Sandwich Microbeams Research Articles

Nonlocal dynamic response of FGP sandwich microbeam with 2D PSH network incorporating adatoms-surface interactions energy under magnetic field

The present work models and studies the resonance frequency change due to adsorption phenomena in a simply-supported adatom-microbeam system under an axial magnetic environment. The microbeam structure is a functionally graded (FG) sandwich that includes a rectangular configuration and a ceramic perforated core with periodic square holes network and FG porous material faces. To evaluate the adsorption-induced energies produced by van der Waals interaction (vdW), the Morse and Lennard-Jones (6–12) potentials are included in conjunction with nonlocal material elasticity to adopt the small-scale impact. Moreover, the explicit formulas for the inertia moments and shear force are developed by the Timoshenko beam equations, considering the residual stress influence as an additional axial load. The Navier-type solution and the differential quadratic method (DQM) are implemented to compute the solution of the governing equations. It is established that the resonance frequency change for the O/Si (100) and H/Si (100) is dependent on the geometrical, perforation, and porosity parameters, adsorption density, mode number, and the magnetic field intensity as well. Therefore, these numerical results have been discussed in detail to properly examine dynamic vibration behavior and a suitable mass detection design of M/NEMS structures.

Nonlinear size-dependent metamaterial-based tunable sandwich microbeams with enhanced vibration characteristics

Nonlinear size-dependent metamaterial-based tunable sandwich microbeams with enhanced vibration characteristics

Size-dependent transient response of sandwich microbeam with three-phase bidirectional FGM face layers under a moving mass

Size-dependent transient response of sandwich microbeam with three-phase bidirectional FGM face layers under a moving mass

Nonlocal dual-phase-lag thermoelastic damping analysis in functionally graded sandwich microbeam resonators utilizing the modified coupled stress theory

Functionally graded (FG) sandwich structures stand as one of the most representative composite structures owing to the thermal resistance and the energy absorption property in non-unfiorm thermal environment. Additionally, accurately estimating thermoelastic damping (TED) is of great importance for the design of high-performance micro/nano-resonators. Nevertheless, the classical TED models fail on the micro/nano-scale structures due to without considering the influences of the spatial size-dependent effects related to heat transfer and elastic deformation. The nonlocal heat conduction model and modified coupled stress theory are responsible for the size-dependent effects. To address this issue, present study aims to conduct the size-dependent TED model of FG sandwich microbeam resonators for TED analysis by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are formulated, and then, the analytical solution is solved by complex frequency method. Exact and closed-form expressions for TED can be obtained through the complex frequency method. The results are validated, and the parameter effects of the nonlocal thermal parameter, the material length-scale parameter, the power-law index and the vibration modes on the TED are analyzed. The results show that the energy dissipation can be reduced by the size-dependent effects resulting in improving the quality factor of microstructures. It is expected that these results may provide a theoretical basis for predicating TED in the design of FG sandwich micro/nano-resonators with high quality factor in extreme heat transfer environment.

Thermoelastic damping analysis of functionally graded sandwich microbeam resonators incorporating nonlocal and surface effects

Functionally graded (FG) sandwich microstructures/nanostructures stand as one of the most promising composite structures due to the capability to resist thermal shock and high noise in extreme thermal environments. Meanwhile, accurately prediction quality-factor based on thermoelastic damping (TED) is of great significance for the design of high-performance microresonators /nanoresonators. However, the classical TED models fail to explain the size-dependent thermo-mechanical behavior. The nonlocal elasticity and surface elasticity are responsible for the size-dependent phenomenon. In this article, a modified TED model is proposed to estimate the impact of the size-dependent effect on the TED of FG sandwich microbeam resonators in unsteady heat transfer processes by combining the nonlocal elasticity model, surface elasticity model, and dual-phase-lag (DPL) heat conduction model. It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of TED is obtained by the complex frequency method. The influences of the factors including the nonlocal parameter, the surface effect, the power-law index, and the vibration modes on the TED are analyzed. These results provide a reasonable theoretical analysis to predicate TED in the design of FG sandwich microresonators/nanoresonators with high performance.

