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In this article, we analyze the effect of transverse cracks on the natural frequencies of a Euler-Bernoulli functional gradient beam. The studied beam was discretized into finite elements and the global matrices of the motion equation are determined by applying the Lagrange equation to the beam kinetic and deformation energies. The material properties are considered to vary in the directions of the beam thickness, the gradation is described by the power-law distribution, the stiffness of the cracked element is determined based on the reduction of the beam cross-section. The numerical results obtained are compared with those available in the previous study. Finally, case studies were carried out to analyses the influence of the power law index, the depth and the opposition of the crack on the natural frequencies of the beam for different boundary conditions; these studies demonstrate the advantage of the FGM beam over the purely metal beam. [ABSTRACT FROM AUTHOR]

Knowing the extent of displacement experienced by railroad bridges when loaded is useful when evaluating the safety and serviceability of the bridge. However, measuring displacements under train crossing events is difficult. If simplified reference-free methods would be accurate and validated, owners would conduct objective performance assessment of their bridge inventories under trains. Researchers have developed new sensing technologies (reference-free) to overcome the limitations of reference point-based displacement sensors. Reference-free methods use accelerometers to estimate displacements, by decomposing the total displacement in two parts: a high-frequency dynamic displacement component, and a low-frequency pseudostatic displacement component. In the past, researchers have used the Euler-Bernoulli beam theory formula to estimate the pseudostatic displacement assuming railroad bridge piles and columns can be simplified as cantilever beams. However, according to railroad bridge managers, railroad bridges have a different degree of fixity for each pile of each bent. Displacements can be estimated assuming a similar degree of fixity for deep foundations, but inherent errors will affect the accuracy of displacement estimation. This paper solves this problem expanding the 1 degree of freedom (1DOF) solution to a new 2 degrees of freedom (2DOF), to collect displacements under trains and enable cost-effective condition-based information related to bridge safety. Researchers developed a simplified beam to demonstrate the total displacement estimation using 2DOF and further conducted experimental results in the laboratory. The authors assumed linearity on properties and connections and used real train crossing event data as input to evaluate the accuracy of the proposed 2DOF method. The estimated displacement of the 2DOF model is more accurate than that of the 1DOF model for ten train crossing events. With only one sensor added to the ground of the pile, this method provides owners with approximately 40% more accurate displacements. Future work includes the study of nonlinearities and parametric study of the effect of resonance in displacement estimation accuracy for practical field implementation. The main application of this research is the optimization of the number of sensors and the simplification of sensor location, for lateral displacement estimation. Infrastructure managers can install a minimum number of sensors in tall piers or structures and determine the transverse displacement. The main practical aspect of this work is that engineers can collect the rotation at the base of the pier by locating sensors in the base. Using both the rotation both at the bottom and the top of the pier, the total displacement at the top can be obtained. In the practical domain, timber railroad piers could demonstrate additional lateral displacement under train crossing events not associated with the rotation above ground. Engineers could observe or collect that lateral displacement and add it to the total estimated displacement to obtain the total transverse displacement. Based on the field observations of the main author of this paper the lateral separation between the timber pile at the base of the pier is small, however it can be a practical next step in further development of the proposed method for practical applications. [ABSTRACT FROM AUTHOR]

Nano-electro-mechanical systems (NEMS) require perforated beams for structural integrity. Hole sizes, hole numbers, and scale effects need to be modelled appropriately in their design. This paper presents a new finite element model to investigate the modal behaviour of longitudinally perforated nanobeams (LPNBs) using the classical Euler–Bernoulli beam theory. A symmetric array of holes arranged parallel to the length direction of the beam with equal spacing was assumed for the perforation. The non-local Eringen’s differential form was used to incorporate the nanoscale sizes. The accuracy of the proposed model was verified by comparing the obtained results with the available analytical solutions for fully filled nanobeams. The effects of aspect ratios, non-local parameters, boundary conditions, and perforation characteristics on the modal behaviour of LPNBs were investigated. The non-local parameter reduced the natural frequency owing to a decrease in the stiffness of the structures. However, the perforation filling ratio led to higher values of the fundamental frequency. Furthermore, compared with other boundary conditions, clamped–clamped boundary conditions demonstrated the best performance in terms of the maximum frequency.

This paper is dedicated to examine the size-dependent nonlinear forced dynamics of MRE-cored sandwich micro-pipes in existence of external distributed load and internal flow. For this aim, Euler-Bernoulli beam theory, considering von-Karman nonlinearity, together with the modified couple stress theory (MCST) are exploited to attain a mathematical formulation of the problem. Employing Galerkin's approach with consideration of two axial and transverse modes, the obtained nonlinear partial differential equations are discretized, from which nonlinear ordinary equations are achieved. Thereafter, static condensation method is utilized in order to reduce the number of the obtained ordinary equations. The acquired nonlinear equations are then solved according to the method of multiple scales, which leads to nonlinear natural frequencies and frequency-response curves of the system. Throughout the numerical analysis, the effect of a smart MRE core existence on the system's response, considering various boundary conditions, is explored. Additionally, a numerical investigation is implemented to highlight the influences of MRE-related intrinsic properties namely the intensity of the applied magnetic potential and MRE core thickness on the natural frequencies, frequency-response and load-response curves of the system. Totally, the substantial role of the MRE core and its intrinsic characteristics on the dynamic response of the system is explored, which implies that, this smart core could be a good candidate in such sandwich structures in order to control and boost the dynamic properties and response of the mechanical systems. [ABSTRACT FROM AUTHOR]

