Lattice Truss Core Research Articles

Energy absorption and low-velocity impact responses of the sandwich panels with lattice truss core

This study investigates the dynamic energy absorption performance of composite sandwich panels with two different configurations of lattice truss core. Two types of core structures were designed and created using polyamide 12 through the selective laser sintering (SLS) additive manufacturing method. These structures, with uniform and graded cell topologies, were created by changing the geometry and layer density of the body-centered cubic (BCC) unit cell. The cores were used to fabricate composite sandwich panels, which were made with E-glass/epoxy face sheets. Then, their ability to absorb energy during low-velocity impact and quasi-static compressive strength was tested using both experimental and numerical methods. It was found that the graded structure absorbed 10, 5, and 3% more energy than the uniform structure for the energy levels of 12.4, 16.5, and 17.9 J, respectively. It was also found that both structures could absorb at least 90% of the impact energy. In terms of strength, the uniform structure was able to tolerate 1.15 times larger impact loads, indicating its higher strength than the graded structure. The uniform structure had 8% more compressive strength.

Nonlinear bending of unsymmetric double-layer lattice truss core sandwich beams

This paper studied the nonlinear bending of unsymmetric double-layer lattice truss core sandwich beams (LTCSBs). Five unsymmetric cases are considered by varying different materials and geometric thicknesses in two layers. To establish a theoretical model for the unsymmetric double-layer LTCSBs, Allen’s model and von Kármán nonlinear theory are employed. The present theoretical model is established by considering the midplane of the mid-sheet as the reference plane. Ritz method is applied to determine the deflection for the nonlinear bending, and verified by the finite element method (FEM). Finally, the effects of the loading direction, unsymmetric factors, and boundary conditions on the nonlinear bending behaviors of LTCSBs are studied. It is found that the nonlinear deflections of unsymmetric LTCSBs may exhibit softening-spring nonlinearity in one direction.

Widening the Band Gaps of Hourglass Lattice Truss Core Sandwich Structures for Broadband Vibration Suppression

Abstract This paper proposes a novel phononic crystal sandwich beam (PCSB) for low-frequency and broadband vibration suppression. The representative volume element (RVE) consists of two hourglass truss unit cells with the same span but different rod radii. After validating the modeling method, a model of the PCSB is established to calculate band structure and transmittance response, and the results show good agreement. It is found that the PCSB can open wider and lower band gaps compared to a traditional sandwich beam (TSB). The band-folding mechanism is applied. The PCSB breaks the spatial symmetry, becomes diatomic, and opens the folding points, finally leading to two band-folding-induced gaps. The experiment is conducted on the PCSB, and the vibration band gap property is confirmed. Subsequently, the impacts of geometric parameters on the PCSB’s band gaps are investigated in detail. Design guidelines for tuning the geometric parameters toward lower frequency and broadband band gap are provided based on the parametric study results. In addition, the higher-order band-folding strategy is proposed. It is shown that a multi-folding PCSB can produce more band gaps. However, through two examples, i.e., second-folding and third-folding PCSBs, it is known that simply increasing the folding order may not be effective and even could deteriorate the vibration attenuation ability. In summary, this work explores a general strategy for designing sandwich beams with low-frequency and broadband vibration suppression ability.

Improved compressive performance of lattice truss core sandwich composites with modified Kagome topologies: An experimental and numerical study

A finite element model (FEM) using a more realistic three-dimensional geometry of lattice truss core was proposed to simulate the flatwise compression test on lattice truss core sandwich composites (LTCSCs). The goal was to reduce the disparity between experimental results and FEM predictions without inclusion of imperfection, as oppose to similar studies. Besides, two modified Kagome topologies were suggested and fabricated by adding vertical composite struts at specific locations. Based on the experimental results, the modified Kagome topologies exhibited superior specific compressive stiffness and strength over the Kagome topology, by about 100%. In addition, facesheet rotation of Kagome topology was found by the FEM, which considerably affect its compressive performance. Facesheet rotation is caused by the arrangement of composite struts of LTCSC. Compressive response of LTCSC was acceptably predicted by the FEM, though there was quite high error for compressive stiffness and strength. Probable sources of discrepancy between experimental and FEM results were discussed.

