimately results in an explicit formulation for TED in miniature rotating ring systems. The study allocates a comprehensive parametric investigation to examine correlations between TED and influential parameters, with emphasis on the characteristic scales incorporated in the NT and MGT model. Computational results confirm that nanoscale behavior modeled through the developed size-sensitive framework substantially deviates from classical theoretical predictions.

This paper presents a theoretical study on the reflection of plane waves in a homogeneous, isotropic bio-thermoelastic diffusion half-space incorporating hyperbolic two-temperature (HTT) effects within the framework of Moore-Gibson-Thompson (MGT) heat conduction. The analysis is performed in two dimensions using dimensionless variables and potential function techniques to simplify the governing equations. Employing normal mode analysis, the study identifies the existence of four distinct longitudinal waves and a single shear vertical (SV) wave, each propagating with different phase velocities. Analytical expressions for the amplitude ratios corresponding to longitudinal (P), thermal (T), chemical potential (Po), and shear vertical (SV) waves are derived and explored as functions of the incident angle, wave frequency, and relevant material parameters. The effects of the HTT parameter, blood perfusion rate, and various thermoelastic theories on the reflection coefficients are investigated through graphical illustrations. Several special cases are also discussed. The findings are relevant to applications in geomechanics, ocean engineering, and biomedical diagnostics, offering valuable insights into wave behavior in bio-thermoelastic diffusion media under the influence of HTT and MGT models. This work contributes a multiscale framework for studying wave propagation in such complex environments.

Piezoelectric devices are often integrated with elastic substrates to ensure their structural reliability and performance. To model the interaction between piezoelectric devices and their substrates, the elastic foundation model is commonly adopted. However, many of these models overlook the significant influence of foundation inertia, which can substantially affect the system’s dynamic response. This paper proposes a theoretical model that accounts for the substrate mass, aiming to investigate its influence on the free vibration and static bending of functionally graded piezoelectric beams resting on elastic foundations. Based on electro-elasticity theory and the elastic foundation model, a state-space method is applied to derive the governing equations for functionally graded piezoelectric beams with material properties that vary continuously through the thickness. The differential quadrature method is further adopted to analyze the natural frequency and bending responses under various boundary conditions. Numerical results reveal that foundation parameters significantly influence the natural frequencies, bending deformation, and electric potential distribution of the beams. It is noted that the beam’s dynamic behavior is highly sensitive to the foundation mass. These findings provide valuable insights for the design and optimization of advanced piezoelectric structures.

Elastomers' hyperelastic properties make them popular for mitigating vibration and shock in a variety of engineering applications. These properties are commonly modeled using hyperelastic models, which require the determination of material constants. In the conventional approach, multiple material test data, such as uniaxial, biaxial, planar, and volumetric data, of each material are required to obtain material constants of a hyperelastic model. Elastomer experimental testing is an expensive and time-consuming procedure. These limitations prompt the development of neural networks that can accurately determine the hyperelastic constants without requiring multiple tests. Therefore, this study focuses on developing a deep neural network (DNN) to determine the material constants of the Ogden third-order model for elastomers. Finite element analyses of uniaxial tension and compression tests are performed using ABAQUS software for randomly generated samples to generate a dataset for training the DNN model. The designed DNN model consists of three hidden layers with tanh activation functions and is trained using the AdamW optimizer. The trained DNN model is validated for hydrogenated nitrile butadiene rubber, polychloroprene rubber, and natural rubber (NR) under uniaxial conditions, and for neoprene and silicone rubbers under uniaxial, planar, and O-ring multi-contact tests. Furthermore, simulation responses using DNN-predicted constants for neoprene rubber at 50 °C and 80 °C closely match the experimental data. Additionally, simulation responses with DNN-predicted constants and experimental data for a shock test case study on NR dampers exhibit close agreement. Thus, the proposed DNN model can determine material constants of the hyperelastic model for any kind of rubber using direct component uniaxial data, eliminating the need for coupon tests.

