Multilayer Beam Research Articles

Rigid–flexible coupling design and reusable impact mitigation of the hierarchical-bistable hybrid metamaterials

Mechanical metamaterials with multistable unit cells featured by negative stiffness or quasi-zero stiffness is attracting increasing attention owing to their unique mechanical properties and reusable potential. In this paper, a hierarchical-bistable hybrid metamaterial with rigid–flexible coupling design is proposed, demonstrating excellent mitigation performance and protection against multiple impacts. The metamaterial consists of a multi-layer bistable beams with a central honeycomb and is manufactured by 3D printing. Firstly, the negative stiffness characteristics of the curved beams in the metamaterial are theoretically determined, and the convergence of the finite element model under different mesh sizes is analyzed. And the quasi-zero stiffness characteristics of the metamaterial have been confirmed, along with its more stable and uniform deformation pattern, through the quasi-static compression experiment. Then the buffering performance of the metamaterial is studied in ball impact tests, showing an average improvement of about 65% compared to the rigid control group, while verifying the accuracy of the finite element model. With the analysis of the deformation modes and strain energy, the mitigation mechanism of metamaterials is demonstrated to extend the contact time and disperse the impact load through the layered deformation to reduce the peak response, instead of relying on plastic strain. Finally, the reusability of the metamaterial is explored by the ten-times plate impacts simulation. The results demonstrate that the metamaterial decreases the plastic strain of its structure by 60% while reducing impact response, thereby preventing the premature failure of core components. These results demonstrate the great potential of the proposed metamaterials for various engineering applications, including aircraft or spacecraft landing protection, vehicle pedestrian protection, and the transportation protection of fragile objects or precision instruments.

An analytic solution for bending of multilayered structures with interlayer-slip

Layered structures are prevalent in both natural environments and engineered composite materials. The elastic bending behavior of these structures is primarily governed by properties of their abundant interfaces. While the behavior of two- and three-layered beams has been extensively studied, this research shifts the focus to the impact of elastic shearing at interfaces on the deflection of multilayered structures comprising a substantial number of layers. We present an analytical solution indicating that the bending properties of multilayered beams and plates are nonlinearly dependent on interfacial stiffness. Denoting Se as the effective bending stiffness of an n-layered beam of length L, and S0 as the bending stiffness of a perfectly bound counterpart, we arrive at SeS0=11+(n2−1)tanhαLαL where αL represents a dimensionless parameter related to geometry and material properties. The analytical solutions, validated through finite element simulations, highlight the substantial variations in stiffness across different layered structures. This solution could also be instrumental in assessing interfacial damage and delamination in lamellar composites.

Vibration of multilayer cantilever beams towards piezoelectric power harvesters

This paper investigates the vibration characteristics of a commonly employed mechanical structure, the cantilever beam, concerning its potential for direct electricity harvesting from piezoelectric crystals. Piezoelectric materials are renowned for their ability to generate electric charges when subjected to mechanical stress. To ensure continuous current generation, these materials require sustained excitation by external forces, typically achieved through vibration. However, piezoelectric crystals lack sufficient elasticity, necessitating attachment to a structurally conducive and easily vibratable framework. The cantilever beam, renowned for its simplicity and widespread use, serves as an ideal platform for this purpose. Layers of piezoelectric material (PZT5H) are affixed to brass-based cantilever beams to create various multilayer configurations. External forces are then applied at the free end of the beam to induce vibration. Given that the harvested power from PZT5H crystals correlates with the mechanical stress they experience, achieving optimal deformation is paramount. This is accomplished by leveraging the resonance effect of vibration, wherein the vibration modes and natural frequencies of the multilayer PZT5H beams must be thoroughly characterized. To this end, numerical methods and Finite Element Analysis via Abaqus software are employed. The vibrations of the brass base layer, as well as single-sided and double-sided PZT5H beams, are analyzed across four distinct mode shapes and corresponding natural frequencies. The study culminates in a comprehensive examination of the relationship between natural frequencies and dimensional parameters of the beams. Ultimately, this research offers valuable insights into the vibration behavior of cantilever beams, laying the groundwork for the development of efficient power harvesting devices utilizing mechanical vibration sources or tailored to specific applications.

Control and Analysis of Swelling Deformation of Hydrogel Beams Through Multilayer Design

In this paper, we suggest a design strategy for multilayer hydrogel beams with controllable swelling deformation and bending, which can be used in soft devices. We adopt a constitutive model that considers the entanglement chains of the hydrogel and an analytical method for solving multilayer hydrogel beams is developed. First, the reliability of the design strategy is provided by comparing analytical solutions and numerical results. Then, guided by the above design strategy, we quantitatively investigate hydrogel beams with gradient distribution and study the effects of material and distribution on the deformation and bending behavior of the structures. The results show that under non-gradient distribution, all structures with an odd number of total layers only undergo in-plane expansion, while all those with an even number of total layers undergo expansion and bending. However, this law will be broken at the gradient distribution. The introduction of entanglement chains and gradient distribution strategy increase the range of adjustment for deformation and bending. This work is expected to provide new insights into the design of multilayer hydrogel beams for material–structure–function integration.

