Showing papers in "Acta Mechanica in 2010"

A novel heuristic optimization method: charged system search

Abstract: This paper presents a new optimization algorithm based on some principles from physics and mechanics, which will be called Charged System Search (CSS). We utilize the governing Coulomb law from electrostatics and the Newtonian laws of mechanics. CSS is a multi-agent approach in which each agent is a Charged Particle (CP). CPs can affect each other based on their fitness values and their separation distances. The quantity of the resultant force is determined by using the electrostatics laws and the quality of the movement is determined using Newtonian mechanics laws. CSS can be utilized in all optimization fields; especially it is suitable for non-smooth or non-convex domains. CSS needs neither the gradient information nor the continuity of the search space. The efficiency of the new approach is demonstrated using standard benchmark functions and some well-studied engineering design problems. A comparison of the results with those of other evolutionary algorithms shows that the proposed algorithm outperforms its rivals.

Multiscale modeling of elastic properties of cortical bone

Abstract: We model cortical bone as a composite material with hierarchical structure. At a nanostructural level, bone is composed of cross-linked collagen molecules, containing water and non-collagenous proteins in their gaps, reinforced with hydroxyapatite-like nanocrystals. Such a nanocomposite structure represents a mineralized collagen fibril, which serves as a primary building block of bone. At a sub-microstructural level (few microns), the mineralized collagen fibrils are embedded in an extrafibrillar hydroxyapatite matrix to form a single lamella, which also contains the lacunar cavities. At a microstructural level (hundreds of microns) one can distinguish two lamellar structures in the mature cortical bone: osteons, made of concentric layers of lamellae surrounding long hollow Haversian canals, and interstitial lamellae made of remnants of old osteons. At a mesostructural level (several millimeters), the cortical bone is represented by a random collection of osteons and resorption cavities in the interstitial lamellae. A macrostructural level is the whole bone level containing both the cortical (compact) and trabecular (spongy) bone types. In this paper, we predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, spanning from the nanostructural to mesostructural levels, using micromechanics methods and composite materials laminate theories. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The predictions are in good agreement with the experimental data reported in literature.

Thermal boundary layers over a shrinking sheet: an analytical solution

Abstract: In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.

Size effects in nanoindentation: an experimental and analytical study

Abstract: This work addresses the size effect encountered in nanoindentation experiments. It is generally referred to as the indentation size effect (ISE). Classical descriptions of the ISE show a decrease in hardness for increasing indentation depth. Recently new experiments have shown that after the initial decrease, hardness increases with increasing indentation depth. After this increase, finally the hardness decreases with increasing indentation. This work reviews the existing theories describing the ISE and presents new formulations that incorporate the hardening effect into the ISE. Furthermore, indentation experiments have been performed on several metal samples, to see whether the hardening effect was an anomaly or not. Finally, numerical simulations are performed using the commercial program ABAQUS.

Transversely isotropic nonlinear magneto-active elastomers

Abstract: Magneto-active elastomers are smart materials composed of a rubber-like matrix material containing a distribution of magneto active particles. The large elastic deformations possible in the rubber-like matrix allow the mechanical properties of magneto-active elastomers to be changed significantly by the application of external magnetic fields. In this paper, we provide a theoretical basis for the description of the nonlinear properties of a particular class of these materials, namely transversely isotropic magneto-active elastomers. The transversely isotropic character of these materials is produced by the application of a magnetic field during the curing process, when the magneto active particles are distributed within the rubber. As a result the particles are aligned in chains that generated a preferred direction in the material. Available experimental data suggest that this enhances the stiffness of the material in the presence of an external magnetic field by comparison with the situation in which no external field is applied during curing, which leads to an essentially random (isotropic) distribution of particles. Herein, we develop a general form of the constitutive law for such magnetoelastic solids. This is then used in the solution of two simple problems involving homogeneous deformations, namely simple shear of a slab and simple tension of a cylinder. Using these results and the experimental available data we develop a prototype constitutive equation, which is used in order to solve two boundary-value problems involving non-homogeneous deformations—the extension and inflation of a circular cylindrical tube and the extension and torsion of a solid circular cylinder.

