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This article aims to investigate the dynamics of clamped-clamped porous viscoelastic double microbeams interconnected via a viscoelastic layer within the framework of the modified couple stress theory (MCST). Different types of porosity distributions are considered to examine the material imperfection effects on the dynamics of the double microbeam. A closed-cell porosity model is employed to model the variation of the material properties in the thickness plane. The coupled longitudinal and lateral equations of motion are derived using Hamilton's principle. The governing equations of motion are solved using the modal decomposition method. The equations of motion are verified against the literature for simplified cases (i.e., a non-porous single viscoelastic microbeam and a porous single microbeam resting on a viscoelastic foundation). The numerical results are validated for simpler versions of the system using the finite element method and against the existing literature for a simplified case of a uniformly distributed porous double macrobeam connected via an elastic layer. Influences of viscoelasticity in the double microbeam, viscoelastic layer, porosity, and small-scale influences on the dynamics of the viscoelastic double microbeams are studied. It was found that increasing the material length-scale factor causes the complex fundamental lateral vibrational frequencies to increase for all the porosity patterns. [ABSTRACT FROM AUTHOR]

Reported in this paper is a cutting‐edge computational investigation into the influence of geometric characteristics on abdominal aortic aneurysm (AAA) rupture risk, beyond the traditional measure of maximum aneurysm diameter. A Comprehensive fluid–structure interaction (FSI) analysis was employed to assess risk factors in a range of patient scenarios, with the use of three‐dimensional (3D) AAA models reconstructed from patient‐specific aortic data and finite element method. Wall shear stress (WSS), and its derivatives such as time‐averaged WSS (TAWSS), oscillatory shear index (OSI), relative residence time (RRT) and transverse WSS (transWSS) offer insights into the force dynamics acting on the AAA wall. Emphasis is placed on these WSS‐based metrics and seven key geometric indices. By correlating these geometric discrepancies with biomechanical phenomena, this study highlights the novel and profound impact of geometry on risk prediction. This study demonstrates the necessity of a multidimensional assessment approach, future efforts should complement these findings with experimental validations for an applicable approach for clinical use. [ABSTRACT FROM AUTHOR]

The specific objective of this study is to analyze the dynamics of functionally graded carbon nanotubes (FGCNT) reinforced double plates. Connected via an elastic layer, the plates have simply supported boundary conditions. In the current study, three carbon nanotubes functionally graded patterns, varying in the thickness direction are considered, including uniformly distributed, functionally graded O-pattern, and functionally graded X-pattern. Following the development of the coupled equations of motion using the Hamilton principle while considering the influences of the elastic layer, the equations are subsequently solved utilizing a two-spatial-variable modal decomposition method. For verification purposes, the equations developed are compared to simplified configurations provided in the existing studies. The solution methodology is verified through comparing against numerical results of simplified configurations of plates obtained from the development of the finite element method and existing studies. Both verifications have shown very good agreement. Influences of plates' dimensions, carbon nanotubes reinforcement, and the stiffness of elastic layer are analyzed and provided in this study. The transverse-motion natural frequencies of the double plates are also identified, and they follow a decreasing trend as the aspect ratio increases for all the cases. The fundamental lateral-motion and axial-motion natural frequency also follows a similar trend as the aspect ratio increases. The reinforcement effect of carbon nanotubes on the transverse-motion natural frequencies is less obvious for thinner plates. An increase in the elastic layer stiffness increases the second series transverse-motion natural frequencies of the double-plate system. Among the considered functionally graded patterns, the functionally graded X-pattern reinforcement provides the largest increase in the transverse-motion natural frequencies. [ABSTRACT FROM AUTHOR]

Robot-assisted rehabilitation is a rapidly advancing field whereby robotic devices are used for the treatment of disabilities. Mechanism design and actuation of these devices play important roles in the treatment and the non-ergonomic designs may even increase the cardiorespiratory load and cause discomfort leading to further gait disorders. This article identifies crucial design and actuation aspects of gait rehabilitation robots and presents the first intrinsically compliant gait robot design with three actuated and five passive degrees of freedom, alleviating the prevalent issues. The gait robot joints remain aligned with the human anatomical joints during the swing and the stance phases due to the use of special bushes and dampers. The intrinsically compliant actuators on the new gait robot make it safe to work with human subjects. Increased degrees of freedom allow for natural walking dynamics instead of canceling or constraining them. The robot firmware, including the kinematic modeling, is designed using multiple adaptive neuro-fuzzy inference system to save on the computational time of the robot controller. The new robot design is finally validated for its intended use in gait rehabilitation, by employing a fuzzy logic controller and evaluating the position, velocity, and acceleration profiles of its joints. [ABSTRACT FROM AUTHOR]

