Acta Mechanica最新文献

Investigating how wave propagation affects the functionality of surface acoustics wave (SAW) macro- and nanosensors is the main objective of the current investigation. Consequently, the surface piezoelectricity theory is used to investigate shear horizontal waves (SH) in an orthotropic PQC layer that is layered on top of an elastic framework (Model I), a piezoelectric substrate, and an orthotropic PQC substrate (Model II). Approach: A variable-separable approach is used in the study. Based on the differential equations and matrix formulation, theoretical forms are created and utilized to display the wavenumber of surface waves in any direction of the piezoelectric medium. Two configurations are examined: an orthotropic piezoelectric material layer over an elastic framework and a piezoelectric material half-space with a nanosubstrate. Analytical expressions for frequency equations are derived for both symmetric and anti-symmetric waves. Study investigates the effects of surface elastic constants, surface density, anisotropic piezoelectric constant, and symmetric and anti-ssymmetric modes on phase velocity. The study is confined to only linear wave propagation. Additionally, the analysis is based on idealized material properties and surface properties of the material. Surface effect study is the novelty which is conducted in the piezoelectric model and their applications in sensors. The findings of this research may be useful in designing surface acoustic wave sensors (SAW) devices.

This study investigates the impact of liquid sloshing on the efficiency of structural response control in a tuned liquid column damper (TLCD). While most research assumes that the free surface of the liquid remains flat and horizontal during oscillatory motion, real-world conditions cause the surface to become curved, exhibiting sloshing behavior. To account for this, a finite element model of the entire liquid domain within the TLCD is used. From the finite element model, sloshing-induced hydrodynamic forces acting on the TLCD walls are estimated. A numerical analysis is conducted on a single-degree-of-freedom structure with attached TLCD. The structure-TLCD system is subjected to both far- and near-field earthquake ground motions. The oscillatory frequency of the liquid in the TLCD is tuned to the natural frequency of the structure. Optimal TLCD design parameters are determined using the ‘fminsearch’ routine of MATLAB. The structural response reduction by the damper is obtained with and without considering the effect of liquid sloshing in the vertical limbs of the TLCD. The results reveal that non-consideration of the sloshing effect results in an overestimation of the control efficiency of the TLCD.

Herglotz’s principle is suitable for dealing with nonconservative phenomena. It is an extension of Hamilton’s principle. The generalized Chaplygin canonical equations are derived from Herglotz principle for nonconservative systems with nonholonomic constraints. The variational equation of Hamilton–Herglotz action for generalized Chaplygin systems is derived by using the Chetaev condition of constraints on virtual displacements. From this, two formulas of non-isochronous variation of the action are deduced. The definitions of Herglotz-type Noether symmetric transformation and quasi-symmetric transformation in phase space are given, and the criterion (i.e., generalized Noether identity) is derived by using total variational formula, and the Herglotz-type Noether-conserved quantities are given. Finally, a nonconservative nonholonomic system is investigated, the Herglotz-type generalized Chaplygin equation and generalized Noether identity are set up, and conservation laws are found by using the theorems we obtained, and the validity of the results is verified.

Mechanical nanosensors embedded within biological systems offer unique opportunities to assess variations in mass, displacements, and forces resulting from subcellular and cellular processes. On the other hand, these mechanical nanosensors establish a foundation for biological measurement devices capable of detecting individual molecules, owing to their exceptional size compatibility with molecular interactions. To enhance the performance of micro-/nanoscale biosensors, various organic layers, including biostructures like RNA, specific antibodies, and DNA, as well as lipid layers, are employed to identify a range of physical, chemical, and biological entities. This study investigates the nonlinear vibrations and primary resonance of a bionanostructure utilizing the first-order shear deformation plate theory (FSDT) in conjunction with the nonlocal strain gradient theory (NSGT). The sandwich nanoplates comprise a functionally graded core (FG) integrated with lipid bilayers on its upper and lower surfaces. The boundary condition is specified as immovable and simply supported, and this nanobiostructure is embedded in a nonlinear elastic foundation. The impact of porosity on both free and forced vibrations of functionally graded (FG) lipid sandwich nanoplates has been examined. The viscoelastic characteristics of the lipid layers were analyzed using the Kelvin–Voigt model. The Hamiltonian principle is utilized to formulate the nonlinear differential equations governing FG/Lipid sandwich nanoplates. The resulting partial differential equations are discretized through the application of the Galerkin method. Then perturbation techniques, including the multiple scale method and the Krylov–Bogoliubov–Mitropolski approach, are employed to analytically solve the system’s equations. A good agreement has been established by juxtaposing the present numerical outcomes with the results of earlier studies. The effects of several parameters, such as nonlocal and strain gradient indices, various foundation types, porosity volume fraction, excitation force magnitudes, different plate theories, and lipid viscoelastic properties, have been comprehensively examined. Drawing from the investigations and analyses conducted in this study, the findings on the nonlinear vibration characteristics of FG/Lipid sandwich nanoplates can be applied by researchers in the development of highly biocompatible nanobiosensors, nanodevices, and resonators.

Understanding the deformation of microchannels is critical for designing microfluidic devices made of soft materials and operating under significant pressure gradients. This study aims to establish an analytic elastic model for the deformation of a shallow microchannel under the action of inner pressure that includes the geometrical parameters of the whole device. By considering a rectangular prism-shaped polymeric block with a straight channel on a rigid substrate, the stress, strain, and deformation of the channel’s roof are analyzed in a plane deformation framework. The outcomes illustrate that deformation is influenced by elastic and geometric variables. This model allows qualitative and quantitative predictions of the deflection in the roof of a microchannel. The model is tested experimentally with a flowing train of droplets, finding a good quantitative agreement. However, qualitative differences might suggest a non-negligible effect of the drops in the overall pressure-flow rate relationship.