MRI-based finite element modeling of head trauma: spherically focusing shear waves

Abstract: A powerful tool for investigating the physical process producing head trauma is finite element (FE) modeling. In this paper, we present a 3D FE model of the human head that accounts for important geometric characteristics of the various components within the human head through an efficient magnetic resonance imaging voxel-based mesh generation method. To validate the FE model, a previous cadaver experiment of frontal impact is simulated, and this is where heretofore unknown wave patterns are discovered. The model is run under either of two extreme assumptions concerning the head-neck junction—free or fixed—and the experimental measurements are well bounded by the computed pressures from the two boundary conditions. In both cases the impact gives rise to not only a fast pressure wave but also a slow and spherically convergent shear stress wave which is potentially more damaging to the brain tissue.

Efficient modeling of smart piezoelectric composite laminates: a review

Abstract: Current research issues in the development of efficient analysis models and their efficient numerical implementation for smart piezoelectric laminated structures are discussed in this paper. The improved zigzag theories with a layerwise quadratic variation of electric potential have emerged as the best compromise between accuracy and cost for hybrid composite, sandwich and FGM beams and plates. The concept of associating surface potentials to electric nodes and internal potentials to physical nodes is very effective in modeling the equipotential electroded surfaces. Unified formulations for shear and extension mode actuation, and modeling of piezoelectric composite actuators and sensors are discussed. Future challenge lies in developing efficient theories capable of predicting the interlaminar transverse shear stresses in hybrid laminates directly from the constitutive equations.

Stable identification of linear isotropic Cosserat parameters: bounded stiffness in bending and torsion implies conformal invariance of curvature

Abstract: We describe a principle of bounded stiffness and show that bounded stiffness in torsion and bending implies a reduction of the curvature energy in linear isotropic Cosserat models leading to the so-called conformal curvature case $${\mu\,\frac{L_c^2}{2}\,\|\,{{\rm dev \, sym}\, abla{\rm axl}\,\overline{A}}^2\|}$$ where $${\overline{A} \in \mathfrak{so}(3)}$$ is the Cosserat microrotation. Imposing bounded stiffness greatly facilitates the Cosserat parameter identification and allows a well-posed, stable determination of the one remaining length scale parameter L c and the Cosserat couple modulus μ c .

Vibrations of functionally graded cylindrical shells based on elastic foundations

Abstract: In this paper, a study on the vibrations of functionally graded cylindrical shells based on the Winkler and Pasternak foundations is presented. The shell equations are amended by inducting the moduli of the Winkler and Pasternak foundations. The wave propagation method is employed to solve the shell dynamical equations. The method is based on the approximate eigenvalues of characteristic beam functions. The validity and accuracy of the present approach are verified by a number of comparisons.

Nano-indentation in FCC metals: experimental study

Abstract: This paper presents the results of an experimental study for nano-indentation size effects for different face centered cubic metals with different purities. The selected materials are: Silver, Copper, Aluminum, Lead, and Nickel. Nano-indentation tests are run using a Berkovich indenter with continuous stiffness measurement procedure where hardness is measured continuously with indentation depth. The results show three distinctive regions for the indentation size effects for the material, where hardness could increase or decrease with increasing indentation. This behavior is modeled through a proposed simple power law model, which includes the effect of grain boundaries.

Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations

Abstract: The investigation of bending response of a simply supported functionally graded (FG) viscoelastic sandwich beam with elastic core resting on Pasternak’s elastic foundations is presented. The faces of the sandwich beam are made of FG viscoelastic material while the core is still elastic. Material properties are graded from the elastic interfaces through the viscoelastic faces of the beam. The elastic parameters of the faces are considered to be varying according to a power-law distribution in terms of the volume fraction of the constituent. The interaction between the beam and the foundations is included in the formulation. Numerical results for deflections and stresses obtained using the refined sinusoidal shear deformation beam theory are compared with those obtained using the simple sinusoidal shear deformation beam theory, higher- and first-order shear deformation beam theories. The effects due to material distribution, span-to-thickness ratio, foundation stiffness and time parameter on the deflection and stresses are investigated.

