Dynamic Response Of Sandwich Beam Research Articles

Dynamic response of sandwich beam with porous core excited by two harmonic loads travelling in opposite directions

This paper presents the time history response of a sandwich beam with a porous core subjected to two moving harmonic loads with opposite directions. In the modelling, the beam is combined of two isotropic face sheets and a porous core with symmetric porosity distribution. The quasi-3D shear deformation beam theory in conjunction with Hamilton's variational principle is utilized to set up the governing equations of motion. The Navier solution is used to obtain the displacement field. The accuracy of the study is validated by comparing with existing results in the literature for specific cases. Effects of the velocity and excitation frequency of the moving loads on the deflection-time history are investigated and discussed. Numerical results reveal that in the case of the double-moving harmonic loads in the antiphase, the resonance phenomenon cannot occur when the excitation frequency approaches the natural frequency of the beam.

Dynamic Response of Sandwich Beam with Flexible Porous Core Under Moving Mass

Dynamic Response of Sandwich Beam with Flexible Porous Core Under Moving Mass

Analysis of low-velocity impact on FG-CNT reinforced cantilever sandwich beams: An FOSNDT approach

This study analyzes the low-velocity impact response of cantilever sandwich beams with foam cores and carbon nanotube (CNT) reinforced facesheets. Using the fifth-order shear and normal deformation theory, we explore three CNT distribution types through the thickness of the facesheets: uniformly distributed UD, functionally graded-V FG-V, and functionally graded-Λ FG-Λ. The contact force during impact is calculated according to Hertz contact law. Our findings indicate that the FG-V distribution offers the highest contact stiffness, resulting in reduced deflection compared to UD and FG-Λ distributions. Additionally, an increase in the core-to-face thickness ratio leads to decreased deflection and increased contact force, attributed to enhanced beam stiffness. The volumetric fraction of CNTs also plays a critical role, increased CNT content raises beam stiffness, decreasing deflection and enhancing contact force. Furthermore, the impactor’s initial velocity directly influences the deflection and contact force, with higher velocities leading to greater deflections due to increased kinetic energy. This comprehensive analysis underscores the significant effects of CNT distribution, volumetric fraction, and geometrical parameters on the dynamic response of sandwich beams under impact conditions.

Dynamic response of foam-filled X-type sandwich beam under low-velocity impact

The dynamic response of a fully clamped foam-filled X-type sandwich beam under low-velocity impact is studied analytically and numerically. The analytical model is developed for the dynamic response of the sandwich beam with foam-filled X-type core under low-velocity impact based on the yield criterion. The numerical calculations are carried out, and analytical results are in good agreement with numerical ones. The effects of face-sheet thickness, X-type folding plate thickness and foam strength on the impact resistance of the foam-filled X-type sandwich beam are discussed. It is shown that face-sheet thickness, X-type folding plate thickness, and foam strength have noticeable effects on the low-velocity impact response of the foam-filled X-type sandwich beam. The present analytical model can be used to predict the low-velocity impact of the foam-filled X-type sandwich beam.

Mantari’s Higher-Order Shear Deformation Theory of Sandwich Beam with CNTRC Face Layers with Porous Core Under Thermal Loading

In the dynamic study of sandwich structures, the analysis of forced vibrations of these structures is particularly important. Also, no exact solution can be found from the forced vibrations of sandwich beams, and mainly by numerical methods, the dynamic response of sandwich beams has been obtained. Also, there is no coupling solution for this type of structure with an exact solution. Therefore, the present work aims to present a method by which an accurate solution to the dynamic response of sandwich beams can be obtained to eliminate the computational error in numerical methods. Hence, the model is a five-layer sandwich beam with a constant moving load. Carbon nanotubes (CNTs) are used as functionally graded (FG) distributions as reinforcements for the core. Mantari’s higher-order shear deformation theory is also used for displacement fields. The governing equations were derived using the Hamilton principle. The Laplace method is used to obtain the exact solution of the dynamic response of the sandwich beam in both longitudinal and transverse directions. For validation, the natural frequency is compared with previous research. In the following, parameters such as voltage, thickness ratio, the volume fraction of CNTs, and velocity of moving load on the dynamic response of piezoelectric sandwich beams in transverse and axial displacement are investigated.

