Truss Core Sandwich Plate Research Articles

Free vibration analysis and multi-objective robust optimization of three-dimensional pyramidal truss core sandwich plates with interval uncertain parameters

In this study, the free vibration analysis and multi-objective robust optimization of three-dimensional pyramidal truss core sandwich plates with interval uncertain parameters are fulfilled. The numerical model for free vibration of the plate is derived by combining the three-dimensional elasticity theory and Rayleigh-Ritz method, and the validity of the model is illustrated by numerical results. On this basis, considering various uncertainties within the plate, a new uncertainty-propagation analysis method is constructed by integrating the numerical model, interval-analysis model, kriging model and optimization. The one-dimensional and multi-source uncertainty-propagation analysis of the fundamental frequency is finished using this method, and the accuracy is proved by comparing with Monte Carlo simulation results. Meanwhile, to minimize the effects of uncertainties on the performance of plates at the design stage, an objective multi-objective robust optimization model with the objectives of maximizing the fundamental frequency and minimizing the robustness factor is established. Finally, an improved pelican optimization algorithm is proposed by introducing the improved opposition-based learning strategy, tracking strategy with step control and convergence strategy. And the Pareto front and corresponding design schemes applicable to different working environments are obtained without repeating the optimization.

Broadband low-frequency sound insulation of double-panel metastructures with a perforated lattice truss-core sandwich plate

Lattice truss-core sandwich plates have drawn increasing attention owing to their excellent mechanical properties and multifunctional characteristics, but they are insufficient in low-frequency sound insulation because of their lightweight feature. To improve the sound transmission loss (STL) of such lightweight sandwich plates while without greatly increasing the structural complexity and the total mass, one faceplate of the sandwich plate is perforated so that the sandwich core can be utilized as an acoustic cavity. A homogenous plate is further introduced to construct a double-panel metastructure together with the perforated sandwich plate. For ease of analysis and design of the double-panel metastructure, a semi-analytical method is developed by combining an effective medium theory of the acoustic domain and a dynamic homogenization method of the sandwich plate. The feasibility of the developed method for efficient STL prediction under different incident angles is verified by comparing with the conventional finite element method. Numerical results show that the double-panel metastructure exhibits a remarkable sound insulation performance within a broadband low-frequency range, owing to the fact that the acoustic domain enclosed by the double-panel metastructure has an unusual equivalent bulk modulus. Then, a parametric study is conducted to reveal the sound insulation capacity and provide a guideline for tuning the STL of the double-panel metastructure. Finally, the actual sound insulation capacity of the double-panel metastructure is validated by experimental measurements of large-scale specimens.

Shock-Induced Vibration of Composite Truss Core Sandwich Plates with Distributed Nonlinear Absorbers by Optimal Locations

In order to solve the problems of limited installation space and strict additional quality, the effects of internal distributed nonlinear energy sinks (NES) considering optimal locations on a composite truss core sandwich plate are investigated in this paper. Choose five NESs here and inset them in the different places of the sandwich plate to suppress the vibration of the plate, which is excited by a half-wave shock. The coupled dynamic equations of the system are derived by the principle of conservation of energy. Then, the vibration-control performances of five NESs are discussed by numerical simulation. The distributions of the five NESs are analyzed, and the optimal position distributions are obtained. Based on the optimal location, the transient responses of the system are studied. Moreover, the performances of five NESs and a single NES are compared in different dimensions. Finally, it is found that the selection of parameters has a great impact on the effectiveness of the five NESs. The new distribution way is introduced to improve the suppression effects of the five NESs in the sandwich plate.

Dynamic stability of different kinds of sandwich plates using third order shear deformation theory

In this paper dynamic buckling of different kinds of sandwich plates under harmonic axial load is analyzed by using combination of numerical finite strip analysis and Bolotin’s solution which offer a kind of method to find the regions of dynamic instability for dynamic stability of plates. The sandwich plates which are considered here consist of homogeneous core sandwich plates, functionally graded sandwich plates, trapezoidal corrugated core sandwich plates, Z and C form corrugated core sandwich plates and truss core sandwich plates. Third order shear deformation theory is used as numerical method to study stability regions of sandwich plates. The effect of damping is neglected and the effect of length to thickness ratio, different boundary conditions, number of face sheet layers and different geometry and material properties of core is studied. According to the results the dynamic buckling should also be investigated in sandwich plate. Also, according to the results, it is observed that the finite strip method has an acceptable accuracy in investigating the dynamic buckling of sandwich plates.