Graphic statics, an old-timer classic method in structural analysis, stands out for its effectiveness and visual appeal in analyzing statically determinate planar trusses using two reciprocal diagrams. However, since it only uses geometric construction to represent the equilibrium of force vectors, it does not involve structural deformation, and thus cannot solve the redundant reactions in statically indeterminate trusses. By incorporating the recently established matrix-algebraic operation on reciprocal diagrams and the unit load method for finding joint displacements, this study is dedicated to developing a methodology for solving externally indeterminate trusses. A key innovation is the introduction of a novel vertex-extrapolated form diagram, constructed by adding virtual vertices and edges at the original truss joints. The incidence matrix of the vertex-extrapolated form diagram can effectively simplify the application of unit loads when using the principle of virtual work. To solve indeterminate trusses, redundant supports are removed by setting their force densities to zero, and compatibility conditions are satisfied by solving the displacement equations. Overall, the approach is well suited to computer-aided design (CAD) environment, leveraging matrix operations for automated analysis. The validity and accuracy of the proposed methodology are demonstrated through practical examples involving both determinate and indeterminate trusses.

This work presents a newly designed, smart design of shape memory alloys (SMAs)-based auxetic structure with auxeticity and stiffness tunability for advanced engineering applications, and then numerically explores its tunability and mechanical information. The SMA component is placed at the right location, helping it be exposed to the maximum load. The numerical homogenization accuracy of the introduced unit cells in the elastic domain is verified experimentally in terms of effective elastic stiffness. Interestingly, the results show significant auxeticity and stiffness tunability of the structure by adjusting the temperature. Astoundingly, a higher frame material stiffness can widen further the range of the auxeticity and stiffness tunability, and the auxeticity of the structure is found to be enhanced with a higher deformation and temperature. Uniquely, the structure possesses an extreme phase transformation-induced anisotropy, and a profile of multiaxial critical stress surface exceptional to that of non-auxetic materials, with critical stress lying on two parallel lines, opposite orientation, and unable to be outside the lower and upper bounds regardless of the change of biaxial load value.

Fractional derivatives, due to their nonlocality, can describe complex processes where historical data is important for future calculations. At the same time, this property brings difficulties in numerical simulations. This paper presents a new discrete operator for approximating the fractional derivative based on the Grünwald–Letnikov definition, the “short memory principle,” memorization and analytical assumptions. This operator significantly reduces the number of operations in the calculation process when solving boundary value problems by saving the calculated data and transforming it for further use with adjustable accuracy. The results obtained showed that the use of this technique on specific problems reduced the execution time from ~ 1262 s to ~ 19 s, which is more than 66 times less than the standard method. It should be taken into account that the use of the modified method showed a worse result compared to the analytical method and amounted to ~ 0.011%.

Porous materials with high energy absorbance capacity are widely incorporated into sandwich construction to reduce the vibration of structures. This paper presents a size-dependent beam model for studying thermoelastic nonlinear dynamics of sandwich microbeams with an functionally graded porous (FGP) core under a moving mass. Considering both the shear deformation and rotary inertia, the beam model based on the sinusoidal beam theory is derived by using the modified couple stress theory (MCST) to capture the microstructural size effect. The nonlinear differential equations of motion with temperature-dependent material properties are established and then transferred to a discretized form using an finite element formulation. The nonlinear dynamic response of the sandwich microbeam with simply supported ends is predicted using the Newton–Raphson iterative procedure in conjunction with the Newmark method. The result reveals that while the effect of porosities on the nonlinear dynamic response is more significant for the sandwich beam having a larger core thickness, that of temperature change decreases as increasing the porosity coefficient. The influence of the porosity distribution, temperature change, the Coriolis and centrifugal forces induced by the moving mass on the nonlinear dynamic behavior of the sandwich microbeams is studied in detail and highlighted.