This article investigates dynamic responses of symmetric and sigmoid FG Timoshenko beam rested on elastic foundation and subjected to moving mass. The gradation is described by symmetrical and sigmoidal law functions. The Hamilton principle is exploited to derive the system equations of motion. Finite element has been developed to convert the partial differential equations to ordinary equations in time domain, those will be solved incrementally by Newmark method. The model is verified. Parametric studies are presented to investigate influences of gradation type, gradation index, elastic foundation stiffnesses, inertia, and variable velocity of the moving mass on the dynamic response. [ABSTRACT FROM AUTHOR]

In this paper, the flutter instability of a conventional two-stage axially moving telescopic UAV wing is investigated. To this aim, and to be as close as possible to the reality, the effects of temporal variation of mass and length, due to the movement of stages and their overlapping, along with the effects of morphing speed are considered for the first time. The bending-torsional dynamics of the two-stage wing is modeled by modifying the Euler–Bernoulli beam theory to take into account the effects of morphing speed and variations of mass and length. Furthermore, the aerodynamic loads are simulated using Peters' unsteady aerodynamic model. The governing aeroelastic equations are discretized using a finite element approach, and a length-based stability analysis is proposed to investigate the aeroelasticity of the wing. The obtained results are compared with those available in the literature, and a good agreement is observed. It is found that the aeroelastic stability of a telescopic wing is more sensitive to the fixed part parameters than the moving part. Also, it is shown that the wing critical length is sensitive to the morphing speed. Therefore, by selecting the telescopic wing morphing parameters properly, the aeroelastic stability of the system can significantly be improved. [ABSTRACT FROM AUTHOR]

Lattice materials possess excellent mechanical properties such as light weight, high specific stiffness and high energy absorption capacity. However, the commonly used lattice materials inspired by Bravais lattice often give rise to property anisotropy that is not desirable for engineering application such as bone implants. For this sake, a design methodology for isotropic stiffness is proposed in this paper. Firstly, an efficient theoretical method for calculating the elastic matrices of lattice materials was presented. The method is based on Euler–Bernoulli beam theory and the assumption of affine deformation of cell vertices applicable to cubic truss-lattice materials. The theoretical approach was validated by comparing with the finite element simulations. Utilizing the validated theoretical method, and by properly combining the lattice configurations with complementary stiffness along different directions, an elastic isotropic lattice material can be obtained. A few examples are presented to demonstrate the effectiveness and adaptability of the proposed design strategy by permutating the combinations of different classic lattices. The method proposed in this paper can provide a new approach in the design of lattice materials with excellent anisotropy control. [ABSTRACT FROM AUTHOR]

Dynamic stability is an important mechanical behavior of nanobeams, which has been studied extensively using the Euler–Bernoulli and Timoshenko beam theories, while the Levinson-beam-theory-based dynamic instability analysis of nanobeams has not been investigated yet. Shear deformation is not or is not suitably considered in the Euler–Bernoulli and Timoshenko theories, so it is very important to introduce the Levinson beam theory in the dynamic stability analysis of nanobeams, which correctly models the combined action of bending and shear in nanobeams with smaller length/height ratios. In this work, the equation of the transverse vibration of a Levinson beam embedded in an elastic foundation is firstly formulated based on the displacement field of Levinson beam theory, and the nonlocal theory is further applied to the Levinson nanobeam. Then, the governing equation of the dynamic stability of the Levinson nanobeam is derived using Bolotin's method to achieve a generalized eigenvalue problem corresponding to the boundaries of regions of dynamic instability. The principal instability region (PIR) is the most important among all regions, so the boundary of the PIR is focused on in this work to investigate the dynamic stability of the Levinson nanobeam. When the width, length/height ratio, density, Young's modulus, Poisson's ratio, size scale parameter, and medium stiffness increase by about 1.5 times, the width of the PIR changes by about 19%, −57%, −20%, 65%, 0, −9%, and −11%, respectively. If a smaller critical excitation frequency and narrower width of the PIR correspond to the better performance of dynamic stability, the study shows that the dynamic stability of the Levinson nanobeam embedded in an elastic medium improves under a larger length and density and a smaller width, height, and Young's modulus, since these factors are related to the natural frequency of the nanobeam which controls the width of the PIR. Additionally, the local model would overestimate the dynamic stability behavior of the Levinson nanobeam. [ABSTRACT FROM AUTHOR]

This research presents the application of a beam finite element, specifically derived for simulating bending–torsion coupling in equivalent box-beam structures with curvilinear stiffeners. The stiffener path was simulated and optimized to obtain an expected coupling effect with respect to four typical static load cases, including geometric constraints related to the additive manufacturing production method. The selected load condition was applied to the centroid of the beam section, and the structure performance was consequently determined. A variation in load position up to one-fourth of the beam width was considered for investigating the stiffener path variation corresponding to a minimum bending–torsion coupling effect. The results demonstrated the capability of such a beam finite element to correctly represent the static behavior of beam structures with curvilinear stiffeners and show the possibility to uncouple its bending–torsion behavior using a specific stiffener orientation. The simulation of a laser powder bed fusion process showed new opportunities for the application of this technology to stiffened panel manufacturing. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories. Design/methodology/approach: Timoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy. Findings: The results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler–Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties. Originality/value: The combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks. [ABSTRACT FROM AUTHOR]