Static and dynamic response of sandwich beams with lattice and pantographic cores

Mechanical performance of 3d-printed polyamide sandwich beams with different type of the lattice cores is investigated. Four variants of the beams are considered, which differ in the type of connections between the elements in the lattice structure of the core. We consider the pantographic-type lattices formed by the two families of inclined beams placed with small offset and connected by stiff joints (variant 1), by hinges (variant 2) and made without joints (variant 3). The fourth type of the core has the standard plane geometry formed by the intersected beams lying in the same plane (variant 4). Experimental tests were performed for the localized indentation loading according to the three-point bending scheme with small span-to-thickness ratio. From the experiments we found that the plane geometry of variant 4 has the highest rigidity and the highest load bearing capacity in the static tests. However, other three variants of the pantographic-type cores (1–3) demonstrate the better performance under the impact loading. The impact strength of such structures are in 3.5–5 times higher than those one of variant 4 with almost the same mass per unit length. This result is validated by using numerical simulations and explained by the decrease of the stress concentration and the stress state triaxiality and also by the delocalization effects that arise in the pantographic-type cores.

Nonlinear transient response of elastoplastic sandwich beam

This paper aims to propose a new theory on the elastoplastic transient response of sandwich beams under large displacement with moderate rotation, including an analysis strategy for multi-dimensional elastoplasticity and the corresponding numerical solving technique. The material behaviors follow the bilinear proportional hardening rule. According to the classifications of stress statuses, the updated structural stiffness of the sandwich beam in time history is acquired and a systematic procedure for the multi-dimensional elastoplastic dynamic analysis is subsequently developed. The dynamic governing equations involving geometric and material nonlinearities are solved by a modified Ritz-based approach, in association with the Newmark-beta technique. The closed linear solution and the finite element simulation validate the accuracy of the proposed nonlinear theory. Case study reveals that the strain hardening has significant effects on the dynamic response of sandwich beams. The application to the blast-resisting study of sandwich beams as sacrificial coatings on ship hulls further proves the effectiveness of the current theory.

Dynamic response of sandwich beam with star-shaped reentrant honeycomb core subjected to local impulsive loading

The star-shaped reentrant honeycomb produces lateral shrinkage but also rotation under compression. With the consideration of such interesting deformation characteristics, the dynamic deformation evolution of the sandwich beam with star-shaped reentrant honeycomb core (SSRHC) was carried out for the first time. In this experiment, the aluminum foam projectile was used to produce local impulsive loading on the sandwich beam to research failure/deformation modes and deformation evolution of the SSRHC. The experimental results demonstrated the simultaneous shrinking and rotating deformations in the core. Finite element model (FEM) was employed to capture the dynamic mechanical response of panels and SSRHC on account of experimental results. Numerical results illustrated that the face panel moved toward the loading area in the early stage of impact, and local shrinkage or expansion was found within different regions of the star honeycomb cores during the entire compression process. In addition, it was found that the rotational deformation of the star honeycomb cells mainly occurred in the local indentation stage of the sandwich beam.

Convergent term of the Galerkin truncation for dynamic response of sandwich beams on nonlinear foundations

Dynamic response of beams on elastic foundations is of great theoretical significance in the field of engineering. Galerkin truncation method is the most commonly used powerful method to study the vibration of these structures. The number of truncation terms affects the convergence of the analysis and determines the accuracy of the dynamic responses. However, there is still no basis for how to choose the appropriate number of truncation terms. In this paper, two effective schemes based on the natural frequency of the corresponding linear conservative system are proposed to determine the convergent terms of the Galerkin truncation. Since determining the natural frequencies of the corresponding linear conservative system are much easier, the convergence determination method is convenient for application. Based on the dynamic response of the sandwich beam on nonlinear foundations under a moving load, the feasibility of the two schemes for determining the convergent term is confirmed. Moreover, the effects of system parameters on the two schemes are presented. In short, this paper provides two simple and easy schemes for selecting the Galerkin truncation terms in the research of the dynamic response of elastic structures resting on elastic foundations.