Hyperelastic materials behavior modeling using consistent strain energy density functions

Abstract: Hyperelastic materials have high deformability and nonlinearity in load–deformation behavior. Based on a phenomenological approach, these materials are treated as a continuum, and a strain energy density is considered to describe their hyperelastic behavior. In this paper, the mechanical behavior characterization of these materials is studied from the continuum viewpoint. For this purpose, the strain energy density is expressed as sum of independent functions of the mutual multiple of principal stretches. These functions are determined by applying the governing postulates on the form of the strain energy density. It is observed that a consistent strain energy density is expressible in terms of the mathematical functions of polynomial, power law, logarithmic and particularly exponential. The proposed strain energy density functions cover modeling both of compressible and incompressible materials. Moreover, the material parameters of these models are calculated based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to investigate the appropriateness of the proposed models, several experimental data for incompressible and compressible isotropic materials under homogeneous deformations are examined in which the predictions of the proposed models show a good agreement with experimental data.

Atomistic-based continuum modeling of the nonlinear behavior of carbon nanotubes

Abstract: It is the purpose of this paper to determine the nonlinear mechanical properties of carbon nanotubes (CNTs). Due to the inherent nano-scale involved in simulating CNT structures, an atomistic description is incorporated via an atomistic-based continuum multiscale modeling technique. In this way, the continuum constitutive relations are derived solely from atomistic formulations. The atomic interactions in the CNT structure are described in a continuum framework using the Modified Morse interatomic potential. The effect of the angle-bending component of the potential is investigated and found to play a significant role in the stability of the structure. The nonlinear response of armchair and zigzag nanotubes under tensile and torsional loading conditions are considered and presented. In addition, the fracture process under tensile loading and the phenomena of torsional buckling are investigated.

Equations of motion for general constrained systems in Lagrangian mechanics

Abstract: This paper develops a new, simple, explicit equation of motion for general constrained mechanical systems that may have positive semi-definite mass matrices. This is done through the creation of an auxiliary mechanical system (derived from the actual system) that has a positive definite mass matrix and is subjected to the same set of constraints as the actual system. The acceleration of the actual system and the constraint force acting on it are then directly provided in closed form by the acceleration and the constraint force acting on the auxiliary system, which thus gives the equation of motion of the actual system. The results provide deeper insights into the fundamental character of constrained motion in general mechanical systems. The use of this new equation is illustrated through its application to the important and practical problem of finding the equation of motion for the rotational dynamics of a rigid body in terms of quaternions. This leads to a form for the equation describing rotational dynamics that has hereto been unavailable.

A general inelastic internal state variable model for amorphous glassy polymers

Abstract: This paper presents the formulation of a constitutive model for amorphous thermoplastics using a thermodynamic approach with physically motivated internal state variables. The formulation follows current internal state variable methodologies used for metals and departs from the spring-dashpot representation generally used to characterize the mechanical behavior of polymers like those used by Ames et al. in Int J Plast, 25, 1495–1539 (2009) and Anand and Gurtin in Int J Solids Struct, 40, 1465–1487 (2003), Anand and Ames in Int J Plast, 22, 1123–1170 (2006), Anand et al. in Int J Plast, 25, 1474–1494 (2009). The selection of internal state variables was guided by a hierarchical multiscale modeling approach that bridged deformation mechanisms from the molecular dynamics scale (coarse grain model) to the continuum level. The model equations were developed within a large deformation kinematics and thermodynamics framework where the hardening behavior at large strains was captured using a kinematic-type hardening variable with two possible evolution laws: a current method based on hyperelasticity theory and an alternate method whereby kinematic hardening depends on chain stretching and material plastic flow. The three-dimensional equations were then reduced to the one-dimensional case to quantify the material parameters from monotonic compression test data at different applied strain rates. To illustrate the generalized nature of the constitutive model, material parameters were determined for four different amorphous polymers: polycarbonate, poly(methylmethacrylate), polystyrene, and poly(2,6-dimethyl-1,4-phenylene oxide). This model captures the complex character of the stress–strain behavior of these amorphous polymers for a range of strain rates.