The static bending of rotating two-layer functionally graded material (FGM) beams with shear connectors resting on imperfect elastic foundations was performed for the first time in this study. Timoshenko beam theory and the finite-element method are used to derive finite-element formulations. The precision of the current approach and mechanical model is shown by comparing the calculated findings of this study to those of previous precise papers. A wide variety of parameter studies are carried out to capture the impact of geometric and material characteristics on the structure's static bending behaviors, such as the distance d , rotational speed, volume fraction index, elastic foundation parameters, and boundary conditions. This paper's theory and mechanical models are fascinating since mechanical systems involving rotational motion are pretty standard in engineering practice. Therefore, the computed results of this work aim to contribute to our understanding of structures of this kind. [ABSTRACT FROM AUTHOR]

We derive analytical solutions based on singular Green's functions, which enable efficient computations of scattering simulations or Floquet–Bloch dispersion relations for waves propagating through an elastic plate, whose surface is patterned by periodic arrays of elastic beams. Our methodology is versatile and allows us to solve a range of problems regarding arrangements of multiple beams per primitive cell, over Bragg to deep-subwavelength scales; we cross-verify against finite element numerical simulations to gain further confidence in our approach, which relies upon the hypothesis of Euler–Bernoulli beam theory considerably simplifying continuity conditions such that each beam can be replaced by point forces and moments applied to the neutral plane of the plate. The representations of Green's functions by Fourier series or Fourier transforms readily follows, yielding rapid and accurate analytical schemes. The accuracy and flexibility of our solutions are demonstrated by engineering topologically non-trivial states, from primitive cells with broken spatial symmetries, following the phononic analogue of the Quantum Valley Hall Effect. Topologically protected states are produced and coexist along: interfaces between adjoining chiral-mirrored bulk media, and edges between one such chiral bulk and the surrounding bare elastic plate, allowing topological circuits to be designed with robust waveguiding. Our topologically protected interfacial states correspond to zero-line modes, and our topological edgestates are produced in accordance with the bulk-edge correspondence. These topologically non-trivial states exist within near flexural resonances of the constituent beams of the phononic crystal and hence can be tuned into a deep-subwavelength regime. [ABSTRACT FROM AUTHOR]

The classical Euler‐Bernoulli beam theory in elastostatic is known to be inconsistent, since the equilibrium equations are not satisfied in local form. Recently, it has been shown that the theory will become consistent if one assumes elastic anisotropy subject to internal constraints. This is shown to be true even for a simple gradient elasticity law. Normally, beam bending is considered as one‐dimensional problem. We summarise in the present paper the results of a previous work concerning two well‐known one‐dimensional formulations of Euler‐Bernoulli beam and gradient elastic material behaviour. The two formulations appear to be different because the functional of internal forces includes the cross‐sectional area of the beam in one but not in the other. It is shown that the two one‐dimensional formulations can be derived as special cases of a three‐dimensional simple gradient elasticity model and that they are equivalent to each other. [ABSTRACT FROM AUTHOR]

In this paper, the bending behavior of nanoscale beams is studied using the 1D nonlocal integral Timoshenko beam theory (NITBT) and the 2D nonlocal integral elasticity theory (2D-NIET) using two types of nonlocal kernels, i.e., the two-phase kernel and a modified kernel which compensates the boundary effects. The governing equations are solved using the finite element method and the COMSOL code. Mesh sensitivity study and numerical verifications are presented. The main differences and similarities in both theories at the nanoscale are revealed. For both theories and both kernels, a softening behavior is found by increasing the nonlocal parameter and decreasing the phase parameter, for different boundary and load conditions. In contrast to the differential theory, no paradoxical behavior for the cantilever conditions is found for both theories. The sensitivity of the 2D-NIET to the nonlocal parameter is found higher than that of the NITBT. The normalized transverse deflection for the 2D-NIET is found independent of the boundary and load conditions. Also, the normalized transverse deflection varies linearly versus the normalized nonlocal parameter for both theories with the two-phase kernel and any condition except for the simply supported beam under distributed load condition in the NITBT. The boundary effect, resulting in a different softening near the boundaries, reduces by increasing the phase parameter. The modified kernel in the 2D-NIET is found sensitive to the pinned not to the free and fixed boundaries. It is in detail shown that for the 2D-NIET especially with the modified kernel, by increasing the nonlocal parameter, the deflection increases with almost the same ratio through the entire length of the beam and for all the boundary conditions. The obtained results can be used for modeling of various beam problems with nonlocal effects at the nanoscale. [ABSTRACT FROM AUTHOR]