Geometrical Nonlinear Effects in the Dynamic Response of Sandwich Beams

AbstractThe geometrical nonlinear dynamic response of sandwich beams is studied using a dynamic high-order nonlinear model. The model is derived using the variational principle of virtual work and uses the Extended High-Order Sandwich Panel Theory approach with consideration of two interfaces between the three layers. A first-order shear deformation theory is adopted for the face sheets, while the kinematic assumption of high-order small deformations that account for out-of-plane compressibility are considered for the core layer. The nonlinearity of the dynamic model is introduced by considering geometrically nonlinear kinematic relations in the face sheets. The nonlinear kinematic relations and the dynamic modeling aim to evaluate the effects of the two features and their coupling on the response. The nonlinear dynamic response of sandwich beams is studied through two numerical cases and comparison of the nonlinear results with their linear counterparts. The first case looks into the coupling of the global geometrical nonlinear behavior with the dynamic behavior. The second case focuses on the local instability of the face sheets and its interaction with the compressibility of the core in the dynamic response of soft core sandwich beams. The comparison of linear and nonlinear dynamic response in the two cases sheds light on the coupling of the geometrical nonlinear and dynamic behaviors. Among other features, the latter is expressed by nonlinear attractors, higher modes response, nonlinear frequency response, and significant wrinkling response.

Semi-active vibration control of SiC-reinforced Al6082 metal matrix composite sandwich beam with magnetorheological fluid core

Dynamic characterization of silicon carbide particles reinforced Al6082 alloy metal matrix composite sandwich beam with magnetorheological fluid core is experimentally investigated. The study is focused on determining the effect of magnetorheological fluid core on the dynamic behavior of the sandwich structure. The magnetorheological fluid core is enclosed between the top and bottom metal matrix composite beams. The metal matrix composite beams are cast with silicon carbide particles in Al6082 alloy varying from 0 to 20 wt%. The magnetorheological fluid is prepared in-house and contains 30 vol.% carbonyl iron powder and 70 vol.% silicone oil. The free vibration test is conducted to determine the natural frequencies and damping ratio. It is found that the natural frequencies and damping ratio of the sandwich beams increased with an increase in the applied magnetic flux density. The experimental forced dynamic response of sandwich beams is carried out using sine sweep excitation. Vibration amplitude suppression capabilities of the sandwich beams subjected to varying magnetic flux densities are determined. The experimental forced vibration results reveal that metal matrix composite–magnetorheological fluid core sandwich beams have excellent vibration amplitude suppression capabilities.

Nonlinear dynamic response of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core

This paper investigates the nonlinear dynamic response of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with four FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed for the first time. The temperature-dependent material properties of both face sheets and core of the sandwich beam are considered. 3D full scale finite element analyses are conducted to investigate the nonlinear dynamic response, and the variation of effective Poisson’s ratio (EPR) of the sandwich beam in the large deflection region. The numerical simulations are carried out for the sandwich beam with FG-NPR honeycomb core, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a comparator. Present results indicate that, when subjected to transverse dynamic pressure, the induced dynamic bending moment of the sandwich beam with core of positive EPR is much bigger than that of the sandwich beam with NPR core, and the thickness of which will extraordinarily increase. The effects of loading types, functionally graded configurations, temperature changes, boundary conditions, and length-to-thickness ratios on the deflection-time curves and EPR-deflection curves of sandwich beams are discussed in detail.

