Acta Mechanica最新文献

To extend the application of ultrasonic nondestructive testing to viscoelastic materials, we investigate the propagation behavior of shear horizontal (SH) waves in functionally graded viscoelastic (FGV) materials and piezoelectric semiconductor composite structures in this paper. Based on elastic dynamics theory, the governing equations are derived in terms of displacement, electric potential, and perturbed carrier concentration. Analytical solutions for viscoelastic and piezoelectric semiconductor layers are obtained using a power series method and a direct approach. The results indicate that the gradient variation of material parameters affects the phase velocity and attenuation of SH waves and that an appropriate bias electric field results in SH wave amplification. The influence of bias electric field on attenuation are close related to the order of the modes. In the first mode and second mode, the bias electric field reduces the attenuation of the SH wave and can amplify the wave when the dimensionless wavenumber is very small. In the third mode, the application of the same bias electric field affects attenuation differently across varying material parameter gradients, yet none induce gain in the SH wave.

This study presents a thorough mathematical analysis of poro-thermo-dependent vibrations in beams of varying thickness, whose core consists of functionally graded porous materials combined with agglomerated carbon nanotube-reinforced polymers. To improve the precision and dependability of the results, displacements are characterized using higher-order shear deformation theory, and the influence of rotation angle is taken into account to implement stress transformations at designated angles. After deriving the governing motion and boundary conditions differential equations, they are converted to algebraic ones with the aid of the generalized differential quadrature method, and then, a broad evaluation of the effects of various mechanical, physical, and geometrical parameters variations on natural frequencies is provided. As there is no comparable study in the literature, the results of this investigation can serve as standards for future research.

This article presents a theoretical model for the coupled thermoelastic transient dynamics of thin nanobeams due to thermal shock loadings, considering the surface energy effect. A transversely isotropic Euler-Bernoulli nanobeam is analyzed, utilizing the extended Gurtin-Murdoch surface elasticity theory to capture its size-dependent thermoelastic behavior. Variationally consistent equations governing the motion of the nanobeam and the associated boundary conditions are derived from the extended Hamilton’s principle, which include rotary inertia, residual surface stresses, and thermal effects on the surface layers. Unlike most existing thermoelastic models, the model does not make any assumption on the across-thickness and longitudinal variations of temperature. The resulting partial differential equations in spatial coordinates in the Laplace domain are solved using a novel application of the homotopy perturbation method. The inverse transform of the obtained solution is performed numerically through Durbin’s method. The proposed model is validated by comparing it with existing benchmark solutions. A numerical study is conducted to analyze the impact of surface, material, and geometrical parameters on the transient behavior of thermoelastic cantilever nanobeams under axially and transversely applied thermal shock loads. The size-dependent nature of the axial displacement, deflection, and axial stress under thermal shock loading is illustrated for the first time.

This paper investigates the dynamic behavior of a circular tunnel in multi-layer soil structures under complex boundary conditions. Initially, seismic SH waves acting on these structures are considered. Using the series expansion method, analytical expressions for the scattering waves in each soil layer are derIVed. Subsequently, an analytical expression for the standing wave, satisfying stress-free conditions at the boundaries of a V-shaped canyon, is established using the fractional-Bessel-function-expansion-method and Graf-addition-theorem. Furthermore, the large-arc assumption method is employed to transform straight boundaries into curved ones within the multi-layer soil structures, and expressions for scattering waves due to these curved boundaries are obtained. Integral equations are formulated based on boundary conditions and solved using orthogonal-function-expansion techniques with efficient truncation. The calculation results analyze and discuss the dynamic-stress-concentration-factor of the tunnel within different soil layers. Additionally, the performance of the analytical solutions is validated by comparing them with finite-element-method solutions.

The study of sliding adhesive contact problem can reveal the mechanisms of interface friction, energy dissipation, and electric force coupling, and solve the problem of device performance degradation caused by contact failure. Based on the three-dimensional (3D) general solution of one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs), the sliding adhesion contact problem of 1D hexagonal PEQCs under a 1D hexagonal PEQCs spherical indenter was studied. The frequency response function of 1D hexagonal PEQCs half-space was analytically deduced and transformed into the corresponding influence coefficient. The numerical solution method composed of adhesion-driven conjugate gradient method (AD-CGM) and discrete convolution-Fourier transform (DC-FFT) is used to calculate phonon and phason displacements and stresses, potential and electric displacement. Numerical analysis provides insights into the effects of the friction coefficient, the total charge and adhesion parameters on the adhesion contact of 1D hexagonal PEQCs on half-space. The research results indicate that the influence of adhesion on surface stress and phason displacement is more pronounced, and the influence on other physical quantities can be ignored. The research results obtained here contribute to the optimization of interface design for quasicrystal materials and the improvement of device reliability.