Dynamic fracture with meshfree enriched XFEM

Abstract: The enrichment of the extended finite element method (XFEM) by meshfree approximations is studied. The XFEM allows for modeling arbitrary discontinuities, but with low order elements the accuracy often needs improvement. Here, the meshfree approximation is used as an enrichment in a cluster of nodes about the crack tip to improve accuracy. Several numerical examples show that this leads to more accuracy for stress intensity factors computations, and to the capability to capture the branching point of a propagating crack from the stresses.

Nonlinear analysis of non-uniform beams on nonlinear elastic foundation

Abstract: In this paper a boundary integral equation solution to the nonlinear problem of non-uniform beams resting on a nonlinear triparametric elastic foundation is presented, which permits also the treatment of nonlinear boundary conditions. The nonlinear subgrade model which describes the foundation includes the linear and nonlinear Winkler (normal) parameters and the linear Pasternak (shear) foundation parameter. The governing equations are derived in terms of the displacements for nonlinear analysis in the deformed configuration and for linear analysis in the undeformed one. Moreover, as the cross-sectional properties of the beam vary along its axis, the resulting coupled nonlinear differential equations have variable coefficients which complicate the mathematical problem even more. Their solution is achieved using the analog equation method of Katsikadelis. Several beams are analyzed under various boundary conditions and load distributions, which illustrate the method and demonstrate its efficiency and accuracy. Finally, useful conclusions are drawn from the investigation of the nonlinear response of non-uniform beams resting on nonlinear elastic foundation.

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

Abstract: A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.

Sliding frictional contact analysis of functionally graded piezoelectric layered half-plane

Abstract: This paper investigates the sliding frictional contact problem of a layered half-plane made of functionally graded piezoelectric materials (FGPMs) in the plane strain state. It is assumed that the punch is a perfect electrical insulator with zero electric charge distribution, and the friction within the contact region is of Coulomb type. The electro-elastic properties of the FGPM layer vary exponentially along the thickness direction. The fundamental solutions for the applied concentrated linear forces perpendicular and parallel to the FGPM layer surface are obtained. Using the superposition theorem, the problem is reduced to a Cauchy singular integral equation which is then numerically solved to determine the contact tractions, contact region, maximum indentation depth, electrical potential and electromechanical fields. Numerical results show that both the material property gradient and the friction coefficient have significant influence on the contact performance of the FGPM layered half-plane.

Variational principles for generalized thermodiffusion theory in pyroelectricity

Abstract: The universal thermodynamic variational principle proposed in the previous papers for nonlinear dielectrics and thermopiezoelectricity is extended to the thermodiffusion theory in pyroelectricity, and it is used as a fundamental physical principle to derive the simple complete governing equations of the generalized thermo-electro-diffuso-elastic theory in this paper. In the generalized thermo-electro-diffuso-elastic theory it is assumed that the variation of temperature needs the extra heat which introduces the inertial entropy, and the variation of chemical potential also needs the extra heat which introduces the inertial concentration, etc. The electro-chemical Gibbs function variational principle, the electric Gibbs function variational principle and the internal energy variational principle are derived in this paper.

