Acta Mechanica最新文献

This study investigates the steady-state problem of SH guided waves impinging on a functionally graded piezoelectric-piezomagnetic strip structure with a circular hole and derives the corresponding analytical expressions. The incident wave field of planar SH guided waves is constructed using the guided-wave expansion method. Subsequently, by integrating the multiple-image technique, the scattering wave field that meets the requirements of the two infinitely long straight boundaries of the functionally graded strip structure is determined. The straight boundaries of the strip are assumed to satisfy stress-free, electrical-field-isolated, and magnetic-field-isolated conditions. The boundary conditions of the circular hole, including stress-free, continuous electric potential and electric displacement, as well as continuous magnetic potential and magnetic induction intensity, are used to further establish an infinite system of linear algebraic equations. Model examples are employed to explore the effects of factors such as inhomogeneity parameters, slab thickness, and the order of guided waves on the dynamic stress concentration factor (DSCF), electric field intensity concentration factor (EFICF), and magnetic field intensity concentration factor (MFICF) around the circular aperture. The results indicate that when the 0-order SH guided wave is incident, the influence of changes in inhomogeneity parameters on the stress concentration around the aperture is significant. In addition, the 0-order high-frequency SH guided wave causes the most substantial damage to the piezoelectric-piezomagnetic laminate structure, which requires special attention. As the laminate thickness increases, the stress concentration near the aperture decreases significantly. Therefore, a rational design of material parameters can effectively reduce stress concentration and protect functionally graded materials from brittle fracture.

This article offers a systematic investigation of energy harvesting from a two-layer piezoelectric sensor under nonlinear single-mode operation with emphasis on the identification of optimal working conditions for maximum power harvesting. Because linear models cannot address high-amplitude near-resonance behavior, a data-driven nonlinear dynamic model is presented based on the Lagrangian approach. This model incorporates a tailored electrical network enthalpy function, which is specifically appropriate to fulfill the nonlinear material characteristics of the piezoceramic. Model parameters like nonlinear damping and stiffness coefficients are obtained using perturbation approaches. The approaches are informed by empirical data from a comparable piezoelectric actuator to guarantee the accuracy and relevance of the model in depicting actual behavior. System analysis reveals the occurrence of high quadratic damping and cubic stiffness, which indicates the need for nonlinear analysis. Nonlinearity-conscious performance analysis, developed from the model, reveals that an optimal electrical resistance value of 8 leads to the optimal nonlinear energy harvesting. This optimized resistance provides a key design parameter for such systems, enabling engineers to achieve much better power output than designs based on linear approximations. The results reveal a significant enhancement of energy harvesting efficiency through the consideration of nonlinear effects as well as the optimization of the electrical load. This research enhances the understanding and practical application of piezoelectric energy harvesting through an empirically verified model that is robust and a crucial design parameter for maximum performance.

Beyond the utilization of linear elastic foundations like the Winkler, Pasternak, and Hetenyi among others, this study deployed a nonlinear elastic foundation to model the deflection of plates amid longitudinal and transverse initial pre-stresses. A promising analytical method has been utilized to construct various exact solutions for the model, which hugely contribute to the experimental and numerical studies, in addition to the analyses of overall linearized dispersion relation and the model’s stability. The numerical examination of the model has it that an increase in both the initial pre-stresses and the coefficient of the cubic nonlinearity coefficient ({M}_{2}) opposes the deflection of waves in the plate. In contrast, an increase in the coefficient of the quadratic nonlinearity ({M}_{1}) increases the vibrational displacement in the medium. In addition, the resulting approximate dispersion relation has it that an increase in both the attenuation parameter (eta) and transverse initial pre-stress ({N}_{2}) smoothly increases the dispersion of flexural waves, while an increase in the longitudinal initial pre-stress ({N}_{1}) opposes the dispersion of waves in the medium. Moreover, future work can be directed toward incorporating various forms of highly nonlinearly terms into the governing plate equation, in addition to an in-depth search for an optimal analytical procedure to perfectly tackle the nonlinearity terms.

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.