Theoretical analysis on the thermal buckling behavior of material-filled truss-core sandwich plates with various boundary conditions

This article presents a theoretical analysis of the thermal buckling behavior of material-filled truss-core sandwich panels, which have load-bearing capacities and multiple functions. The homogeneous stiffness matrix of the filled truss core is solved by the energy equilibrium method. The governing equations are derived based on Hamilton’s principle. The eigenvalue method is used to solve the governing equations, and the buckling matrix is determined. By simplifying this buckling matrix, buckling formula has been derived. A three-dimensional finite element model is developed to validate the theoretical results. Finally, the effects of geometrical parameters, material properties and boundary conditions on the thermal buckling temperature of material-filled sandwich panels are analyzed.

Slow-fast dynamics in the truss core sandwich plate under excitations with high and low frequencies

In this manuscript, slow-fast motions in a two degrees of freedom model under slow parametric and fast external excitations are analyzed using analytical and numerical methods. By expressing the state variables as the sums of slowly varying average and fast oscillations, the averaged equations which govern the slow dynamics for different magnitudes of external amplitude are obtained. For the averaged equations, analyzation about the equilibria and the corresponding stability shows that, the averaged slow manifolds constitute a pitchfork structure. Meanwhile, the harmonic balancing method is used to compute the slowly varying envelopes of the fast oscillations. On the other hand, bifurcation diagrams of the fast sub-system show structures in accordance with the pitchfork obtained from averaged equations as well as the amplitude curves computed by harmonic balancing method. Two forms of relative location between the folds of cycle on the handle and pitchfork bifurcation point are presented. Based on these, concerning on the slow-fast flow, two patterns of transition behavior between the handle and the upper (lower) branch of pitchfork namely “pitchfork/pitchfork” and “fold/pitchfork” types are analyzed, which indicate the dynamic buckling behaviors. Particularly, discussion about the influence of external excitation shows that, for case of near-resonant external frequency, increasing the amplitude of external excitation will change the local structures as well as the quantitative properties of the pitchfork, but holistic form of pitchfork type is a topological invariant.

Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate

This paper presents the study on the chaotic wave and chaotic dynamics of the nonlinear wave equations for a simply supported truss core sandwich plate combined with the transverse and in-plane excitations. Based on the governing equation of motion for the simply supported sandwich plate with truss core, the reductive perturbation method is used to simplify the partial differential equation. According to the exact solution of the unperturbed equation, two different kinds of the topological structures are derived, which one structure is the resonant torus and another structure is the heteroclinic orbit. The characteristic of the singular points in the neighborhood of the resonant torus for the nonlinear wave equation is investigated. It is found that there exists the homoclinic orbit on the unperturbed slow manifold. The saddle-focus type of the singular point appears when the homoclinic orbit is broken under the perturbation. Additionally, the saddle-focus type of the singular point occurs when the resonant torus on the fast manifold is broken under the perturbation. It is known that the dynamic characteristics are well consistent on the fast and slow manifolds under the condition of the perturbation. The Melnikov method, which is called the first measure, is applied to study the persistence of the heteroclinic orbit in the perturbed equation. The geometric analysis, which is named the second measure, is used to guarantee that the heteroclinic orbit on the fast manifold comes back to the stable manifold of the saddle on the slow manifold under the perturbation. The theoretical analysis suggests that there is the chaos for the Smale horseshoe sense in the truss core sandwich plate. Numerical simulations are performed to further verify the existence of the chaotic wave and chaotic motions in the nonlinear wave equation. The damping coefficient is considered as the controlling parameter to study the effect on the propagation property of the nonlinear wave in the sandwich plate with truss core. The numerical results confirm the validity of the theoretical study.