One of the long-standing goals of rough wall fluid dynamics research is to determine the drag penalty of surfaces based solely on their topographical parameters. The most important length scale or roughness parameter that best describes a surface in relation to friction drag has not been agreed upon yet, despite the many studies that, over the years, have attempted to identify the most appropriate surface parameter. The concept of an equivalent sand-grain roughness (ks) was introduced to standardize different types of roughness in wall-bounded turbulence, serving as an input parameter for predicting the roughness function Δ U + . To anticipate Δ U + generated by a rough surface under turbulent flow conditions, experts use roughness correlations that establish a correspondence between the topographical characteristics of the surface and ks. Therefore, a chronological compilation of roughness correlations is presented, detailing the parameter ranges and types of roughness used in their development. This study evaluates the effectiveness of predictive correlation functions and aims to formulate a universal function by exploring a comprehensive assortment of three-dimensional (3D) surface textures available in the literature. The results suggest that a correlation based on surface height skewness (ksk) and streamwise effective slope (ESx) can predict the ratio ( k s / k q ), where kq is the root mean square roughness height for 3D roughness in the fully rough regime. Despite the fact that the correlation is restricted to 3D surface roughness, which is a more realistic representation, the model demonstrated a high level of accuracy in predicting ks for over 120 distinct rough surfaces. [ABSTRACT FROM AUTHOR]

In this paper, the mechanics of shear deformable micro beams is investigated via finite element analysis, and a machine learning technique (Deep Learning Neural Network (DLNN)). DLNN is provided for the first time to accurately model and predict this behavior. Using the Finite Element Method (FEM), the obtained coupled equations of motion for shear deformable micro-scale beams are solved using a combination of Timoshenko beam theory and the modified couple stress theory (MCST). The results are compared with literature for each analysis to show the accuracy and the proposed finite element model. After presenting the mechanical model, by using Finite Element Analysis (FEA), a deep learning neural network model is developed for small-scale structures and the capability of this model in predicting different mechanical behavior under thermo-mechanical loading is investigated. It is shown that the presented model has great accuracy in predicting both static and dynamic behavior of small-scale structures with a significant reduction in the computational cost. The application of DLNN for modeling the machines of small- scale structures is a step forward for predicting the behavior of Nano/Micro Electro Mechanical Systems (NEMS/MEMS). [ABSTRACT FROM AUTHOR]

Aortic dissection is a life‐threatening condition with a rising prevalence in the elderly population, possibly as a consequence of the increasing population life expectancy. Untreated aortic dissection can lead to myocardial infarction, aortic branch malperfusion or occlusion, rupture, aneurysm formation and death. This study aims to assess the potential of a biomechanical model in predicting the risks of a non‐dilated thoracic aorta with Stanford type A dissection. To achieve this, a fully coupled fluid–structure interaction model was developed under realistic blood flow conditions. This model of the aorta was developed by considering three‐dimensional artery geometry, multiple artery layers, hyperelastic artery wall, in vivo‐based physiological time‐varying blood velocity profiles, and non‐Newtonian blood behaviours. The results demonstrate that in a thoracic aorta with Stanford type A dissection, the wall shear stress (WSS) is significantly low in the ascending aorta and false lumen, leading to potential aortic dilation and thrombus formation. The results also reveal that the WSS is highly related to blood flow patterns. The aortic arch region near the brachiocephalic and left common carotid artery is prone to rupture, showing a good agreement with the clinical reports. The results have been translated into their potential clinical relevance by revealing the role of the stress state, WSS and flow characteristics as the main parameters affecting lesion progression, including rupture and aneurysm. The developed model can be tailored for patient‐specific studies and utilised as a predictive tool to estimate aneurysm growth and initiation of wall rupture inside the human thoracic aorta. [ABSTRACT FROM AUTHOR]