In recent years, flexoelectric and piezoelectric effects have been investigated in many studies, but these effects have not been studied simultaneously in a rotating microbeam, taking into account the size effects. The simultaneous investigation of these effects is necessary to better understand the vibrational behavior of flexoelectric microstructures. It will be possible to identify the flexoelectric and size-dependent effects and their influence on the vibration frequency as a result of this analysis. Furthermore, it can lead to improved design of microstructures. Under the influence of the flexoelectric effect, the current research analyzes the free vibrations of a rotating piezoelectric microbeam. Also, all rotating microbeams are affected by the flexoelectric effect, and therefore the study of this phenomenon is of great importance. Due to the small strain and moderate rotation of the beam, Euler–Bernoulli beam theory and von Karman strain–displacement relations are employed in this article. The Gibbs energy function presented in this research includes the effects of couple stress, piezoelectric and flexoelectric. Hamilton's principle is used to obtain the equations of motion and boundary conditions of the rotating microbeam. In the final step, it has been examined in this study how parameters such as slenderness ratios, changes in rotation speed, and coefficients related to flexoelectric and piezoelectric properties affect the vibration of a rotating microbeam. The results show that the natural frequency increases as the rotation speed increases. Further, the use of piezoelectric and flexoelectric effects has increased the structure's stiffness and, as a result, increased its natural frequency. [ABSTRACT FROM AUTHOR]

The L-shaped cantilever beam structure has many unique advantages such as large flexibility, strong designability, full utilization of space and various deformation modes during vibration, and is widely regarded and studied. A differential quadrature method was proposed to solve the natural frequencies and modes of rectangular-section homogeneous slender L-shaped cantilever beams with additional end masses. In the double coordinate systems, the dynamic equations for the L-shaped cantilever beam based on the Euler-Bernoulli beam theory were established. With selected roots of the Chebyshev polynomial as the node coordinates, the Lagrange interpolation basis function was employed, the weight coefficients of each order were solved, and the boundary conditions were considered, to obtain the natural frequencies and modes of all orders of the structure through resolution of the generalized matrix eigenvalue problem. The theoretical solution of the natural frequencies was verified in comparison with the previous theoretical results and the finite element results. Finally, the effects of the end mass, the length ratio, the width and the thickness of the inner and outer beams on the natural vibration characteristics of all orders were discussed. This method can be further applied to the study of related structural vibrations. [ABSTRACT FROM AUTHOR]

The propagation properties of a circular cosine-hyperbolic Gaussian beam (CiChGB) in a strongly nonlocal nonlinear media (SNNM) are theoretically investigated. Based on the Snyder-Michell model and Collins formula, the closed-form expressions of the complex amplitude, beam width, and curvature radius for an on-axis incident CiChGB in SNNM are derived, and their evolution behaviors are illustrated with numerical examples. It is demonstrated that a CiChGB evolves periodically in SNNM, similarly to a spatial breather, due to the interplay between the nonlinearity process and diffraction. The period of evolution and beam intensity pattern is closely dependent on the input power, initial beam parameters, and SNNM factor. Under the critical input power, the intensity distribution, width and curvature radius of the beam can keep invariant upon propagation, so the CiChGB behaves like a soliton. The research results could have potential applications in beam shaping, optical switch, and micromanipulation. [ABSTRACT FROM AUTHOR]

Steel piles are widely used in deep foundation systems to transfer significant structural loads to strong soil layers. A steel pile may buckle or fail by forming multiple plastic hinges at different locations. The pile's plastic hinge distributions and failure mode are considerably affected by soil–pile interactions (SPIs). A proper consideration of SPIs is essential for the successful design of a steel pile foundation. In practice, empirical calculation or numerical modeling analysis methods are commonly utilized. Nevertheless, the conventional design methods are cumbersome in the modeling process and may be inaccurate in considering SPIs. This paper develops a new integrated soil–pile element to explicitly reflect SPIs and capture steel piles' inelastic behaviors based on the plastic hinge method and the Euler–Bernoulli beam theory. Two virtual nonlinear springs, the concentrated rotational and distributed lateral springs, are used to simulate the plastic hinge deformations and the soil responses, respectively. The rotational and lateral springs are assigned at both ends and the Gauss integration points of an element, respectively. The Gaussian quadrature method is utilized to consider the soil reactions and generate the soil stiffness matrix. Based on the numerical integration and condensation methods, the virtual springs are directly integrated into the element formulation, simplifying the programming and practical modeling process. The updated Lagrangian approach is adopted for describing the element kinematic motions. The element tangent and secant relations between nodal forces and displacements are derived based on the potential energy principle. Several verification examples are presented to demonstrate the capability of the proposed element. [ABSTRACT FROM AUTHOR]

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. The current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory. [ABSTRACT FROM AUTHOR]

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The nonlinear governing equations of nanobeam taking into consideration its curvature, resting on an elastic Winkler-Pasternak foundation and based on non-local Euler-Bernoulli beam theory is analyzed. The equation of motion and the boundary conditions are modeled within the framework of a simple supported nanobeam which accounts the presence of a mechanical impact and nonlinear von-Karman strain. The resulting nonlinear differential equations are reduced to only one differential equation which is studied by means of the Optimal Auxiliary Functions Method (OAFM). An explicit analytical solution is proposed for a complex problem. The main quality of our technique consists in the existence of some auxiliary functions derived from the expressions of the solution for the initial linear equation and the form of nonlinear term calculated from the above solution of the linear equation. The convergence-control parameters present in the auxiliary functions are evaluated by a rigorous mathematical procedure. The obtained solutions are in very good agreement with the numerical solution. [ABSTRACT FROM AUTHOR]