Analytical model of the dynamic response of clamped metallic sandwich beam subjected to underwater impulsive loading

An analytical model is developed for the dynamic response of clamped metallic sandwich beam subjected to underwater impulsive loading. Considering the coupling interaction of different response stages, the theoretical dynamic response is achieved for the large deflection of metallic sandwich beams with a new yield criterion during the structural deformation stage. The computational and theoretical dynamic response of the sandwich beam are compared with the previous experimental results in terms of the response time, response rate, velocity of the faces, and transverse deflection. The results indicate that the tighter solution of transverse deflection from the new circumscribing and inscribing yield surfaces exhibits a good agreement with the experimental and numerical results, demonstrating that the analytical prediction is more accurate than the previous analytical model. The optimization shows that sandwich beams not always outperform the monolithic beams. The optimal sandwich beam designs are sensitive to the span of the beam and the longitudinal strength of the core.

Low-velocity impact of sandwich beams with fibre-metal laminate face-sheets

Low-velocity impact of fully clamped sandwich beams with fibre-metal laminate face-sheets and metal foam core struck by a heavy mass is investigated. Analytical solutions are developed for the dynamic response of sandwich beams with fibre-metal laminate face-sheets considering the interaction of bending and stretching induced by large deflections. According to the rigid-plastic material approximation with modifications, simple formulae are obtained for the large deflection of sandwich beams with fibre-metal laminate face-sheets. Numerical calculations are carried out, and analytical solutions capture numerical results reasonably. The effects of the composite volume fraction, the ratio of metal layer strength to composite layer strength, and core strength on the structural response are discussed. Using the analytical formulae, optimal design charts are constructed to minimize the mass of sandwich beams. It is demonstrated that the present analytical model can predict the post-yield behaviour of sandwich beams with fibre-metal laminate face-sheets reasonably.

Dynamic blast loading response of sandwich beam with origami-inspired core

Abstract Four kinds of 3D models of origami tubes are developed by employing the Miura origami pattern and then assemble into stacked folded structures which are used as the cores of sandwich beams. The quasi-static mechanical behaviors of stacked folded structures and dynamic responses of sandwich beams were theoretically and numerically investigated. The Possion's ratio, force-displacement, back-facet deflection and energy dissipation were considered. The results indicate that the original folding angle has significant effect on Poisson's ratio. The origami tubes with unique mechanical properties can be used as programmable materials to fit specified engineering demand. The arrangement of layers has little influence on the anti-blast performance of corresponding sandwich beams. Compared with the traditional sandwich beams, the influence of core relative density on deformation modes of sandwich beam with foldable core can be ignored.

Effect of integral viscoelastic core on the nonlinear dynamic behaviour of composite sandwich beams with rectangular cross sections

This paper deals with geometrically nonlinear transient analysis of sandwich beams with viscoelastic cores and laminated composite skins. The formulation is based on the Full Layerwise theory (FLWT) and the Boltzmann's superposition principle and using weakly singular Koltunov-Rzhanitsyn kernel for modelling the viscoelastic core. The nonlinear governing integro-partial differential equations (IPDEs) of the sandwich beams are derived using Hamilton's principle. The Galerkin method in combination with the Newmark-Beta procedure, which is coupled to the Newton-Raphson algorithm, are employed to solve the obtained nonlinear IPDEs. The effects of using integral model and considering the history of strain for viscoelastic core on the dynamic response of sandwich beams are investigated. The results indicate that, employing the integral model with Koltunov-Rzhanitsyn kernel in the constitutive equation affects the amplitude and the frequency of the dynamic response of sandwich beam. For comparison purpose, the finite element analysis is carried out within ANSYS software environment and the user-material subroutine is developed to model the Koltunov-Rzhanitsyn kernel. The results of the used semi-analytical model agree well with those obtained from finite element method (FEM) of analysis. It should be noted that, because of employing a large number of degrees of freedom in the FEM analysis for accurate modelling of the viscoelastic sandwich beams, the FEM analysis is rather computationally inefficient in comparison to the presented method. Moreover, the Koltunov-Rzhanitsyn kernel is capable of modelling the viscoelastic behaviour accurately with lower number of rheological parameters in comparison to the Prony series.