Designs of lattice truss core sandwich structures with improved compressive strength and stiffness

Lattice truss core sandwich composite (LTCSC) panels can exhibit high compressive performance until failure is caused by compressive fracture of the composite strut. Early failure of the core-facesheet and central nodes, as well as fiber misalignment, can hinder the full potential of an LTCSC. This study aimed at improving the compressive stiffness and strength of LTCSC panels through minimizing the fiber misalignment and fabrication issues, while strengthening the central and core-facesheet nodes. The lost-molding technique was used to fabricate LTCSC panels, which were then subjected to quasi-static flatwise compression testing. Relative positioning of neighboring composite struts, modification of the carbon fiber path, and strengthening of the core-facesheet node significantly improved the compressive performance of the panels. Based on the findings, compressive strength and stiffness of LTCSC panels can be improved about 100% and 300%, respectively, with minimal increase in weight. Fabricated LTCSC panels were found to demonstrate competitive specific compressive properties in comparison with conventional core materials.

Free vibration analysis and multi-objective optimization of lattice sandwich beams

The free vibration dynamic modellings of sandwich beams with periodic lattice truss cores are established by combining the Bernoulli–Euler beam theory and Timoshenko beam theory, and the fundamental frequency and unit cell mass of lattice sandwich beams are optimized based on the non-dominated sorting genetic algorithm-II (NSGA-II). Firstly, the vibration control equation of lattice sandwich beams is derived using Hamilton’s principle. Then, it is compared and verified by modal experiment and finite element numerical simulation. On this basis, the influence of different truss cores on the structure’s natural frequency is further analyzed. Finally, taking the sheet thickness, core thickness, and radius of the truss as the optimization design variables and taking the structural fundamental frequency maximization and mass minimization as the optimization objectives, the Pareto front is obtained by NSGA-II, and the optimization results are verified by theoretical and numerically. The research results show that the theoretical method in this article can well predict the natural frequencies of sandwich beams with different truss cores. The optimized sandwich structure has higher fundamental frequency with lighter weight, which effectively improves the anti-vibration ability.

Softening-spring nonlinearity in large amplitude vibration of unsymmetric double-layer lattice truss core sandwich beams

In recent years, many novel sandwich structures with multilayer or graded lattice truss cores that exhibited superior structural performance have been proposed. However, only limited works have studied the nonlinear behavior of sandwich structures with unsymmetric lattice truss cores. This paper aims to provide an analytical study on the nonlinear vibration of the unsymmetric double-layer lattice truss core sandwich beams (LTCSBs). The double-layer LTCSB is designed to be unsymmetric and possesses varying material property and structural geometry in each layer. In this study, six unsymmetric cases of LTCSB classified as two categories according to the midplane locations are considered. Subsequently, an analytical model for the unsymmetric double-layer LTCSB is developed based on the Allen’s model and von Kármán nonlinear theory. The axial displacement of the midplane of LTCSB is considered in the analytical model, therefore the proposed model is more generalized compared with previous models for the symmetric double-layer LTCSB. The Ritz method with a direct iterative procedure is applied to solve the nonlinear governing equations and determine the nonlinear frequencies for the unsymmetric double-layer LTCSB. Finally, the effects of six unsymmetric cases of LTCSBs on the nonlinear frequency ratio versus amplitude curve under three different types of boundary conditions are discussed detailly. An interesting phenomenon of softening-spring nonlinearity is found for hinged–hinged and clamped–hinged sandwich beams with large bending–extension coupling.

Nonlinear vibration responses of lattice sandwich beams with FGM facesheets based on an improved thermo-mechanical equivalent model

An investigation on the nonlinear vibration behaviors of a lattice sandwich beam with pyramidal truss core and functionally graded material (FGM) facesheets under thermo-mechanical loads is performed with consideration of the temperature-dependency of material properties. In present work, an improved equivalent methodology is proposed to determine the transverse shear modulus of pyramidal core subjected to a non-uniform thermal field across thickness direction and makes lattice truss core transformed to a continuous layer. Finally, the lattice sandwich beam is modeled as a three-layered sandwich structure. The facesheets are made of FGMs with mixture of ceramics and metals in a pow-law form. The outer surfaces of facesheets are ceramic-rich, while the inner surfaces are metal-rich. The nonlinear strain–displacement relations are established based on the von Kármán large deflection and classical beam theory. The Lagrange method are implemented to yield equations governing the free and forced vibration behaviors. With the help of Newton-Raphson iteration technique as well as the Newmark-β method, the nonlinear time-independent responses of the sandwich beam under thermal environment are solved. A comprehensive parameter study is directed to address the effects of non-uniform thermal environment, FMG facesheets, external load, and lattice core on the nonlinear vibrations of the beams.