Vibration reduction in truss core sandwich plate with internal nonlinear energy sink

The effects of an internal nonlinear energy sink (NES) on a truss core sandwich plate in dynamics are investigated. The energy dissipation of the NES is studied with the sandwich plate excited by a half-wave shock. It is found that exceptional vibration absorption is achieved by the NES. Moreover, the relative motion between the sandwich plate and the NES remains in the acceptable range of the hollow truss core until the shock amplitude becomes too large. The slow flow equation and the frequency response of the system are obtained by employing the complexification-averaging method. Although the NES exhibits excellent performance when the sandwich plate is under an excitation with a relatively small amplitude, the efficiency is gradually diminished with the emergence of a stable higher branch and the merging of higher and lower branches. During the entire process, the NES does not collide with the face sheet of the sandwich plate. Further, the variation of vibration absorption performance of the NES with the increase of strut radius is investigated. It is demonstrated that the variation of the strut radius has a greater influence on the vibration absorption with a harmonic load in comparison to absorption with a shock load.

Nonlinear dynamic analysis and hypernormal form of truss core sandwich plates.

Truss core material, which is a new type of ultra-light material with comprehensive properties, is used in the aerospace industry. The aim of this paper is to investigate the dynamic behavior of three-dimensional Kagome sandwich plates with truss core under transverse and in-plane excitation in the case of 1:1 internal resonance. Firstly, the averaged equation is obtained by means of the method of multiple scales. Then, the nonlinear system is analyzed applying the theory of normal form. Eventually, we analyze the dynamic behavior, mainly periodic motions, for the truss core sandwich panels by using numerical simulation. Numerical results are presented here for the nonlinear dynamic behavior of the model of truss core sandwich plates, which provides theoretical guidance to vibration control. Considerable insight has been gained concerning the sign of parameter of the model controlled by material property.

Active Vibration Control of Composite Pyramidal Lattice Truss Core Sandwich Plates

AbstractThe vibration characteristics of composite pyramidal truss core sandwich plates with piezoelectric actuator/sensor pairs were investigated, and the active vibration control methods of the s...

Free vibration analysis of composite sandwich plates with different truss cores

ABSTRACTThe free vibration of composite truss core sandwich plates is investigated. The natural frequencies of the sandwich plate are calculated by using the classic laminated plate theory, the first-order shear deformation theory, Reddy's third-order shear deformation theory, and a Zig-Zag theory. The differences between the natural frequencies, obtained from the four theories, are compared. The influences of structural parameters on the natural frequencies and the ratios of natural frequency to equivalent density of the sandwich plates with pyramidal core, tetrahedral core, and 3D-Kagome core are studied with the aid of the Zig-Zag theory.

Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

The Shilnikov‐type single‐pulse homoclinic orbits and chaotic dynamics of a simply supported truss core sandwich plate subjected to the transverse and the in‐plane excitations are investigated in detail. The resonant case considered here is principal parametric resonance and 1:2 internal resonance. Based on the normal form theory, the desired form for the global perturbation method is obtained. By using the global perturbation method developed by Kovacic and Wiggins, explicit sufficient conditions for the existence of a Shilnikov‐type homoclinic orbit are obtained, which implies that chaotic motions may occur for this class of truss core sandwich plate in the sense of Smale horseshoes. Numerical results obtained by using the fourth‐order Runge–Kutta method agree with theoretical analysis at least qualitatively. Copyright © 2017 John Wiley & Sons, Ltd.

Parametric study on nonlinear vibration of composite truss core sandwich plate with internal resonance

Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy’s third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude.

Dynamic properties of truss core sandwich plate with tetrahedral core

The dynamic properties of a simply supported at four edges truss core sandwich plate with tetrahedral core are investigated in this paper. The nonlinear governing equation of motion for the truss core sandwich plate is derived by using the Hamilton’s principle, the von Karman type equation for the geometric nonlinearity and a Zig-Zag theory. The partial differential equation is reduced to a single degree of freedom ordinary differential equation by applying the Galerkin’s approach. The two-dimensional averaged equation is derived by using the method of multiple scales and the frequency response equation is obtained. The influences of the core height, the strut radius and the inclination angle of the truss core on the first-order linear natural frequency and the nonlinear frequency response of the sandwich plate are studied. The changing rules and its mechanisms of the natural frequency and the hardening behavior of the sandwich plate with different structural parameters are presented.