Vibration and aeroelastic instability analysis in GPL-porous multi-layered beam with the rotation effect

This research studies the vibrations and instability of a rotating three-layer beam under aerodynamic forces consisting of two functionally graded (FG) composite surfaces and a porous intermediate layer. Linear poroelasticity theory is used for modeling the porous layer while Young’s modulus and density vary along the thickness. Equivalent coefficients of the graphene nanoplatelets-reinforced composite (GPLs) are extracted by modified Halpin-Tsai theory, according to five different configurations. The equations of motion in the GPL-porous multi-layered beam are derived using the Euler–Bernoulli beam (EBB), Timoshenko beam (TB), and Reddy’s higher-order shear deformation theory (HSDT) theories, as well as the energy method and Hamilton’s principle. The most important results show the effect of reinforcements and their different configurations, porosity and its distribution, speed of rotation on natural frequency, critical flutter point, and loss factor for a GPL-porous multi-layered beam. The unique properties of GPL-reinforced porous materials facilitate the design of components capable of effectively managing dynamic loads and resisting aeroelastic instabilities. This results in more efficient, reliable, and durable systems across various industries.

Free vibration analysis of multi-layer perforated fibre-reinforcement damping composite beam

This paper investigates the effective elastic constants of the perforated fibre-reinforcement damping membrane, taking into account the variations in perforation array and ply orientation angle using the homogenization method and the off-axis stress-strain relation. The equations for the free vibration of the composite beam with multi-layer perforated fibre-reinforcement damping membranes are derived using the first-order shear deformation theory and the Hamilton principle. These equations are then solved using the Navier method. The novelty of this paper lies in the achievement of an effective elastic constants model and vibration analysis for the multi-layer composite beam under simply supported boundary conditions. The calculated results are then compared with experimental values and finite element results to validate the theoretical model and method. Furthermore, the paper explores the graphical variation of mechanical performance with system parameters, providing a theoretical foundation for future researchers in the composite field.

Analysis of multilayered two-dimensional decagonal piezoelectric quasicrystal beams with mixed boundary conditions

Piezoelectric quasicrystals have a broad spectrum of promising applications and research value due to their unique atomic arrangement and multi-field coupling effects. This paper presents a mechanical analysis of the static bending and free vibration problems of two-dimensional multilayered decagonal piezoelectric quasicrystal laminated beams. Mechanical models of the beams are established, and the differential quadrature method in conjunction with the state-space method is utilized to obtain the solutions for the beams with mixed boundary conditions. We first investigated the static response and free vibration problem of quasicrystal laminated beams. By degrading them into crystalline materials, we verified the accuracy of the method by comparing the results with the existing ones. Then, the effects of different boundary conditions and slenderness ratios on the stresses, displacements, electric potentials, and electric displacements of quasicrystal laminated beams under normal mechanical loading and free vibration are investigated. Subsequently, the effects of different laying modes on the mechanical properties of the quasicrystal laminated beams when the material principal axis of the beam is changed are also analyzed.

Seismic behavior of reinforced concrete shear walls using a combined model of multi-layer shell and fiber beam elements

Seismic behavior of reinforced concrete shear walls using a combined model of multi-layer shell and fiber beam elements

Initial factors impacting vertical displacement, stresses, and propagation of cracks in three-layered steel fiber concrete beams

The main aim of the study is to examine the input parameters of three-layered steel fiber concrete beams. Bending RC beams is studied by many different scientists. Multilayer RC beams using SF concrete are one way. In high compressive and tensile stress zones, this method improves beam load strength and reduces cracks. The main goal is to decrease beam stress. Repairing broken three-layered SF-reinforced concrete beams by adding more concrete on top or below the current layer is a benefit. Modifying input parameters during three-layered beam design greatly affects beam efficacy. In this paper, the authors conducted a study using ANSYS simulation and nonlinear material analysis. The objective was to investigate the behavior of three-layered bending RC beams subjected to two concentrated loads. Specifically, the study examined the impact of varying the content of SF in the RC, as well as the effects of stirrup at the ends of the beams. Furthermore, the study explored the influence of changes in the quantity and size of steel bars in the region of tensile strength, along with the effect of varying the SF concrete layer's thickness. The survey results on three-layered beams were used to create diagrams that depict the relationship between load and vertical displacement and load and stress area. These diagrams also help determine the initiation and progression of cracks in three-layered beams, starting from the application of load until the beams become damaged. Ultimately, this information allowed us to identify the specific load level that caused the beams to crack and become damaged.