Electrostatic layer jamming represents a lightweight, low energy consumption, electrically tunable, and cost-effective variable stiffness structure. Flexible parallel electroadhesive structures are the simplest form of electrostatic layer jamming. There is a lack of comprehensive and experimentally validated theoretical variable stiffness models of flexible parallel electroadhesive structures. Here we present the first variable stiffness model of flexible parallel electroadhesive structures under three-point bending, cantilever beam bending subjected to tip concentrated forces, and cantilever beam bending subjected to uniformly distributed forces, using the Euler–Bernoulli beam theory and considering friction and slip between layers by integrating the Maxwell stress tensor into the model. We find that: (1) three-point bending and cantilever beam bending under tip concentrated forces only have pre-slip and full-slip, whereas cantilever beam bending under uniformly distributed forces has an additional partial-slip which can be used for stiffness modulation; (2) the stiffness during the pre-slip stage is four times larger than the stiffness in the full-slip stage; and (3) increasing the voltage, dielectric permittivity, and coefficient of friction can elongate the pre-slip stage, thus enhancing the structural load capability. A customized three-point bending and a cantilever beam bending experimental setup were developed and the experimental deflection–force curve agreed relatively well with the theoretical one. The model, which considered electrode thickness and Young's modulus, and the results presented in this work are useful insights for understanding the variable stiffness mechanism of electroadhesive layer jamming and are helpful for their structural optimization towards practical applications. [ABSTRACT FROM AUTHOR]

The composites reinforced by graphene and its derivatives have demonstrated great potential in developing high-performance and smart materials and structures. This paper numerically studies the dynamic characteristics of functionally graded (FG) graphene platelets (GPLs) reinforced composite (FG-GPLRC) dielectric beam subjected to damping, mechanical excitation and electrical field. Required mechanical and physical properties of the composites are evaluated by effective medium theory (EMT). Governing equations for the structure are established based on Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship. Differential quadrature (DQ) and incremental harmonic balance (IHB) together with an arc-length algorithm are combined to discretize and solve the highly nonlinear equations. The effects of the geometry and concentration of GPLs, attributes of electrical field, FG distribution profile, excitation and damping on the dynamic characteristics of the beam are comprehensively investigated. Two transition regions for the effect of AC (alternating current) frequency of the electrical field on the dynamic performances of the beam are identified. There exist thresholds for GPL concentration, FG slope factor and aspect ratio for the dynamic response of the composite beam. It is indicated that the dynamic performances of the FG composite beam can be actively tuned by changing the attributes of the electrical field. The numerical investigation is envisaged to provide guidelines for the design and optimization of developing smart engineering structures. [ABSTRACT FROM AUTHOR]

In this article, theoretical modeling and vibration characteristics of a spinning double-blade beam assembly restricted by elastic supports are studied. Graphene nanoplatelet (GPL) reinforcement and porous foamed metal matrix are adopted to make up the assembly structure. Due to the nonuniformity of the porosity and graphene nanofillers, the material properties of the attached blades and beam are considered to change along the blade thickness and beam radius, respectively. They are obtained via the rule of mixture, the open-cell scheme and the Halpin-Tsai micromechanics model. These attached blades and beam are modeled in accordance with the Euler-Bernoulli beam theory and the Rayleigh beam theory, respectively. Via employing the Lagrange's equation, the equations of motion of the double-blade beam are derived. Then, the natural frequencies of the spinning nanocomposite double-blade beam are calculated by the substructure modal synthesis method and the assumed modes method. A detailed parameter analysis is performed to study the influences of dimension, distribution pattern and weight fraction of GPLs, distribution and coefficient of porosity, length and location of the blades, stiffness and location of supports, and spinning speed on the mechanical behaviors of the double-blade beam assembly. [ABSTRACT FROM AUTHOR]

We investigated the thermal buckling temperature and nonlinear free vibration of functionally graded fiber-reinforced composite laminated (FG-FRCL) beams. The governing nonlinear partial differential equations were derived from the Euler–Bernoulli beam theory, accounting for the von Kármán geometrical nonlinearity. Such equations were then reduced to a single equation by neglecting the axial inertia. Thus, the Galerkin method was applied to discretize the governing nonlinear partial differential equation in the form of a nonlinear ordinary differential equation, which was then solved analytically according to the He's variational method. Three different boundary conditions were selected, namely simply, clamped and clamped-free supports. We also investigated the effect of power-index, lay-ups, and uniform temperature rise on the nonlinear natural frequency, phase trajectory and thermal buckling of FG-FRCL beams. The results showed that FG-FRCL beams featured the highest fundamental frequency, whereas composite laminated beams were characterized by the lowest fundamental frequency. Such nonlinear frequencies increase for an increased power index and a decreased temperature. Finally, it was found that FG-FRCL beams with [0/0/0] lay-ups featured the highest nonlinear natural frequency and the highest thermal buckling temperature, followed by [0/90/0] and [90/0/90] lay-ups, while a [90/90/90] lay-up featured the lowest nonlinear natural frequency and critical buckling temperature. [ABSTRACT FROM AUTHOR]