Thermal buckling analysis of truss-core sandwich plates

Thermal buckling analysis of truss-core sandwich plates

Nonlinear dynamic responses of a truss core sandwich plate

Nonlinear dynamic behaviors of a simply supported 3D-Kagome truss core sandwich plate subjected to the transverse and the in-plane excitations are investigated in this paper. The truss core sandwich plate is equivalent to a laminated plate with three laminas according to the equivalent sandwich plate method. The governing equation of motion for the truss core sandwich plate is derived by using the von Karman type equation for the geometric nonlinearity and the Reddy’s third-order shear deformation plate theory. The nonlinear governing partial differential equation is reduced to the ordinary differential equation by applying the Galerkin’s approach. The four-dimensional averaged equation is obtained by using the method of multiple scales. The frequency–response curves are obtained under consideration of strongly coupled of two modes. The results indicate that there are the hardening and softening nonlinearities in the truss core sandwich plate under the specific resonant case. The influences of the amplitudes for the in-plane and transverse excitations on the frequency–response curves are investigated. The results of numerical simulations for the two-degree-of-freedom nonlinear equation exhibit the existence of the period, multi-period and chaotic responses with the variation of the excitations, which demonstrate that those motions appear alternately.

Thermal buckling analysis of truss-core sandwich plates

Truss-core sandwich plates have received much attention in virtue of the high values of strength-to-weight and stiffness-to-weight as well as the great ability of impulse-resistance recently. It is necessary to study the stability of sandwich panels under the influence of the thermal load. However, the sandwich plates are such complex three-dimensional (3D) systems that direct analytical solutions do not exist, and the finite element method (FEM) cannot represent the relationship between structural parameters and mechanical properties well. In this paper, an equivalent homogeneous continuous plate is idealized by obtaining the effective bending and transverse shear stiffness based on the characteristics of periodically distributed unit cells. The first order shear deformation theory for plates is used to derive the stability equation. The buckling temperature of a simply supported sandwich plate is given and verified by the FEM. The effect of related parameters on mechanical properties is investigated. The geometric parameters of the unit cell are optimized to attain the maximum buckling temperature. It is shown that the optimized sandwich plate can improve the resistance to thermal buckling significantly.

Equivalent Elastic Constants of Truss Core Sandwich Plates

A plate structure of a triangular truss core sandwiched by two panels is treated as an equivalent homogeneous laminated plate by obtaining equivalent anisotropic elastic constants. The equivalent elastic constants are obtained by considering generalized Hook’s law of a three dimensional elastic body with no a priori assumption and the equilibrium of a segment deformed by bending moments. To verify the accuracy of the equivalent elastic constants, a linear static analysis of sandwiched aluminum plates subjected to lateral pressure is carried out. The results of the finite element analysis applied to the equivalent laminated plates are compared with those of a NASTRAN analysis of the original structural layouts. The results are also compared with a closed-form solution, which simplifies the sandwiched plate as a homogeneous orthotropic thick plate continuum (Lok and Cheng, 2000, “Elastic Stiffness Properties and Behavior of Truss-Core Sandwich Panel,” J. Struct. Eng., 126(5), pp. 552–559). As the maximum deflections of three analyses agreed closely, one has assurance that the method of the homogeneous plate with equivalent elastic constants is valid and useful.

Analysis of Sandwich Plates of Arbitrary Shape

A linear, static bending analysis of truss-core sandwich plates for arbitrary shape and boundary conditions is presented. The three-dimensional truss-core sandwich plate is idealized as an equivalent two-dimensional structurally orthotropic thick plate continuum. This analysis is based on the small deflection, first-order shear deformation theory of composite plates, which utilizes the Reissner–Mindlin plate theory. The behavior of the plate is governed by a system of differential equations expressed in terms of deflection and slopes. The numerical procedure is developed to solve these equations based on the combination of the Ritz and R-function methods. The numerical results obtained demonstrate the efficiency and accuracy of the proposed technique.

Performance of sandwich plates with truss cores

Sandwich plates with truss cores fashioned from straight struts have distinct advantages relative to other constructions, including those with honeycomb cores. In addition to opportunities afforded by their open architecture, the truss core sandwich plates meet or exceed the load carrying capacity of other competitive constructions. The weight of truss core sandwich plates subject to a crushing stress and arbitrary combinations of bending and transverse shear are optimized subject to buckling and plastic yielding constraints and then compared with the weight performance of other types of optimized plates. Several issues central to the optimization process are addressed by a fundamental model study. These include the relation of designs based on a pure moment loading to those based on combined moment and transverse shear and the accuracy needed to model the various modes of buckling that must be taken into account in the design process.