Dual-phase-lag thermoelastic damping analysis of a functionally graded sandwich micro-beam resonators incorporating double nonlocal effects

Functionally graded sandwich micro/nano-structures have attracted great attention due to the capability to resist high noise and thermal stress in a non-isothermal environment. Additionally, the design of high quality-factor micro/nano-resonators requires accurate estimation of their thermoelastic damping. However, the classical thermoelastic damping models fail at the micro/nano-scale due to the influences of the size-dependent effects related to heat transfer and elastic deformation. This work aims to investigate the influences of the size-dependent effects on the thermoelastic damping of functionally graded sandwich micro-beam resonators by combining the nonlocal dual-phase-lag heat conduction model and the nonlocal elasticity model. It is assumed that the functionally graded sandwich micro-beam resonators consist of a ceramic core and functionally graded surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of thermoelastic damping is obtained by complex frequency method. Numerical results are analyzed for the effects of the thermal nonlocal parameter, the elastic nonlocal parameter, the power-law index, and the vibration modes on the thermoelastic damping of functionally graded sandwich micro-beam resonators. The results show that the thermoelastic damping of functionally graded sandwich micro-beam resonators can be adjusted by the suitably modified parameters, which strongly depends on the double nonlocal effects and the power-law index.

Size-dependent vibration of multi-scale sandwich micro-beams: An experimental study and theoretical analysis

A series of multi-scale sandwich cantilever micro-beams are prepared to investigate the size-dependent phenomenon in this paper. The sandwich micro-beam samples consist of a titanium substrate with a thickness of 1.996μm and two symmetrical nickel coatings with thickness between 106.6 and 362.6 nm by employing a physical vapor deposition method. The vibration responses of these composite micro-beams are excited by an acoustic exciter and measured by a laser Doppler vibration measurement system. It is revealed that with the decreasing of coating thickness, the dimensionless bending rigidity of nickel coating increases, and the dimensionless natural frequency of micro-beam increases first then decreases. Based on the non-classical continuum theories, the theoretical model of the sandwich micro-beam is established. Then the material length scale parameters are derived. The applicability of the non-classical continuum theories is verified when the material characteristic size of the structure is smaller than the material length scale parameter. The results are of great significance to the design and optimization of micro-/nano-electro mechanical systems.

Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects

In this paper, size-dependent vibration and dynamic analysis of an advanced sandwich composite microbeam including piezoelectric layers based on higher-order strain gradient and surface effects theories are investigated. To evaluate and analyze the effect of surface energy, length scale parameters and dynamic response on the transverse vibration and stability of sandwich smart composite microbeam with piezoelectric layers, the partial differential equation of motion is obtained using Hamilton's principle. Subsequently, this equation is transformed into a set of ordinary differential equations according to the generalized differential quadrature method. The influences of various material length scale associated with strain gradient theory, geometry and surface parameters such as thickness to material length scale parameter, surface residual stress, Young's modulus of surface layer, surface mass density and surface piezoelectric constant on structural dynamic deflection behavior and natural frequency have been investigated. In addition, the vibration and dynamic responses of the model were compared with those micro sandwich beams based on modified couple stress and classical theories. The obtained results are compared with the results available in the literature to validate the correctness of the present solution method. The results indicated that strain gradient theory with considering the surface effects increases the model stiffness and shifts the amplitudes to lower magnitude faster in comparison to other theories. Moreover, the influences of material length related to dilatation gradient on vibrational frequency are significant among the other parameters. Also, the free vibrational frequency increases with decreasing the length to thickness ratio.

Buckling analysis of curved sandwich microbeams made of functionally graded materials via the stress-driven nonlocal integral model

Size-dependent buckling analysis for slightly curved sandwich microbeams made of functionally graded (FG) materials is performed via a stress-driven nonlocal model. The Fredholm integral constitutive equations are transformed into the Volterra type of the first kind and then solved analytically using the Laplace transformation and its inversion under different boundary conditions. The exact solutions are validated against those existing results. The effect of the nonlocal parameter, thickness ratio of core-to-skin layers, FG power-law index, and length-height ratio on the buckling loads, as well as on the ratio of the result predicted by two common beam-theories is investigated.

Free vibration analysis of pre/post-buckled rotating functionally graded sandwich micro-beams

This paper deals with free vibrations of pre/post-buckled rotating functionally graded sandwich micro-beams. The thermo-mechanical characteristics of functionally graded material phases are temperature dependent. The governing equations are in the framework of Euler–Bernoulli beam assumptions alongside with the von-Karman strain–displacement relation. The size effect is introduced into the equations of motion by employing the modified couple stress theory. The finite element technique is applied to the nonlinear governing equations to discretize the equations of motion. The Newton–Raphson technique is accompanied by a proposed algorithm to release the fundamental pre/post-buckling natural frequency. The significance of the material length scale parameter, the power law exponent, the rotation speed, the slenderness ratio and the rotor radius on the outcomes is examined.