This paper investigates a system of thermoelastic laminated beams with structural damping where Maxwell-Cattaneo's law, popularly referred to as the second sound, governs the heat flux. We unexpectedly achieve an exponential stability result depending only on the wave speeds of the system instead of the complicated stability number introduced in some papers in the literature. Consequently, our result substantially improves some of the results in the literature. [ABSTRACT FROM AUTHOR]

Helical springs with nonlinear geometric parameters nowadays have shown great advantages over classical linear springs, especially due to their superior performance in diminishing dynamic responses in high-speed situations. However, existing studies are mostly available for springs with linear properties, and the sole FE spring models using solid elements occupy significant computational resources. This study presents an FE spring model based on Timoshenko beam theory, which allows for high-speed dynamic simulations of nonlinear springs using a beehive valve spring sample. The dynamic results are also compared with the results of the FE model using solid elements and the results of the engine head test and indicate that the proposed FE model can accurately predict dynamic spring forces and the phenomenon of coil clash when simulating the beehive spring at engine speeds of both 5600 and 8000 RPM. The results also indicate that rapid coil impact brings significant spike forces. It should also be noted that the FE spring model using beam elements displays sufficient accuracy in predicting the dynamic responses of nonlinear springs while occupying much fewer computational resources than the FE model using solid elements. [ABSTRACT FROM AUTHOR]

To study the influence of interlayer stiffness and interlayer damping on the dynamic response of multi-layer beams under moving loads, a method for calculating the dynamic response of a multi-layer beam system considering random interlayer stiffness or random interlayer damping under successive moving loads based on the Karhunen-Lo'eve expansion and point estimation method is proposed. The accuracy of the proposed method was verified by using several numerical examples. The influence of interlayer stiffness, interlayer damping, standard deviation of interlayer stiffness, and standard deviation of interlayer damping on the dynamic response of a girder-rail system was analyzed by using the proposed calculation method. The results show that when the moving load velocity is high, the number of critical velocity of the rail significantly increases with decreasing interlayer stiffness. In addition, dynamic responses of the rail and girder increase with decreasing interlayer damping and the dynamic response of rail at the midspan significantly increases as the standard deviation of interlayer stiffness increases. Neglecting interlayer damping can lead to significant fluctuation in the dynamic response of rail, a significant increase in the number of critical velocity of rail, and increases in the dynamic responses of rail and girder. Changing interlayer stiffness, interlayer damping, standard deviation of interlayer stiffness, or standard deviation of interlayer damping will have no obvious influence on the dynamic response of girder. [ABSTRACT FROM AUTHOR]

In this paper, the flexural vibration of uniform and non-uniform rotating shafts based on the Timoshenko beam theory is investigated. Considering shear deformation and gyroscopic effects to build an exact framework of a solution, the fourthorder differential equation of vibration is solved by an analytical method. The overall transfer matrix of the system formed by a series of flexible distributed in addition to lumped elements is achieved. The results obtained by the distributed lumped modeling technique (DLMT) are verified with other techniques. The damped frequencies obtained by the hybrid modeling method for a multistep gas turbine rotor system using the Euler-Bernoulli and Timoshenko beam theories are compared with the results of the transfer matrix method (TMM). It is shown that the presented method provides highly accurate results, while with no compromise, it can be simply and effectively employed for complex systems. It is also shown how the Hooke and Jeeves and the ant colony optimization (ACO) besides the direct enumeration method can be applied to obtain the damped natural frequencies of complicated vibrational systems such as the gas turbine rotors. The comparison between the frequency and damping ratio values obtained by the optimization and direct enumeration methods shows less than 1% error for different cases. [ABSTRACT FROM AUTHOR]

This paper studies the vibration band-gaps of a non-uniform beam with periodically continuous variable cross sections and hinged supports. The governing equation of the beam is obtained by using spectral element method. The frequency responses of the beam under external excitation are shown. The accuracy and efficiency of the spectral element method are validated. The advantages of the proposed beam are discussed. The influences of the structural and material parameters on the band-gap properties are explored, such as the height curve, the disordered vibration absorbers, and the material attributes. The coupling effects of the local resonance band-gaps and the Bragg scattering band-gaps are explored and can be used to design the band-gap structure. The displacement amplitudes of the beam for different excitation frequencies are shown. [ABSTRACT FROM AUTHOR]