Effect of high-low temperature on the compressive and shear performances of composite sandwich panels with pyramidal lattice truss cores

Composite sandwich panels with pyramidal lattice truss cores (CSPPLTCs) were manufactured employing waterjet-cutting technology and interlocking assembly. The effect of high-low temperature environments on the out-of-plane compressive and shear performance of the panels was studied using theoretical and experimental methods. In particular, the out-of-plane compressive stiffness, strength of sandwich panels with pyramidal lattice truss cores, their shear stiffness, and strength in high-low temperature environments were predicted using theoretical equations. The study found that in low-temperature environments, the movement of molecular chain segments in the epoxy is hindered, futhermore, the mismatched thermal expansivity of carbon fiber and epoxy resin leads to the improvement of interface bonding performance, thus improving the out-of-plane compressive and shear performance of CSPPLTCs; in high temperature environments, the movement of molecular chain segments in the epoxy gets more active and tends to move freely, so the resin turns into a flexible state with high elasticity from the stiff glass state, which finally causes a deterioration in out-of-plane compressive and shear performance of CSPPLTCs. According to observations, the failure mode depends on temperature environments. Brittle fracture and crushing failure happen in the composite struts at low temperature; plastic microbuckling may happen in the composite struts at high temperature.

Multiscale modeling and design of lattice truss core sandwich metastructures for broadband low-frequency vibration reduction

Lattice truss core sandwich structures are advanced lightweight structures that have broad application prospects in many fields, but the attenuation of low-frequency vibrations in these structures is still challenging. To achieve broadband low-frequency vibration reduction in lattice truss core sandwich structures, we propose a design of multiscale lattice truss core sandwich metastructures which exhibit a coupling effect of local resonance and Bragg scattering mechanisms. For ease of analysis and design of such multiscale metastructures, we develop an efficient semi-analytical multiscale modeling method based on a combination of the dynamic homogenization method and the spectral element method. The multiscale modeling method is verified by comparing it with the conventional finite element method, and it is further employed to design multiscale metastructures. Numerical and experimental results demonstrate that the low-frequency bandgap and vibration reduction band can be greatly broadened via an appropriate multiscale design. Specifically, a typical multiscale finite metastructure, fabricated by embedding only three identical local resonators, achieves a significant vibration reduction within the super-wide low-frequency range of 295–905.4 Hz. The normalized vibration reduction bandwidth is as large as 1.02, which is much broader than that of a conventional equi-scale metastructure designed with the same added resonator mass ratio.

Vibration of a Satellite Structure with Composite Lattice Truss Core Sandwich Panels

Composite materials are widely employed in spacecraft, aiming at increasing mass savings and load bearing capacities. Due to the excellent static and dynamic performance, lattice truss core sandwich structures have become one alternative of satellite structure materials. In addition, the dramatic potentials of multifunctional integration accelerate development of new spacecraft technology. In this investigation, a novel satellite structure concept with composite lattice truss core sandwich panels is proposed. A series of vibration tests and a finite element analysis campaign are conducted to determine the dynamic responses of the satellite structure. The developed finite element models provide a feasible numerical analytical scheme to address the vibration performance and structural integrity inspection. And the current satellite structure prototype demonstrates outstanding prospects of significant mass reduction and rapid assembly process.

An experimental and numerical study on the vibration characteristics of glass fiber composite sandwich panel with lattice cores

This research aims to design, manufacture, and determine the vibration characteristics of a composite sandwich panel with lattice cores. For this purpose, first, a glass fiber sandwich panel with lattice truss core has been fabricated in the laboratory. In this part, the vacuum-assisted resin transfer molding method has been used to achieve laminates without any porosity. Afterward, the modal tests have been performed to obtain the natural frequencies, shape modes, damping ratio, and frequency responses of the sandwich panel. In addition, a finite element analysis has been developed to calculate the natural frequencies, damping ratio, and mode shapes of the composite sandwich panel. Then the experimental data have been compared to numerical simulation, and good agreement has been found.