The impact of roughness skewness ( k s k ) on turbulent boundary layer (TBL) flow with a zero pressure gradient over three-dimensional (3D) sinusoidal rough surfaces was experimentally investigated using a single hotwire anemometer. Nine 3D sinusoidal profiles were manufactured with positive, negative, and zero roughness skewness values. Measurements were taken at three different freestream velocities for each surface and compared with smooth wall TBL results. This study covered a range of friction Reynolds numbers (R e τ ) from approximately 1000 to 4000, with δ / k ≈ 20 ± 2 , where δ represents the local boundary layer thickness, and k is the maximum height of the roughness, measured from the valley to peak. The results indicate that the wall-unit normalized streamwise mean velocity profiles for all rough surfaces exhibit a downward shift compared to the smooth wall profiles. Surfaces with positive roughness skewness produced the highest drag, leading to the largest downward shift. The friction coefficient ( C f ) decreased as k s k decreased. The percentage increase in C f and Δ U + (the roughness function) was much larger when moving from negative to zero roughness skewness than when moving from zero to positive roughness skewness. The small differences in turbulence intensity profiles and higher-order turbulence statistics in the outer region of the TBL support the outer layer similarity hypothesis for the roughness considered in this study. The autocorrelation study revealed that surfaces with positive roughness skewness tend to shorten the average length of turbulence structures in the near-wall region. [ABSTRACT FROM AUTHOR]

A developing zero pressure gradient (ZPG) turbulent boundary layer (TBL) over different three-dimensional (3D) sinewave roughnesses is investigated experimentally using single hot-wire anemometry. Seven different sinewave profiles are fabricated with the same amplitude and with different wavelengths in the streamwise ( s x ) and spanwise ( s z ) directions. The effects of varying s x and s z on turbulence statistics and the drag coefficient ( C f ) are assessed. The wall-unit normalized streamwise mean velocity profile is shifted downward compared with the smooth wall profile for all roughnesses. The streamwise spacing to height ratio s x / k has a more significant effect on the roughness function Δ U + and C f compared with the spanwise spacing to height ratio s z / k. However, s z / k has a large impact on the streamwise turbulence intensities in the log and outer layer. An excellent collapse is observed among the mean streamwise velocity profiles plotted in defect form in the outer region. However, a lack of similarity between TBLs over different rough surfaces is observed in the outer region for the turbulence intensities profiles. For isotropic 3D sinusoidal roughness (equal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing spacing to height ratios. For anisotropic 3D sinusoidal roughness (unequal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing s z / s x from half to two in this study. [ABSTRACT FROM AUTHOR]

In this study, a comprehensive analysis of visco-hyper-elastic thick soft arches under an external time-independent as well as time-dependent loads is presented from bending and internal resonance phenomenon perspectives. Axial, transverse and rotation motions are considered for modelling the thick and soft arch in the framework of the Mooney–Rivlin and Kelvin–Voigt visco-hyper-elastic schemes and third-order shear deformable models. The arch is assumed to be incompressible and is modelled using von Kármán geometric nonlinearity in the strain–displacement relationship. Using a virtual work method, the bending equations are derived. For the vibration analysis, three, coupled, highly nonlinear equations of motions are obtained using force-moment balance method. The Newton–Raphson method together with the dynamic equilibrium technique is used for the bending and vibration analyses. A detailed study on the influence of having visco-hyper-elasticity and arch curvature in the frequency response of the system is given in detail, and the bending deformation due to the applied static load is presented. The influence of having thick, soft arches with different slenderness ratios is shown, and the forced vibration response is discussed. Moreover, internal resonance in the system is studied showing that the curvature term in the structure can lead to three-to-one internal resonances, showing a rich nonlinear frequency response. The results of this study are a step forward in studying the visco-hyper-elastic behaviour of biological structures and soft tissues. [ABSTRACT FROM AUTHOR]