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

SummaryThis study aims to analyze the buckling and post‐buckling behaviors of multilayer nanocomposite beams reinforced with graphene oxide powders (GOPs) at low concentrations. The GOPs are randomly oriented and evenly distributed throughout the composite layers, with their weight fraction varying in the thickness direction. The Halpin‐Tsai model is employed to estimate each layer's effective material properties. The nonlinear governing equations for the FG‐GOPRC beam are derived based on the first‐order shear deformation beam theory, and a nonlinear algebraic system is formulated using the principle of potential energy. In this research, a comprehensive parametric analysis is conducted to examine the influence of various factors on the buckling and post‐buckling behaviors of the composite beams. These factors include the distribution pattern and weight fraction of graphene platelets (GPLs) nanofillers, as well as the geometry, size, slenderness ratio, and boundary conditions of the beams. Through the analysis, the study highlights the significant strengthening effect of these factors on the buckling and post‐buckling performance of the composite beams. The findings from this investigation contribute to a deeper understanding of the behavior of multilayer nanocomposite beams reinforced with GOPs. This knowledge can be valuable in designing and optimizing of composite structures for enhanced buckling resistance and post‐buckling performance.

Method for producing identical spectral copies of ultra-broadband arbitrary light fields.

An ultra-broadband beam splitter arrangement, with a spectral amplitude response that is over seven orders-of-magnitude more uniform than broadband, multi-layer dielectric beam splitters, can be created by the combination of multiple Fresnel events on an uncoated, optical flat when used at a specific angle-of-incidence. This beam splitter arrangement produces three, spectral copies of the original, two of which have identical spectral phase. In this manuscript we derive the precise angle at which this maximally flat spectral amplitude response occurs for any material and present this angle's material and polarization dependence.

Multilayered Inhomogeneous Beams under Torsion and Bending: An Analytical Study of Energy Dissipation

The present theoretical paper is devoted to the problem of energy dissipation in multilayered inhomogeneous beam structures of visoelastic behaviour. In particular, our attention is concentrated on studying the energy dissipation for the case of a beam that is loaded simultaneously in torsion and bending. Both torsion and bending moments which are applied on the beam change with time so that the angles of twist and rotation of the beam end vary continuously with time. The viscoelastic mechanical behaviour of the beam under torsion is treated by a viscoelastic model that has two linear springs and a linear dashpot. The model is under time-dependent shear stress. The viscoelastic behaviour of the beam under bending is modelled in a similar way. An analytical approach of deriving the energy dissipation is applied. The approach treats a multilayered beam that has an arbitrary number of layers of different thicknesses and material properties. The layers are longitudinally inhomogeneous. An investigation of the energy dissipation is carried-out to clarify the effect of the parameters of the time-dependent bending and torsion moments, the material inhomogeneity and the beam size on the energy dissipation.

Modeling of multi-material beams in analytical SEA

This study presents a method for predicting vibrations in multi-material, multi-layer beams using Analytical Statistical Energy Analysis (ASEA) by considering them as homogeneous beams with equivalent bending characteristics. This approach enables the simultaneous achievement of weight reduction and noise and vibration performance, which is essential in the current trend of using lightweight materials such as high strength steel, aluminum, and fiber-reinforced plastics in vehicle body structures. The proposed method is validated through Finite Element Method (FEM) calculation and the vibration energy transfer characteristics of multi-layer beams are examined. Additionally, an example of replacing a steel single-unit beam with a multi-layer beam is presented to demonstrate the potential of the proposed method in achieving lightweight and low vibration.

Multilayered inhomogeneous beam under relaxation: an analytical delamination investigation

Delamination in a multilayered inhomogeneous viscoelastic beam structure under relaxation is analyzed. The moduli of elasticity of beam layers change with time. A linear viscoelastic model with two springs and a dashpot is used for describing the relaxation behaviour. The response of the model is obtained by considering the equilibrium of its components. The material properties vary continuously along the width of layers. Besides, the modulus of elasticity of one of the springs changes with time. Time-dependent strain energy release rate (TDSERR) for the delamination is found by using the time-dependent strain energy (TDSE) in the beam. The TDSERR is found also by analyzing the compliance. The results are identical. The influence of different factors and parameters on the delamination is evaluated.