Architected latticed structural systems, known as metamaterials or metastructures, have recently garnered significant attention due to their superior performance under various loading conditions. This class includes metamaterials exhibiting multistability, characterized by negative stiffness, which enables energy entrapment during transitions between equilibrium states, making them suitable for applications such as lightweight protective systems. In this study, in three folds, we investigate the mechanical performance of a negative stiffness honeycomb metamaterial (NSHM) with unit cells composed of curved double beams. First, the quasi-static compressive response is numerically examined using the finite element method, revealing that this response is independent of the number of cells. Next, we analyze the transient dynamic response of both mono-material NSHMs and bi-material composites, where the stiffeners are replaced by brittle polystyrene, under localized striker and uniform plate impacts. Finally, we present an analytical model for the total potential energy, with solutions obtained through an optimization technique, and validate these results against the numerical simulations. Through these analyses, we study the effects of several parameters influencing multistability. Our findings demonstrate that the bistability ratio significantly impacts the overall response of the honeycomb, and the desired negative stiffness can be achieved with high bistability ratios. Additionally, the contact force peaks resulting from striker impact are found to be independent of the number of constituent elements. The optimized geometry of the lattice is determined through a trade-off between porosity and stiffness, achieved by thicker cell walls.

Piezoelectric sensors have been extensively utilized for the specific identification of biomolecules and the detection of chemical toxins. The optimization of piezoelectric micro-beam sensor design is crucial for applications in medical and environmental protection. This study analytically addresses the bending of piezoelectric micro-beams under surface stress by reformulating it as a plane stress problem within the framework of elasticity. A polynomial solution for stress and electric displacement is derived using the semi-inverse method for both cantilever and simply supported micro-beams. The numerical results concerning the components of stress, deflection, and electric potential are thoroughly discussed. Additionally, the influence of material parameters on the stresses, deflection, and electric potential of the piezoelectric micro-beams is examined in case of three kinds of common piezoelectric materials, thereby validating the plane-section assumption of material mechanics. The study provides theoretical guidance for the design and optimization of piezoelectric micro-beam sensors.

The oscillatory motion in flexible pipes due to internal flow constitutes one of the classical problems of fluid–structure interactions. Studies on the pipe dynamics must consider two features: (i) they are open systems, in which there is mass exchange through its boundaries, and (ii) the existence of dynamic instabilities, so there is a critical internal flow velocity above which the system becomes unstable. In this work, a nonlinear reduced-order model of a planar cantilevered pipe conveying fluid is derived via the extended Hamilton’s principle for nonmaterial volumes. The derivation considers the influence that the axial strain rate of the pipe must have in the internal plug flow velocity so that the proposed model becomes fully consistent in terms of conservation of mass. This condition makes the relative velocity of the flow explicitly dependent, not only on the instantaneous configuration of the pipe, but also on its rate of change, leading to the emergence of new terms in the equations of motion. Within the formalism of the extended Hamilton’s principle for nonmaterial volumes, some of these terms can be interpreted as being related to the “transport of kinetic energy”, which has not been discussed in previous studies. In order to assess the dynamic behavior of the proposed model, root loci graphs and parametric diagrams are obtained and comparisons are performed with selected models found in the literature. Also, the resulting nonlinear equations of motion are numerically integrated to show the dynamic behavior predicted by the linear analysis.

The fractional theory addresses microscopic physical processes and predicts delayed responses to stimuli observed in nature. This study establishes a mathematical model that incorporates the non-local Caputo-type temporal fractional-order derivative in the heat conduction equation to analyze the thermal behavior of a thermosensitive multilayered annular disk. The disk’s inner and outer layers are subjected to convective heat exchange constraints to emphasize the significance of the fractional framework. Using Kirchhoff’s variable transformation and considering the material’s inherent thermal nonlinearity, the equations are linearized. The resulting linear equations are solved using the integral transformation method to derive mathematical expressions for deflection, resultant forces, shear forces, resultant moments, and thermal stresses. Finally, a three-layered disk composed of copper, zinc, and aluminum is constructed for numerical calculations using a fractional-ordered thermosensitive structure, enabling graphical representation of how various fractional parameters influence temperature and thermal fluctuations.

A nanocolumnar polycrystalline copper (NCPC) model containing prefabricated cracks with random grain orientation is constructed and modified with a high-entropy grain boundary. The effects of crack length, location, and grain boundary modification on the tensile mechanical properties and crack extension behavior of NCPC are investigated by uniaxial tensile simulation by LAMMPS. Once the crack length exceeds 1 nm (limiting threshold), the peak stress in NCPC decreases significantly with increasing prefabricated crack length. Peak stress and yield limit of NCPC are dramatically enhanced after high-entropy grain boundary modification. High initial dislocation density and strong dislocation pinning due to the high-entropy grain boundaries significantly enhance the tensile mechanical properties of NCPC. The crack extension rate of high-entropy grain boundary-modified polycrystalline copper is faster than that of NCPC, and there is a more obvious difference in the crack growth evolution. The crack extension of high-entropy grain boundary-modified polycrystalline copper is mainly driven by grain boundary slip, which leads to the extension along the direction of an “X-type” shear band, while the crack extension of NCPC consists of a combination of grain dislocations and grain boundary slip.