This paper presents a critical review of the nonlinear dynamics of hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. Hyperelasticity requires specific constitutive laws to describe the mechanical properties of different materials, which are characterised by a nonlinear relationship between stress and strain. Due to recent recognition of the high potential of hyperelastic structures in soft robots and other applications, and the capability of hyperelasticity to model soft biological tissues, the number of studies on hyperelastic structures and materials has grown significantly. Thus, a comprehensive explanation of hyperelastic constitutive laws is presented, and different techniques of continuum mechanics, which are suitable to model these materials, are discussed in this literature review. Furthermore, the sensitivity of each hyperelastic strain energy density function to coefficient variation is shown for some well-known hyperelastic models. Alongside this, the application of hyperelasticity to model the nonlinear dynamics of polymeric structures (e.g., beams, plates, shells, membranes and balloons) is discussed in detail with the assistance of previous studies in this field. The advantages and disadvantages of hyperelastic models are discussed in detail. This present review can stimulate the development of more accurate and reliable models. [ABSTRACT FROM AUTHOR]

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, k = 1.6 and 2.4 mm, and five different streamwise spacing of sx = 6k to 24k, (ii) three-dimensional (3-D) printed triangular ribs with heights of k = 1.6 mm and spacing of sx = 8k and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, k = 1.6 and 2.4 mm, and spacing of sx = 8k. These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height (23 < δ/k < 41), where δ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for sx = 8k. In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio sx/k exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope (ES) and the height skewness (ksk) appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for ks, the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime. [ABSTRACT FROM AUTHOR]

Coronary optical coherence tomography (OCT) is an intravascular, near-infrared light-based imaging modality capable of reaching axial resolutions of 10–20 µm. This resolution allows for accurate determination of high-risk plaque features, such as thin cap fibroatheroma; however, visualization of morphological features alone still provides unreliable positive predictive capability for plaque progression or future major adverse cardiovascular events (MACE). Biomechanical simulation could assist in this prediction, but this requires extracting morphological features from intravascular imaging to construct accurate three-dimensional (3D) simulations of patients' arteries. Extracting these features is a laborious process, often carried out manually by trained experts. To address this challenge, numerous techniques have emerged to automate these processes while simultaneously overcoming difficulties associated with OCT imaging, such as its limited penetration depth. This systematic review summarizes advances in automated segmentation techniques from the past five years (2016–2021) with a focus on their application to the 3D reconstruction of vessels and their subsequent simulation. We discuss four categories based on the feature being processed, namely: coronary lumen; artery layers; plaque characteristics and subtypes; and stents. Areas for future innovation are also discussed as well as their potential for future translation. [ABSTRACT FROM AUTHOR]

In this study, the time-dependent mechanics of multilayered thick hyperelastic beams are investigated for the first time using five different types of shear deformation models for modelling the beam (i.e. the Euler–Bernoulli, Timoshenko, third-order, trigonometric and exponential shear deformable models), together with the von Kármán geometrical nonlinearity and Mooney–Rivlin hyperelastic strain energy density. The laminated hyperelastic beam is assumed to be resting on a nonlinear foundation and undergoing a time-dependent external force. The coupled highly nonlinear hyperelastic equations of motion are obtained by considering the longitudinal, transverse and rotation motions and are solved using a dynamic equilibrium technique. Both the linear and nonlinear time-dependent mechanics of the structure are analysed for clamped–clamped and pinned–pinned boundaries, and the impact of considering the shear effect using different shear deformation theories is discussed in detail. The influence of layering, each layer's thickness, hyperelastic material positioning and many other parameters on the nonlinear frequency response is analysed, and it is shown that the resonance position, maximum amplitude, coupled motion and natural frequencies vary significantly for various hyperelastic and layer properties. The results of this study should be useful when studying layered soft structures, such as multilayer plastic packaging and laminated tubes, as well as modelling layered soft tissues. [ABSTRACT FROM AUTHOR]

Parallel robots are preferred over serial robots owing to their enhanced accuracy and rigidity which comes from their higher stiffness. However, there are applications both in industry and in healthcare where higher accuracy is required alongside high compliance (reduced stiffness). Accuracy and compliance being conflicting to each other are difficult to achieve simultaneously. To address this issue, an intrinsically compliant 6-dof parallel robot is proposed in this work. Kinematic and analytical modeling is performed for its conceptual design to obtain the Jacobian matrix and thereby map the joint and Cartesian spaces. Robot's structure design is analyzed, and the wrench analysis is also carried out to estimate the link forces and stiffness. It is shown that by small changes in the proposed robot design; its compliance can be altered making it suitable for a range of applications. It is also shown mathematically that the robot design can be optimized to maintain higher accuracy together with higher compliance. To carry out design optimization, three important performance criteria, namely; global condition number (for higher accuracies), norm of link forces (to reduce actuator power requirement) and robot compliance (for response to an external wrench) are mathematically formulated. Later, a multi-criteria optimization is performed using an evolutionary algorithm to simultaneously optimize these performance criteria. From the final robot design selected, it is evident that a higher robot compliance with optimal condition number and link forces can be achieved. [ABSTRACT FROM AUTHOR]