3D models for wave-induced pore pressures near breakwater heads

Abstract: Wave-induced pore pressure is one of the important factors in the analysis of foundation stability around coastal structures. Existing models for the wave-induced seabed response around breakwater heads have been limited to poro-elastic soil behavior and de-coupled oscillatory and residual mechanisms for the rise in excess pore water pressure. To overcome the shortcoming of the existing models, in this study a new three-dimensional poro-elastoplastic model is established, in which both oscillatory and residual mechanisms can be simulated simultaneously. The reduced cases of the proposed model are verified with existing 2D experimental data available and a 3D poro-elastic analytical solution in front of a breakwater. With the proposed new model, a parametric study is conducted to investigate the relative differences of the predictions of the wave-induced pore pressure and liquefaction with poro-elastic and poro-elasto-plastic models. Based on numerical examples, it can be concluded that relative differences between elastic and elasto-plastic models are significantly affected by wave periods and water depths. Wave height significantly affects the development of residual pore pressure versus time. Plastic soil behavior plays an important role in a seabed of low permeability. Plastic soil behavior has more significant influence on wave-induced residual pore pressure than the amplitude of the oscillating pore pressure. Furthermore, poro-elastic analysis tends to under-estimate the size of the liquefaction regions around breakwater heads.

Wave propagation in a prestressed piezoelectric half-space

Abstract: Reflection of plane waves at a traction-free and electrically shorted/charge-free surface of a prestressed piezoelectric medium is studied. The reflection coefficients of qP and qSV waves are derived for electrically shorted and charge-free cases. The effect of initial stress on the reflection coefficients is discussed for a particular example of Lithium niobate.

Experimental studies on the quasi-static bending behavior of double square tubes filled with aluminum foam

Abstract: Quasi-static experiments were performed on empty tubes and aluminum foam-filled single and double tubes to study the effects of different filler arrangements on their three-point bending behavior. The load-carrying capacity and energy absorption of different structures are compared. The results confirm the advantage of the foam-filled structures. In particular, the double tube structure with aluminum foam filler enhances the load-carrying capacity, crashworthiness, and total and specific energy absorptions of the structure, in comparison with the foam-filled single tube. It was also found that increasing the wall thickness of the inner tube improves the performance of the structure within the experimental range, and adhesion between foam and tube has a negative effect.

Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads

Abstract: A semi-analytical method is proposed for investigating the stability of planar equilibrium configurations of an inextensible elastic rod under end-loading conditions. The method is based on representing the second variation of the constrained strain energy of the rod as a diagonal quadratic form using the eigensolutions of an auxiliary Sturm–Liouville problem. The coefficients of the resulting form which determine the sign of the second variation are analyzed by numerically solving an initial-value problem. Examples of curvilinear configurations of rods and a circular ring under point loads are considered and their stability is analyzed using the proposed method.

Static and free vibration analyses of continuously graded fiber-reinforced cylindrical shells using generalized power-law distribution

Abstract: In this study, based on the three-dimensional theory of elasticity, static and free vibration characteristics of continuously graded fiber-reinforced (CGFR) cylindrical shells are considered by making use of a generalized power-law distribution. In the present formulation, the cylindrical shell is assumed to be made of an orthotropic material. The CGFR cylindrical shells have a smooth variation of matrix volume fraction in the radial direction. Symmetric and asymmetric volume fraction profiles are presented in this paper. Suitable displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by a generalized differential quadrature method. The fast rate of convergence of the method is demonstrated, and comparison studies are carried out to establish its very high accuracy and versatility. The main contribution of this work is to illustrate useful results for a cylindrical shell continuously graded fiber reinforced in the radial direction. Finally, these results are compared with a similar discrete laminated composite cylindrical shell.

Analysis of phase-lag effects on wave propagation in a thick plate under axisymmetric temperature distribution

Abstract: The main objective of the present paper is to analyze the effects of phase lags on wave propagation in a two dimensional thick plate due to an axisymmetric temperature distribution. The problem is formulated by employing three recent theories of thermoelasticity in a unified way, namely thermoelasticity of type III (Green and Naghdi in J Therm Stress 15:253–264, 1992), thermoelasticity with dual phase lags (Tzou in ASME J Heat Transf 117:8–16, 1995) and thermoelasticity with three phase lags (Roychoudhuri in J Therm Stress 30:231–238, 2007). The lower and upper surfaces of the plate are assumed to be traction free and subjected to a given axisymmetric temperature distribution. A potential function approach together with the Laplace and Hankel transform method is employed to derive the solution in the transform domain. The Hankel inversion is performed analytically and the solution in the Laplace transform domain is obtained. Detailed analyses on wave propagation and discontinuities of different fields of the medium are presented by using a method due to Boley (Quart Appl Math 19:273–284, 1962). By employing a numerical method for the Laplace inversion the distributions of different fields like temperature, displacement and stresses in the middle plane of the plate have been computed and depicted graphically. Findings are analyzed along with the comparison with the corresponding results obtained in earlier works.