Underwater impulsive response of sandwich structure with multilayer foam core

Abstract The coupling between fluid-solid interaction and structural response is a crucial factor in understanding the resistance of sandwich structures to underwater blasts. In this study, we present a theoretical model that predicts the dynamic response of multilayer foam core sandwich beams subjected to underwater impulses. We carried out a time-scale intercoupling analysis by considering the compressible core in both incident impulse and structural response. In the incident impulse coupling phase, the one-dimensional fluid-structure interaction in terms of cavitation evolution is conducted to obtain the incident pressure profile. A four inter-stages response model is proposed for further analyze the structural response coupling phase and its coupling with core strength. Explicit finite element calculations are performed to verify the theoretical results in terms of the velocity profile, transverse deflection, and core compression. The results suggest that the interaction between the four stages of the dynamic response is significantly influenced by the impulsive intensity and core strength, and the sandwich beam does not undergo all the four stages. The equivalent core strength used in the theoretical analysis is confirmed accurate to predicts impact resistance of the corresponding graded core sandwich beam, which is inferior to the sandwich beam with uniform cores, despite having the same areal mass.

Geometrically nonlinear effect on forced vibrational behavior of superlight composite beams with auxetic core layer under harmonic excitation based on FSDT

The growing use of light composite materials in different industries such as automotive and aerospace has caused the need for more studies to analyze their behavior. In this study, an analytical solution for the nonlinear forced vibrational behavior of a multilayered superlight composite beam with a honeycomb core layer and adjustable Poisson’s ratio subjected to a harmonic excitation has been presented. The beam has two isotropic upper and lower layers with one honeycomb core layer. The Poisson’s ratio of the honeycomb core layer can be adjusted by changing the honeycomb cell parameters in a range of negative to positive values. The equations of motion have been extracted using the first-order shear deformation theory and nonlinear von Kármán relations. The equations are a system of coupled nonlinear partial differential equations that have been solved using the perturbation technique. To investigate the effect of different geometry and honeycomb cell parameters on the nonlinear response, a parametric study has been conducted. The effect of nonlinearity on the chaotic behavior and primary resonance is studied. The finite element method has been used to compare the results. It is observed that by adding a honeycomb layer, the total weight has been dropped by about 50% while the dynamic responses nearly remain the same.

Solving the Stress Singularity Problem in Boundary-Value Problems of the Mechanics of Adhesive Joints and Layered Structures by Introducing a Contact Layer Model. Part 1. Resolving Equations for Multilayered Beams

Solving the Stress Singularity Problem in Boundary-Value Problems of the Mechanics of Adhesive Joints and Layered Structures by Introducing a Contact Layer Model. Part 1. Resolving Equations for Multilayered Beams

Thermal buckling and postbuckling of functionally graded multilayer GPL-reinforced composite beams on nonlinear elastic foundations

Under the influence of axial forces and uniform temperature variations, the thermal buckling and postbuckling of composite beams reinforced of functionally graded multilayer graphene platelets (GPLs) resting on nonlinear elastic foundations are examined. The Halpin-Tsai model is used to calculate the elastic modulus of each layer of GPL-reinforced composite (GPLRC). According to the virtual work principle, the nonlinear governing equations for the beam are obtained from the first-order shear deformation beam theory. The impact of axial force and nonlinear elastic foundation on thermal buckling and postbuckling is discussed using the differential quadrature method (DQM), and the analytical expression is given by the two-step perturbation method (TSPM). The effects of axial force, boundary conditions, slenderness ratio, GPL geometry, GPL weight fraction, GPL distribution pattern, and elastic foundation coefficient on thermal buckling and postbuckling are examined through parameter analysis.

Hysteretic behavior of multi-layered beams with Coulomb friction interface law

Hysteretic behavior of multi-layered beams with Coulomb friction interface law

Multi-Layer Beam Scanning Leaky Wave Antenna for Remote Vital Signs Detection at 60 GHz.

A multi-layer beam-scanning leaky wave antenna (LWA) for remote vital sign monitoring (RVSM) at 60 GHz using a single-tone continuous-wave (CW) Doppler radar has been developed in a typical dynamic environment. The antenna's components are: a partially reflecting surface (PRS), high-impedance surfaces (HISs), and a plain dielectric slab. A dipole antenna works as a source together with these elements to produce a gain of 24 dBi, a frequency beam scanning range of 30°, and precise remote vital sign monitoring (RVSM) up to 4 m across the operating frequency range (58-66 GHz). The antenna requirements for the DR are summarised in a typical dynamic scenario where a patient is to have continuous monitoring remotely, while sleeping. During the continuous health monitoring process, the patient has the freedom to move up to one meter away from the fixed sensor position.The proposed multi-layer LWA system was placed at a distance of 2 m and 4 m from the test subject to confirm the suitability of the developed antenna for dynamic RVSM applications. A proper setting of the operating frequency range (58 to 66 GHz) enabled the detection of both heart beats and respiration rates of the subject within a 30° angular range.