Acta Mechanica最新文献

This paper presents an analytical study focused on the free vibration analysis of doubly curved composite micro panels that incorporate piezoelectric layers. We derive the total potential energy of the system using a combination of the modified Sander's shell theory and the first-order shear deformation theory. Applying Hamilton's Principle leads us to establish the governing equations, resulting in five mechanical equilibrium equations and two electrical equations. In our approach, we consider panels with different boundary conditions and utilize the Chebyshev–Ritz formulation to obtain numerical results. Additionally, we explore three different distribution patterns of graphene platelets within our study. The material properties for each layer of the micro composite shell, enhanced with graphene platelets, are determined through the Halpin–Tsai model. To validate our formulation and solution, we present a comparative study. Our case studies examine how boundary conditions, material and geometrical properties, as well as the applied voltage, influence the vibration behaviors of the doubly curved composite micro panels.

Functionally graded materials (FGMs) are widely used in engineering due to their superior mechanical properties. However, their impact behavior is typically studied through numerical simulations or experimental methods, which are often time-consuming and resource-intensive. In this study, we investigate the impact response of a two-phase functionally graded plate by establishing the governing equations based on the Zener model and a modified Hertz contact law. Compared with prior studies relying on numerical or experimental techniques, this analytical approach offers a more efficient and cost-effective tool. This study is the first to extend the homotopy method—previously applied to homogeneous plates—to derive analytical solutions for functionally graded plates under impact. From the analytical solution, we derive explicit expressions for the maximum impact force, maximum impact depth, total contact time, total compression time, and the coefficient of restitution. These expressions enable us to analyze the influence of the functionally graded index, as well as the ratios of elastic modulus and density between the top and bottom surfaces of the plate during the impact process. The results quantitatively explain the superior performance of functionally graded plates and determine the optimal functionally graded index corresponding to the maximum coefficient of recovery.

To address challenges in unified matrix integration and computational complexity for arbitrary cross-sectional beams in the Absolute Nodal Coordinate Formulation (ANCF), this study introduces Monte Carlo integration into the framework of fully parameterized 3D ANCF beam elements. A unified element matrix numerical integration scheme for beams with arbitrarily shaped cross-sections is developed. Further optimizations include the separation of axial and cross-sectional integrations: Gaussian quadrature is applied along the axial direction, while a quasi-Monte Carlo method with low-discrepancy sequences is adopted for cross-sectional integration. These enhancements significantly improve both accuracy and computational efficiency. Additionally, the proposed method is extended to multi-layer cross-sectional beams, enabling the modeling of structures such as sandwich beams with fillers and composite transmission lines, where material properties vary across layers. Static and dynamic numerical validations demonstrate good relative agreement between the proposed beam models and theoretical solutions or finite-element benchmarks. Among them, the dynamic prediction accuracy of the proposed double-layer cross-section beam element reached 98.61%. Results confirm the feasibility of this unified approach for constructing ANCF beam elements with arbitrary cross-sections.

In-plane analysis of a piezoelectric layer with several embedded and edge cracks is conducted using the distributed dislocation technique. The modeling of the crack is done by employing the continuous distribution of dislocations along its surface. By applying the integral transform method, we derived the stress and electric displacement fields induced by Volterra climb and glide edge dislocations, as well as electric dislocations, in the piezoelectric strip. These fields are employed to formulate integral equations governing the behavior of a cracked piezoelectric strip under in-plane electro-mechanical loading. The singular integral equations with the well-known Cauchy-type singularity are numerically solved for the dislocation density functions by generalizing a numerical method to obtain field intensity factors at the tips of embedded and edge cracks. Several examples are analyzed to investigate the fracture behavior of a piezoelectric strip weakened by edge and embedded cracks with various orientations. The effects of crack orientation, crack location, and electromechanical loading parameters under various mixed-mode conditions are investigated on Mode I and II stress intensity factors, as well as electric displacement intensity factors, for multiple interacting embedded and edge cracks. This study presents a novel analytical solution for the simultaneous modeling of embedded and edge cracks in a piezoelectric strip under mixed-mode loading conditions, a problem not previously addressed in the literature. Furthermore, the related problem is formulated for an arbitrary straight crack, which can also be used to analyze curved cracks.

This study investigates the dynamics and control of an undamped suspended Euler–Bernoulli beam suspended from an overhead crane, to eliminate residual vibrations during rest-to-rest maneuvers. The system governing equation is discretized using the finite difference method, and modal analysis is applied to construct the modal model matrix. Modal characteristics derived from this model are used to generate transfer functions, which form the basis for implementing input shaping methods and determining the corresponding input amplitudes. Two multimode input shaping methods, Multimode Zero Vibration and Multimode Zero Vibration and Derivative, are evaluated for their effectiveness in vibration suppression and parameter uncertainty. To streamline practical implementation, fitted functions of the input amplitudes are introduced to generalize the input profiles across various operating conditions. An Effectiveness Index is also proposed to assess input performance in terms of motor stress and maneuver time. Experimental validation is conducted on a scaled overhead crane setup, with beam responses analyzed in the frequency domain. Results demonstrate that both methods effectively reduce vibration, with Multimode Zero Vibration and Derivative showing greater robustness, while Multimode Zero Vibration yields smoother motion. The study highlights the importance of vibration modes in input shaping design and robustness evaluation for controlling flexible crane systems.

This study presents a comprehensive investigation into the vibrational behavior of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) plates interfacing with elastic substrates of variable stiffness. Utilizing a Winkler–Pasternak model, we examine how discrete substrate stiffness zones influence dynamic responses. Temperature-dependent material properties are rigorously characterized using a combined Halpin–Tsai micromechanical model and the rule of mixtures, capturing the nuanced effects of thermal environments. The governing equations, derived from Reddy’s third-order shear deformation theory and incorporating von Kármán geometric nonlinearity, are solved using the Galerkin method. The accuracy of the proposed approach is rigorously validated through comparisons with finite element method (FEM) simulations and benchmark results from the existing literature. This study explores key phenomena, including natural frequencies, central deflection time histories, resonance, and harmonic beat effects, while systematically assessing the impacts of thermal conditions, graphene reinforcement, applied voltage, and geometric parameters. Notably, an in-depth analysis of substrate stiffness variations leads to the formulation of a novel constraint equation for elastic substrates with equivalent stiffness. These findings not only enhance the theoretical framework of FG-GPLRC plates but also provide valuable insights for advancing structural design and engineering applications.

Metal-halide perovskites are gaining significant attention as highly promising materials for next-generation solar cells and optoelectronic devices. However, their structural responses under combined optical, electrical, thermal, and mechanical fields remain insufficiently understood, hindering their practical applications. This study introduces an opto-electro-thermo-elastic model for lead halide perovskites, incorporating photostriction, photothermal effects, electrostriction, and piezoelectricity, to analyze their buckling and vibration behaviors under multi-physical interactions. The governing equations for perovskite plates are formulated based on third-order shear deformation theory and solved analytically using the Navier method. Extensive parametric studies explore the effects of multi-physical fields on key performance metrics, including critical light intensity, critical electric field, critical temperature, and free vibration. The results demonstrate that light exposure, photo-induced heating, and external electric fields significantly influence natural frequencies, and bifurcation buckling. These factors must be carefully considered in the design of perovskite-based optoelectronic systems to optimize performance and reliability.

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.