Finite deformation of thin shells in the context of analytical mechanics of material surfaces

Abstract: In the framework of the direct approach shells are considered as deformable surfaces consisting of particles, and the relations of the theory are obtained with the methods of analytical mechanics. In the present work we assign to each particle five degrees of freedom, namely three translations and two in-plane rotations. The principle of virtual work produces all the relations of the theory of shells: equations of equilibrium, boundary conditions, definition of the force factors and the general form of constitutive equations. Remarkable consistency and clarity is achieved both in the relations of the theory and in the derivation process. A new formulation of the Piola tensors for a shell is suggested in order to transform the equations to the reference configuration. To analyze the effects of buckling or geometric stiffening, we linearize these equations in the vicinity of a pre-deformed configuration. Some new semi-analytical results on buckling and supercritical behavior of an axially compressed cylindrical shell are presented. The correspondence between the equations and the variational formulation is discussed in view of development of efficient numerical procedures for modeling nonlinear deformations of shells. Results of finite element modeling of the nonlinear deformation of a shell structure are discussed in comparison with the fully three-dimensional solution of the problem.

An analytical method for thermal stresses of a functionally graded material cylindrical shell under a thermal shock

Abstract: In this paper, the thermal stresses of a thin functionally graded material (FGM) cylindrical shell subjected to a thermal shock are studied. An analytical method is developed. The studied problem for an FGM cylindrical shell is reduced to a plane problem. A perturbation method is used to solve the thermal diffusion equation for FGMs with general thermal properties. Then, the transient thermal stresses are obtained. The results show that the thermal shock is much easier to result in failure than the steady thermal loading. The present method can also be used to solve the crack problem of an FGM cylindrical shell with general thermal properties.

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

Abstract: The nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity is investigated. Based on the linear viscoelastic differential constitutive law, the extended Hamilton’s principle is utilized to derive the generalized third-order equations of motion for the axially translating viscoelastic Bernoulli–Euler beam. The coupling effects between the axial motion and transverse vibration are assessed under various prescribed time-varying velocity fields. The inertia force arising from the longitudinal acceleration emerges, rendering the coupling terms between the axial beam acceleration and the beam flexure. Semi-analytical solutions for the governing PDE are obtained through the separation of variables and the assumed modes method. The modified Galerkin’s method and the fourth-order Runge–Kutta method are employed to numerically analyze the resulting equations. Further, dynamic stabilization is examined from the system energy standpoint for beam extension and retraction. Extensive numerical simulations are presented to illustrate the influences of varying translating velocities and viscoelastic parameters on the underlying dynamic responses. The material viscosity always dissipates energy and helps stabilize the transverse vibration.

Electromechanical dynamic buckling phenomenon in symmetric electric fields actuated microbeams considering material damping

Abstract: The dynamic behavior of a clamped-clamped microbeam loaded by a symmetric combined voltage, which is composed of a direct current (DC) voltage and an alternating current (AC), is investigated in this paper. Based on the Euler-Bernoulli hypothesis and the standard anelastic solid model, the equation of motion of this microbeam with considering the material damping is got, and then by using the Galerkin method a reduced-order model is derived. An instability phenomenon named as electromechanical dynamic buckling in this system is shown, and the condition of instability is determined by the averaging method. To validate our results, a numerical simulation model is set up. The effects of the fringing field, residual stress, applied DC voltage, environmental damping and material damping on the electromechanical dynamic buckling are discussed.