Clamped sandwich beams with thick weak cores from central impact: A theoretical study

A theoretical model is obtained to predict the dynamic response of a clamped sandwich beam with thick weak core impacted centrally by a projectile. The core is weak and thick enough that only part or all of the front face sheet and the core undergo permanent plastic deformations, while the back face sheet undergoes an elastic vibration. The core is taken to be rigid-plastic and the front face sheet is treated as an individual rigid-plastic beam resting on a foundation. The back face sheet is modeled as an Euler–Bernoulli beam. Based on the rigid-perfectly theory and Galerkin method, two types of the sandwich beam response are given, i.e., intermediate strength and low strength core type responses. The critical kinetic energy of the projectile as the back face sheet reaches its elastic limit is studied. The localized indentation and response history of the sandwich beam are presented. It is found that the dynamic response of the sandwich beam is sensitive to the core strength, mass ratio, breadth and impact velocity of the projectile. The finite element (FE) simulation is also carried out to verify the analytical predictions and a good agreement is achieved.

Impact load mitigation in sandwich beams using local resonators

Dynamic response of sandwich beams with resonators embedded in the cores subjected to impact loads is studied. Using finite element models the effectiveness of various local resonator frequencies under a given impact load is compared to the behavior of an equivalent mass beam. It is shown that addition of appropriately chosen local resonators into the sandwich beam is an effective method of improving its flexural bending behavior under impact loads. The effect of a given local resonance frequency under different impact load durations is also studied. It is demonstrated that the choice of appropriate local resonance frequency depends on the impact duration. Further, by performing transverse impact experiments, the finite element models are verified and the advantage of using internal resonators under impact loading conditions is demonstrated.

Dynamic Response of Composite Sandwich Beams With Arbitrary Functionally Graded Cores Subjected to Low-Velocity Impact

Using an improved higher-order sandwich panel theory (IHSAPT), the dynamic response of a sandwich beam with arbitrary cores (foam or functionally graded materials) subjected to single impact at arbitrary impacted face sheet and arbitrary locations is studied. The formulation uses the first-order shear deformation theory for the composite face sheets and a polynomial description of the displacements fields in the core, which is based on the displacement field of the second Frostig's model. The unknowns are the coefficients of these polynomials in addition to the displacements of the various face sheets. It is assumed that the impactor impacted normally and simultaneously over the top or bottom face sheets. The impact force between the impacted face sheet and the impactor is treated as the internal force of the system and in this study, for the first time, in order to simulate the impact phenomena, two models are presented: first, the linearized spring–mass model with two degrees of freedom (simply called TDOF), which can be solved by a new analytical method; second, the modified Hertz's model, which uses the perfect form of contact law (perfect model). An impact problem of sandwich beam is first solved and the results obtained from TDOF and perfect models are validated by comparing them with the analytical and numerical results published in the literature and also together. The agreement between the results is quite good. Then, the effect of various types of FGM function and its power and core to beam thickness ratio on the dynamic behavior of sandwich beam are studied.

Active control of geometrically non-linear transient response of sandwich beams with a flexible core using piezoelectric patches

Active control of geometrically non-linear dynamic response of sandwich beams impacted by blast pulses with integrated piezoelectric sensor/actuator patches is addressed. The analysis is based on a higher-order structural model using the first-order shear deformation theory for the face sheets and piezoelectric patches, and the extended high-order sandwich theory for the flexible core. Geometrical non-linearity is considered in the von Karman sense. Hamilton’s principle is employed to introduce a novel smart sandwich beam element which has eighteen physical nodes with mechanical and electric potential degrees of freedom plus two electric nodes for the electric potentials of the electroded surfaces. The presented smart sandwich beam element is used to develop finite element equations of motion. Constant negative velocity feedback algorithm is adapted in the active control. The solution of non-linear equations is sought by Newmark and the modified Newton–Raphson methods for dynamic analysis. Furthermore, the model behavior in free vibrations is assessed by using a direct iteration technique suitably modified for non-linear eigenvalue problems based on the QZ algorithm. A detailed analysis of the influence of geometrical non-linearity, core flexibility and piezoelectric patch arrangement on the dynamic response, frequency and loss factor of active sandwich beams is carried out.