Machine learning models are widely used for decades in various engineering applications, such as structural health monitoring, optimization of the properties of engineering systems or structures. For instance, in structural engineering, researchers have investigated machine learning techniques for the prediction of the natural frequencies, damage detection, and design optimization of beams, frames, plates, and many other structures. Using machine learning is advantageous since machine learning can reduce the cost and time consumption to solve real-world problems. These techniques do not require powerful computers and software, unlike numerical analysis methods to solve such problems. To benefit such positive aspects of the machine learning techniques, the prediction of the first ten natural frequencies of aluminum and steel very thin, thin, and thick beam structures under fixed-free, fixed-simply supported, and simply supported boundary conditions by using Radial Basis Function Regressor, Random Forest Regressor, Multilayer Perceptrons Regressor, and Support Vector Machine Regressor with Pearson VII Universal Function Kernel (Puk) has been presented. The dataset required for the analysis is obtained via the Finite Element Analysis considering Euler-Bernoulli and Timoshenko Beam Theories. The performance of the machine learning models has been investigated and compared by examining (i) the thickness-length ratio, (ii) boundary conditions, and (iii) natural frequencies of the beam structures. Results indicate that the considered regression machine learning models are effective in predicting the natural frequencies of beam structures. Among all four regression machine learning models, Support Vector Machine Regressor with Puk and Random Forest models are robust and accurately predict the natural frequency values of the structures by an average accuracy of 98.78% and 98.88% regardless of the boundary conditions and thickness-length ratio of beam structures. On the other hand, Radial Basis Function Regressor and Multilayer Perceptron Regressors predict the first ten natural frequencies by 96.36% and 94.17%, respectively. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core. Design/methodology/approach: The FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature. Findings: A series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model. Originality/value: This paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Euler-Bernoulli beam theory for bending boundary value problem into mechanically coupled system. We follow the inverse approach to find the exerted force on two beams separated by elastic material. The theory was utilized in two ways: in the first approach, we calculate the force exerted on the beams using known values for the stiffness constant and measured values for the beam deflections. In the second method, we calculate the stiffness constant using a single known force and measured deflections. These problems are typically illposed problems whose solution does not depend continuously on the boundary data. To minimize the variational functional, we develop an iterative algorithm based on the system of three equations: the direct, adjoint, and control equations. Then, we present numerical examples to obtain the solutions. [ABSTRACT FROM AUTHOR]

In this study, the post-buckling behavior of a transverse functionally graded beam is investigated. Euler–Bernoulli beam theory (EBT) and shear deformable beam theories are taken into account in deriving the mathematical models of the beam using the vector approach. Timoshenko theory (TBT) and six different higher order beam theories (HOBT), namely Reddy, Touratier, Soldatos, Karma, Akavcı and Violet, are considered as shear deformable beam theories. It has been shown that mathematical models of shear deformable beam theories can be obtained using the vector approach. There are two different models developed for shear deformable beam theories depending on normal and shear forces and moment. It is found that the model which is named as Model 2 in this study yield inappropriate results. The functionally graded materials are characterized by using power law functions. The non-dimensional integro-non-linear differential equations system is solved analytically. The critical load values calculated for EBT, TBT and HOBT theories depending on different material conditions and slenderness ratio values are presented in tables. In addition, pitchfork bifurcation diagrams are drawn showing the post-buckling behavior of the beam. In addition, the regions where the examined beam theories are valid depending on the slenderness coefficient are shown. [ABSTRACT FROM AUTHOR]

This study investigates the size-dependent buckling behavior of Timoshenko nanobeams resting on Winkler-Pasternak foundations in a non-uniform thermal environment. A non-uniform temperature distribution is established through nonlocal heat conduction. Subsequently, the equivalent thermal load due to the obtained temperature distribution and boundary constraints is derived using the governing equations of the axial thermal deformation of the beams based on the stress-driven nonlocal elastic model. To obtain the critical buckling load of the nanobeams, the quadrature element method is used to numerically resolve the eigenvalue problem. In the numerical simulation section, we have presented a series of examples to analyze the effects of length-to-height ratios, nonlocal scale parameters, and Winkler-Pasternak foundation parameters on the buckling loads of the nanobeams under various boundary conditions. Moreover, we examine the effect of comprehensively considering both the elastic and thermal nonlocality on the thermal loads and finally mechanical buckling loads. [ABSTRACT FROM AUTHOR]

This paper presents a numerical procedure for evaluating the thermo‐mechanical response of Ultra‐High Performance Concrete (UHPC) beams exposed to fire. The numerical model is based on a macroscopic finite element formulation and utilizes sectional moment‐curvature relations to trace the response of UHPC beams from the linear elastic stage to collapse under combined effects of fire and structural loading. Fire‐induced spalling, temperature‐dependent properties of concrete and steel reinforcement, and realistic failure criteria are incorporated into the analysis. Specifically, an advanced analysis approach for evaluating spalling is incorporated in the model by considering the stresses arising from the combined effects of thermal gradients, structural loading, and pore pressure generated in the concrete section. Comparisons of the predictions from the model with data from fire resistance experiments show a good correlation, indicating the proposed model can reliably predict the thermo‐mechanical response, including the extent of spalling in UHPC beams subjected to fire exposure. The applicability of the model for undertaking advanced analysis is shown by conducting a case study to illustrate the influence of load level and fire scenario on the fire response of the UHPC beams. [ABSTRACT FROM AUTHOR]

Based on a dynamic discrete model of an out-of-plane curved beam with a constant curvature, eigen-properties of the spatial curved beam structure in undamaged and damaged configurations are considered in this paper. In the literature, based on the equivalent section reduction method, a distributed damage modeling method is proposed. Accoding to Euler-Bernoulli beam theory, the stiffness matrix of shear, bending and torsion coupling is derived. Combined with the lumped mass matrix and the characteristic equation of the multi degree of freedom system, natural frequencies of the undamaged and damaged structures are calculated. [ABSTRACT FROM AUTHOR]

In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement. [ABSTRACT FROM AUTHOR]