Free vibration of sandwich micro-beam with porous foam core,GPL layers and piezo-magneto-electric facesheets via NSGT

The aim of this research is to investigate free vibration of a novel five layer Timoshenko microbeam which consists of a transversely flexible porous core made of Al-foam, two graphen platelets (GPL) nanocomposite reinforced layers to enhance the mechanical behavior of the structure as well as two piezo-magneto-electric face sheets layers. This microbeam is subjected to a thermal load and resting on Pasternak\'s foundation. To accomplish the analysis, constitutive equations of each layer are derived by means of nonlocal strain gradient theory (NSGT) to capture size dependent effects. Then, the Hamilton\'s principle is employed to obtain the equations of motion for five layer Timoshenko microbeam. They are subsequently solved analytically by applying Navier\'s method so that discretized governing equations are determined in form of dynamic matrix giving the possibility to gain the natural frequencies of the Timoshenko microbeam. Eventually, after a validation study, the numerical results are presented to study and discuss the influences of various parameters such as nonlocal parameter, strain gradient parameter, aspect ratio, porosity, various volume fraction and distributions of graphene platelets, temperature change and elastic foundation coefficients on natural frequencies of the sandwich microbeam.

Size-dependent behaviour of functionally graded sandwich microbeams based on the modified strain gradient theory

This paper studies the bending, buckling and free vibration analyses of functionally graded (FG) sandwich microbeams using the third-order beam theory. The modified strain gradient theory (MSGT) with three material length scale parameters (MLSPs) is used to capture the size effect. The Mori-Tanaka homogenization scheme is employed to model the material distributions through the thickness. Finite element model is formulated to solve the problems. Verification studies for epoxy and FG microbeams are carried out to validate of the present model. Comparisons of the results of three different models such as MSGT, the modified couple stress theory (MCST) and classical continuum theory (CCT) are presented. Effects of small size, gradient index, shear deformation and boundary conditions on the structural behaviours of microbeams are investigated. Some new results of FG sandwich microbeams for both models (MCST and MSGT) are presented for the first time and can be used as benchmark in future studies.

Free Vibration Response of FG Porous Sandwich Micro-Beam with Flexoelectric Face-Sheets Resting on Modified Silica Aerogel Foundation

The free vibration analysis of sandwich micro-beam (SMB) which is subjected to electrical field is investigated by adopting the Euler–Bernoulli beam theory (EBBT) and modified strain gradient theory (MSGT). SMB is made of three layers, including a functionally graded (FG) porous core and two flexoelectric face-sheets. The porosities are assumed to be distributed over the beam thickness based on the two distribution functions. Also, due to the electric properties of flexoelectric materials, face-sheets of SMB are subjected to the external electric field. The modified Silica Aerogel foundation model is employed to consider the effects of elastic foundation on SMB. The size-dependent governing equations of motion are derived using Hamilton’s principle and solved by Navier’s solution method for a case of simply supported SMB. The effects of various parameters, such as length to thickness ratio, porosity index, flexoelectric loadings (the load applied to the flexoelectric face-sheets caused by external electric field), small scale parameter and foundation parameters on dimensionless frequency of SMB, are assessed. The results of this work can be used for optimum design and control of micro-electro-mechanical devices.

Free vibration and buckling analysis of laminated composites and sandwich microbeams using a transverse shear-normal deformable beam theory

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios.

Exact solution for frequency response of sandwich microbeams with functionally graded cores

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton’s principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the frequency response of clamped and simply supported microbeams. Numerical results show that in the case of clamped microbeams, the essential and natural size-dependent boundary conditions have a significant effect on the resonance frequency and transverse deflection of microbeams. Also, it is seen that an optimal layup (without change in total volume of each material) can significantly improve the frequency characteristics of sandwich microbeams.

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

AbstractIn this study, free vibration of the sandwich microbeam with porous core and FG carbon nanotubes reinforced composite face sheets which is rested on Winkler‐Pasternak substrate is investigated. It is assumed the beam is in thermal environment and is subjected to thermal load and the displacement components are described based on sinusoidal shear deformation beam theory. The small scale effects are taken into account according to the modified couple stress theory. The core and face sheets properties are diffused through the thickness. The motion equations are derived and solved using Hamilton's principle and Navier's method, respectively. Effect of different parameters such as porosity coefficient and distributions, different types of CNTs distribution, small scale and geometrical size of the beam is considered. The results show by enhancing the porosity, the frequency decreased. The findings of the current study can be used to design prominent role in modern engineering applications.

Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory

Within this study, the free vibration behavior of rotating two-directional functionally graded porous sandwich microbeams is studied based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory. The effects of the thickness to material length scale parameter accompanying with the porosity volume fraction coefficient, boundary condition, aspect ratio, hub ratio, dimensionless rotation speed and gradient index on the dimensionless fundamental frequencies of the two-directional functionally graded porous sandwich microbeams are investigated. It is found that the dimensionless fundamental frequencies are significantly affected by the variation of the thickness to material length scale parameter, hub ratio, dimensionless rotation speed and porosity volume fraction coefficient. The normal deformation effect is very important especially while the variations of the dimensionless rotation speed, hub ratio and gradient index are considered. Moreover, the mode shapes of the rotating two-directional functionally graded porous sandwich microbeams are also influenced with respect to the variation of the porosity volume fraction coefficient. As a result, the optimum design of the microstructures accompanying with the lightweight and low-cost objectives can be achieved by controlling the material and porosity distribution through the body of the microstructure.

Computational hygro-thermal vibration and buckling analysis of functionally graded sandwich microbeams

In this study, for the first time, hygro-thermal behaviour of functionally graded (FG) sandwich microbeams based on nonlocal elasticity theory is investigated. Temperature-dependent material properties are considered for the FG microbeam, which are assumed to change continuously through the thickness based on the power-law form. The equations of motion are obtained on the basis of first-order shear deformation beam theory via Hamilton's principle. The size effects are considered in the framework of the nonlocal elasticity theory of Eringen. The detailed variational and finite element procedure for FG sandwich microbeams are presented with a five-noded beam element and numerical examinations are performed. The influence of several parameters such as temperature and moisture gradients, material graduation, nonlocal parameter, face-core-face and span to depth ratios on the critical buckling temperature and the nondimensional fundamental frequencies of the FG sandwich microbeams are analysed. Based on the results of this study, temperature and moisture rise soften the FG sandwich microbeam and result in the reduction of the critical buckling load and vibration frequency. In addition, the FG sandwich microbeam with a thicker ceramic core can resist higher temperature and moisture gradients.

On the vibration of size dependent rotating laminated composite and sandwich microbeams via a transverse shear-normal deformation theory

In this paper, the eigenfrequencies of rotating laminated composite (LC) and sandwich microbeams with different boundary conditions (BCs) are studied. The size-dependent variational formulation of the problem is obtained based on the Modified Couple Stress Theory (MCST) by employing a transverse shear-normal deformable beam theory and finite element method (FEM) formulation. The convergence and verification studies of the developed code are carried out and computed results in terms of dimensionless fundamental frequencies (DFFs) are compared with the available ones in the open literature. Various BCs, aspect ratios, fiber orientation angles, thickness to material length scale parameter (MLSP) ratios, core thickness to face layer thickness ratios, dimensionless rotation speeds (DRSs) and hub ratios are employed for the extensive analyses. It is found that the DFFs of the LC microbeams are highly affected by the small size effect accompanying with the orthotropy ratios, DRSs, hub ratios and fiber orientation angles. The effect of the small size on the DFFs of the rotating clamped-clamped LC microbeams is more pronounced than on those of the rotating clamped-free LC microbeams. The hub ratio has a significant effect on the DFFs of the rotating LC microbeams than the rotation speed.

Active control of three-phase CNT/resin/fiber piezoelectric polymeric nanocomposite porous sandwich microbeam based on sinusoidal shear deformation theory

Vibration control in mechanical equipments is an important problem where unwanted vibrations are vanish or at least diminished. In this paper, free vibration active control of the porous sandwich piezoelectric polymeric nanocomposite microbeam with microsensor and microactuater layers are investigated. The aim of this research is to reduce amplitude of vibration in micro beam based on linear quadratic regulator (LQR). Modified couple stress theory (MCST) according to sinusoidal shear deformation theory is presented. The porous sandwich microbeam is rested on elastic foundation. The core and face sheet are made of porous and three-phase carbon nanotubes/resin/fiber nanocomposite materials. The equations of motion are extracted by Hamilton's principle and then Navier's type solution are employed for solving them. The governing equations of motion are written in space state form and linear quadratic regulator (LQR) is used for active control approach. The various parameters are conducted to investigate on the frequency response function (FRF) of the sandwich microbeam for vibration active control. The results indicate that the higher length scale to the thickness, the face sheet thickness to total thickness and the considering microsensor and microactutor significantly affect LQR and uncontrolled FRF. Also, the porosity coefficient increasing, Skempton coefficient and Winkler spring constant shift the frequency response to higher frequencies. The obtained results can be useful for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.