Failure of carbon fiber composite sandwich cylinders with a lattice core under axial compressive loading

Sandwich cylinders with a low-density pyramid-like truss core made of plain-woven carbon fiber fabrics are manufactured using a sequential hot press method. Then, the structural compressive strengths corresponding to four possible failure modes (Euler buckling, axisymmetric buckling, local buckling and face panel crushing of the sandwich cylinders) are obtained by theoretical analysis. The 3D failure mechanism map is accordingly generated to guide the design and preparation of the cylinder specimens. Thereafter, axial compressive tests are performed on the specimens to investigate the failure mechanisms of these structures and to validate the theoretical predictions. The errors between theoretical and experimental results, including both the axial compressive ultimate loads and failure modes, are acceptable. The developed 3D failure mechanism map provides an intuitive guide for the design of sandwich cylinders with a pyramid-like lattice truss core against buckling failure.

Delamination Testing of AlSi10Mg Sandwich Structures with Pyramidal Lattice Truss Core made by Laser Powder Bed Fusion

Sandwich structures possess a high bending stiffness compared to monolithic structures with a similar weight. This makes them very suitable for lightweight applications, where high stiffness to weight ratios are needed. Most common manufacturing methods of sandwich structures involve adhesive bonding of the core material with the sheets. However, adhesive bonding is prone to delamination, a failure mode that is often difficult to detect. This paper presents the results of delamination testing of fully additive manufactured (AM) AlSi10Mg sandwich structures with pyramidal lattice truss core using Laser Powder Bed Fusion (LPBF). The faces and struts are 0.5 mm thick, while the core is 2 mm thick. The inclination of the struts is 45°. To characterise the bonding strength, climbing drum peel tests and out-of-plane tensile tests are performed. Analytical formulas are derived to predict the expected failure loads and modes. The analytics and tests are supported by finite element (FE) calculations. From the analytic approach, design guidelines to avoid delamination in AM sandwich structures are derived. The study presents a critical face sheet thickness to strut diameter ratio for which the structure can delaminate. This ratio is mainly influenced by the inclination of the struts. The peel tests resulted in face yielding, which can also be inferred from the analytics and numerics. The out-of-plane tensile tests didn’t damage the structure.

Optimization and Mechanical Properties of Fabricated 2D Wood Pyramid Lattice Sandwich Structure

In order to obtain a lightweight, high strength, and large design space wooden sandwich structure to meet the needs of modern wooden buildings, the mechanical properties of a fabricated 2D wooden pyramid lattice sandwich structure were studied. In this paper, the mechanical and compressive properties of the specimens with different arrangement of Lattice Sandwich unit cells are studied. The upper and lower panels and core materials are made into a single unit cell by inserting glue, and the prefabricated 2D wooden pyramid lattice truss core sandwich structure is prepared by the mortise tenon splicing method. The results show that the arrangement of the unit cells in the specimen has a significant effect on the bearing capacity, energy absorption, and failure mode of the specimen, and the flat compression performance of the panel-reinforced specimen is better than that of the specimen with unreinforced veneer. The results of finite element analysis are consistent with the test results. The main failure modes are core fracture and panel cracking. These results provide a theoretical basis for the system design of wood-based lattice sandwich structure in the future.

Theoretical and Experimental Study of the Vibration Dynamics of a 3D-Printed Sandwich Beam With an Hourglass Lattice Truss Core

3D printing (also known as additive manufacturing) has been developed for more than 30 years. The applications of 3D printing have been increasingly extended to a variety of engineering fields in recent years. The sandwich material with a high strength and overall low density is a kind of artificial material that has been extensively used in various industrial and daily life applications. This paper presents a comprehensive vibration analysis and passive control technique for a cantilevered sandwich beam with an hourglass lattice truss core fabricated with 3D printing technology. The governing equation of the beam is established by using a homogenized model and the Hamilton's principle, from which the natural frequencies are determined. The theoretical model is verified by the results from the existing literature and the finite element analysis. The frequency response of the sandwich beam measured experimentally further validates the proposed model. Subsequently, a non-linear energy sink (NES) is proposed for being employed to passively suppress the vibration of the sandwich beam. A parametric study based on the theoretical model confirms the viability of using NES to effectively control the vibration of the sandwich beam. This work presents a good demonstration of using 3D printing technology for fabricating sandwich beams with a complicated lattice core. More importantly, some guidelines regarding the dynamic analysis of sandwich beams are provided. In addition, the analytical method presented in this work provides a potential means to theoretically explore the advantages of using sandwich beams for energy harvesting in the future.