This paper has developed a Finite Element Method (FEM) to calculate the dynamic response of a continuous sandwich beam resting on elastic support subjected to moving vehicles. The equation of motion is derived using the classical beam theory and FEM. The vehicle model is a two Degree of Freedom (2DOF) system that moves with a constant velocity. The governing equation of motion is integrated by applying the Wilson-θ time integration method to obtain the dynamic response in each time step. Numerical examples investigate the displacement of the sandwich beam with various values of the structure and vehicle velocity. The effects of the stiffness of elastic support and the vehicle velocity on displacement are studied. [ABSTRACT FROM AUTHOR]

The warping effects may predominate in geometrically nonlinear analysis of open cross-section members. The formulation of conventional beam-column elements incorporating the warping effects is cumbersome due to the method considering the inconsistency between the shear center and centroid. To develop a concise warping element formulation, this paper presents a transformation matrix to integrate the inconsistent effects into the element stiffness matrix. The co-rotational (CR) method used to establish the element equilibrium conditions in the geometrically nonlinear analysis is adopted to simplify the element formulation and improve the efficiency of nonlinear analysis. A new beam-column element explicitly considering the warping deformation and the Wagner effects is derived based on the CR method and the Euler–Bernoulli beam theory. A detailed kinematic description is provided for considering large deflections and rigid body motions. Based on the mechanical characteristic, the coordinate and the rigid body motion transformation matrices are given. The secant relationship is developed to evaluate the element internal forces accurately and effectively in each iteration. Several verification examples are provided to validate the proposed method's reliability and robustness. The verifications demonstrate that the proposed element leads to considerable computational advantages. The results of this paper are useful for future upgrading of frame analysis software with warping degrees-of-freedom (DOFs). [ABSTRACT FROM AUTHOR]

In this study, nonlinear vibration and stability of a pipe conveying fluid, with axially moving supports, immersed in an external fluid is studied. The equation of motion is derived with the aid of the Newtonian method via employing the Euler–Bernoulli beam theory and plug flow assumption. Considering the stretching effect, the nonlinear equation of motion is obtained, and it is discretized via the Galerkin method. Afterward, the stability of the system is investigated using two different approaches, and their results are compared. Numerical simulations show the system has complex dynamic behavior. To unveil the dynamics of the system, various analysis techniques such as bifurcation diagram of Poincaré map, phase portrait, power spectrum, and time trajectories are used. Limit cycle, period-n, quasi-periodic, and chaotic regime are observed. It is found that pipe can flutter around the trivial solution or post-buckling equilibrium points. Moreover, the influences of some system parameters on the chaotic behavior of the pipe are discussed. [ABSTRACT FROM AUTHOR]

In this study, the critical load and natural vibration frequency of Euler–Bernoulli single nanobeams based on Eringen's nonlocal elasticity theory are investigated. Cantilever nanobeams with attached sprung masses were subjected to compressed concentrated and distributed follower forces. The parameter that determines the direction of nonconservative follower forces was given the positive and negative values, therefore, sub-tangential and super-tangential load were analyzed. The stability analysis is based on dynamical stability criterion and was carried out using a numerical algorithm for solving segmental nanobeams with many boundary conditions. The presented algorithm is based on the exact solutions of motion equations which are derived from equilibrium conditions for each separated segment of the nanobeam. Two comparison studies are conducted to ensure the validity and accuracy of the presented algorithm. The excellent agreement of critical load for Beck's nano-column on Winkler foundation observed was confirmed as reported by other researchers. The effect of different values of the nonlocality parameter, tangency coefficient, spring stiffness coefficient, location of sprung mass and the greater number of attached sprung masses on a critical load of nanobeams compressed by nonconservative load are discussed. One of the presented results shows that significant differences between local and nonlocal theory appear when the beam subjected to follower forces loses its stability by flutter. [ABSTRACT FROM AUTHOR]

Failure of pipelines below road pavement results to the disruption of both the traffic movement and the consumers of the pipelines. Intermediate safeguard layer can be used to protect the pipeline from heavy traffic loads. The present study proposed analytical solutions to obtain the dynamic response of buried pipe below road pavement with and without considering safeguard based on the concept of triple and double beam system respectively. Pavement layer, safeguard and the pipeline are considered as Euler Bernoulli's beam. Advanced soil model is used (viscoelastic foundation with shear interaction between springs) to model the surrounding soil. Self-weight of soil is also considered in the present study. The obtained governing coupled differential equations are solved adopting finite sine Fourier transform, Laplace transform and their inverse transformation. The proposed formulation is initially verified with the past numerical and analytical studies and then validated with the three-dimensional finite element based numerical analysis. From parametric study it is perceived that the stability of the pipe can be significantly increased by providing intermediate barrier. Further, pipe deformation is increases with increasing traffic loads. At very high-speed range (> 60 m s−1), pipe deformation is significantly rises with increasing traffic speed. The present study can be useful in preliminary design stage before performing rigorous and expensive numerical or experimental study. [ABSTRACT FROM AUTHOR]

The article discusses a study on 3D-printed micrometer-scale wireless magnetic cilia with metachronal programmability, published in the journal"Science Advances" The research team fabricated the cilia by printing silk fibroin hydrogel beams onto hard magnetic FePt Janus microparticles, offering a solution for creating bio-inspired microcilia in microfluidic systems, biomedical engineering, and biocompatible implants.