A unique Moore–Gibson–Thompson (MGT) thermal conductivity model with memory-dependent derivatives is introduced in this work, which offers a fresh exploration of the thermo-electro-elastic transient response of a transversely isotropic piezoelectric hollow sphere. By addressing intricate interactions that are frequently missed in earlier research, the study offers a new look at the combined thermo-electro-mechanical behavior of the sphere under laser pulse heating applied to its traction-free inner surface. Detailed quantitative insights are obtained by solving the governing equations using a robust Laplace transform-based approach. Critical parameters, relaxation time, thermal conductivity rate, the kernel function, and pulse parameter time are all thoroughly examined in relation to the dynamic physical response. A variety of techniques, including both graphical and analytical ones, are used to analyze the system’s behavior. The results show significant advancements in our knowledge of the dynamic behavior of piezoelectric materials under complex mechanical and thermal loading scenarios. This study provides a major breakthrough in the field by combining the piezoelectric analysis with the memory-dependent MGT model. Its results represent a significant advancement in thermoelastic piezoelectric analysis and could be used to design next-generation materials, optimize thermal management systems, and create smart material technologies.

The energy-saving H-infinity control problem for an improved two-degree-of-freedom (2DOF) vibration isolator is investigated in this study. Firstly, the model of the improved 2DOF active control vibration isolator is presented, and the dynamic equations of the system are established. Subsequently, an energy-saving H-infinity optimal controller based on output feedback is designed for the improved 2DOF active control vibration isolator model, resulting in an output control force with energy-saving effects. The novel controller is characterized by the replacement of a portion of the active control force with the negative stiffness mechanism, thereby reducing the overall active control force under optimal conditions. To validate the energy-saving effects of the new controller, numerical simulations are conducted under three types of inputs. The results indicate significant energy-saving effects, with the root mean square (RMS) values of the actuator output force reduced by 57.14%, 92.67%, and 90.82%, respectively. Further numerical simulations are performed considering actuator time delays. Under the same three excitation inputs, the improved vibration isolator is shown to outperform the original isolator in terms of vibration isolation performance, while also demonstrating greater energy-saving capabilities, with reductions of 54.28%, 87.22%, and 4.03%, respectively.

This study presents a theoretical framework to calculate the influence of image forces on the strength of Frank-Read (FR) sources near free surfaces. We present a line tension model that explicitly incorporates image stress forces to establish the critical conditions of a FR source operation at various distances from the surface. A quasi-static nested loop (QNL) computational framework is developed to calculate the critical stress of FR source operation, and predictions are validated against discrete dislocation dynamics (DDD) simulations. Our analysis identifies a critical threshold surface proximity below which image stresses dominate, preventing the stable formation of a bowed-out segment regardless of the applied stress. Additionally, we derive a generalized analytical model expressing source strength as a function of both segment length and surface distance, capturing the transition from surface-dominated to bulk-dominated activation regimes. These findings provide insights into the mechanisms behind size-dependent phenomena in confined crystals (e.g., microbeams, thin films), such as enhanced yield strength, stochastic strength variability, and strain avalanche. The proposed approach contributes to the development of more accurate constitutive models and DDD simulations of microscale plasticity in confined crystalline volumes by providing a more accurate assessment of dislocation source strength in the presence of free surfaces.

To design and optimize piezoelectric quasicrystal (PQC) surface acoustic wave (SAW) devices, a detailed study of surface wave propagation—specifically Rayleigh and Love waves—in PQC-layered structures with weak interfaces is conducted. A hybrid Legendre–Laguerre polynomial approach is developed to analytically solve the wave dynamic equations in these structures, overcoming the limitations of traditional Laguerre polynomial methods. The interplay between piezoelectric effects and weak interface characteristics is thoroughly analyzed. Notably, new phenomena are uncovered: weak interfaces in the phonon and phason fields reduce structural stiffness, whereas weak interfaces in the electric field increase it. These effects are especially prominent at frequencies exhibiting significant dispersion. Additionally, the weak interface is found to diminish the piezoelectric coupling of phonon modes in Love waves. The findings provide a strong theoretical basis for the design and optimization of PQC-based SAW devices.

Film bulk acoustic resonators (FBARs) are essential in RF front-end applications due to their high performance, microsize, and ease of integration. This paper presents a one-dimensional analytical model for predicting the nonlinear forced vibrations of thickness–extensional AlN FBARs based on nonlinear piezoelectric theory. The model incorporates geometric and material nonlinearities, viscous damping, and electrode mechanical effects. Analytical expressions are derived to describe the excitation frequency–current relationship, including the effects of an external circuit. The influences of driving voltage, higher-order elastic constants, viscous damping, and electrode materials on the nonlinear frequency response are examined. Results indicate that increasing voltage strengthens nonlinear effects, leading to resonance frequency hardening and response multi-stability. The critical voltage marking the transition from linear to nonlinear behavior is also identified. Additionally, electrode properties, fourth-order elastic constants, and damping significantly affect the nonlinear response. Proper electrode and circuit design can mitigate nonlinear effects and extend the linear operating range. The proposed analytical model serves as an efficient tool for predicting nonlinear FBAR vibrations, providing valuable insights for device optimization.