Low-frequency flexural wave attenuation in metamaterial sandwich beam with hourglass lattice truss core

Though lightweight sandwich structures have been extensively applied in practical engineering, it remains a challenge to control wave propagation and vibration in these structures in a low-frequency range. In this work, the band structure of flexural waves in a metamaterial sandwich beam (MSB) with hourglass lattice truss core is investigated using the transfer matrix method (TMM). The hourglass truss structure with lumped masses is modelled as a series of local resonators with determined equivalent stiffnesses and masses. A metamaterial dual-beam (MDB) model is then established to describe the MSB, and the MDB model is noted to be equivalent to the conventional metamaterial beam (CMB) model under base excitation. The MSB is further studied directly by the finite element method that confirmed the MSB can be represented by the CMB through the transmittance analysis and band structure analysis. Subsequently, parametric study is performed to investigate the effects of the material and structural parameters on the band structures of the MSB. This work provides a roadmap of modelling of lightweight lattice sandwich beams with complex core structures and presents guidelines for applying sandwich beams to control wave propagation.

Effect of elevated temperature on the out-of-plane compressive properties of nickel based pyramidal lattice truss structures with hollow trusses

In this study, the effect of elevated temperatures on the out-of-plane properties of nickel based pyramidal lattice truss structures with hollow trusses were investigated through theoretical analysis, experimental measurements and numerical prediction. It is found that, with the increase of temperature from 25 °C to 450 °C, the compressive strength, compressive modulus and energy absorption capacity of the sandwich structures fabricated via SLM additive manufacturing decrease by 37.98%, 33.25% and 38.36%, respectively. The theoretically predicted failure modes and compressive strength of the hollow lattice truss cores are in well agreement with experimental measurements and numerical predictions. Comparison with competing lightweight sandwich constructions reveals that the nickel based pyramidal lattice truss structure with hollow truss exhibits superiority in the specific strength under high temperature.

Characteristics of an improved boundary insert for sandwich panels with lattice truss cores

Composite sandwich panels with lattice truss cores have dramatic static and dynamic characteristics, which are widely used in aerospace industry. Owing to the inability to sustain localized loads of joining, valid inserts are required to enable the interconnection of the sandwich panels. The present study develops a novel boundary insert parallel to the facesheets for pyramidal lattice truss core sandwich panels. Analytical-mechanical models are addressed for the proposed boundary insert subjected to in-plane pull-out, in-plane shear as well as out-of-plane shear loads and experimental tests are carried out to characterize mechanical behaviors. Failure sequences and mechanisms are discussed comprehensively and good correspondence is obtained with analytical prediction. Finite element simulation models are developed for visualization of internal load distribution. Experimental results show that significant improvements in load capacities can be achieved by the developed boundary insert compared with the interconnection concepts for honeycomb sandwich panels.

Concurrent Identification of Impact Location and Force Magnitude on a Composite Panel

Simultaneous estimation of both the location and force history of an impact applied on a lattice truss core sandwich panel is inversely carried out utilizing velocity signals collected by means of a scanning laser Doppler vibrometer. The algorithm assumes that several impact forces are exerted concurrently on a number of specified locations on a panel, provided that the magnitude of all impact forces but one is actually equal to zero. This condition equates to a scenario where an impact occurs at only one location. The purpose is therefore to detect the actual impact location among all potential locations, together with its force history, through minimizing error functions. Two algorithms, the one-to-one (even-determined) approach and the superposition approach, are considered. The one-to-one approach solves the reconstruction problem independently for each pair of impact and measurement points. However, in the superposition approach, the impact forces at all potential locations are concurrently reconstructed through a single matrix equation. It is shown that the one-to-one approach fails to detect the true impact location while the superposition approach recognizes the actual impact location based on some qualitative evaluating criteria. Adopting the superposition approach, for a problem with four possible impact locations, two scenarios one with four and one with 12 measurement points, are investigated. It is observed that the additional measurement points do not necessarily enhance the efficiency and accuracy of the proposed method. It is found that different arrangements of measuring points lead to identification of the location and the magnitude of the impact force, though the use of four evenly distributed measurement points seems to be most effective in simultaneous identification of the location and magnitude of the impact force. Further, a quantitative index based on the concept of similarity search for time-series using wavelet transformation is proposed and it is demonstrated that the index can successfully identify the true impact force location in a fully automated way.