This article examines the free size-dependent vibration behaviour of an Euler–Bernoulli type double-microbeam system, made of two microbeams elastically connected, with simply supported, clamped–clamped and clamped–pinned boundary conditions using an assumed-mode expansion technique (AMET) along with finite-element verifications; effects of altering the couple-stress-tensor-related parameter and the stiffness coefficient of the elastic connection are studied. The double-microbeam problem is formulated nonlinearly utilising Hamilton's principle, alongside the modified couple stress theory (MCST), and energy terms. Employing the AMET, the free vibration characteristics were obtained through solving motion equations. For the double-microbeam system and the elastic connection, a finite-element method (FEM) based model and simulations are developed which enabled us in a partial verification of our results; the agreement is excellent. Moreover, another set of partial verifications is performed with available data in the literature by neglecting one of the microbeams and the spring connection. The study revealed increasing either the couple-stress-tensor-related parameter or stiffness coefficient of the elastic connection increases the natural frequencies of the double-microbeam system. It is also found that both the microbeams vibrate in the same manner in the first mode expansion and out of phase by 180° in the second mode expansion. Altering the boundary effect from pinned–pinned to clamped–pinned, and again to clamped–clamped was found to increase the natural frequencies of the double-microbeam system accordingly. [ABSTRACT FROM AUTHOR]

In this study, by functionally grading carbon nanotube (CNT) fibres through the axial direction of deformable beams, a new model for strengthening such structures is formulated. The strengthened deformable beam is additionally supported by a varying elastic foundation which is modelled via the Winkler–Pasternak elastic foundation. CNT distribution in the longitudinal direction is modelled using a power-law function presenting general forms of variation from linear to parabolic models. Equations of motion are determined using Hamilton's principle and are solved by employing the generalised differential quadrature approach method. A comprehensive parametric investigation is presented in order to indicate the influence of having CNT fibres distributed functionally through the length. It is shown that grading CNT fibres axially have a significant effect in varying the natural frequency parameter. Moreover, the influence of having Winkler–Pasternak elastic bed on the free vibration of such structures is discussed considering different types of foundation stiffness variation through the length. A comprehensive comparison study is presented to verify the current methodology and formulation by using previous literature for foundation modelling and FE modelling for linearly varying CNT's longitudinal distribution, which for all the cases, a good agreement between the results is observed. [ABSTRACT FROM AUTHOR]

A coupled nonlinear nonlocal strain gradient theory (NSGT) is developed for functionally graded Timoshenko nanoscale (FGTN) beams. This highly nonlinear-scale-dependent continuum model is solved numerically for dynamical responses for the first time. Hamilton's energy minimisation technique is used for rotation-equation of the nanobeam in addition to axial-displacement and transverse-displacement equations; these equations are coupled both nonlinearly and linearly, where decoupling is not possible. The functional nature of the material of the nanobeam is incorporated via the Mori–Tanaka mixture scheme. Small-scale influences are taken into account via the NSGT which is able to incorporate both softening/hardening effects. The coupled/nonlinear model is reduced to a high-dimensional system using Galerkin's method. The dynamics of the FGTN beam is analysed and the influence of functionally graded nature as well as the softening/hardening effects due to the NSGT is highlighted. [ABSTRACT FROM AUTHOR]

The application of robotic devices in providing physiotherapies to post-stroke patients and people suffering from incomplete spinal cord injuries is rapidly expanding. It is crucial to provide valid rehabilitation for people who are experiencing abnormality in their gait performance; therefore, design and development of newer robotic devices for the purpose of facilitating patients' recovery is being actively researched. In order to advance the traditional gait treatment among patients, exoskeletons and orthoses were introduced over the last two decades. This article presents a thorough review of existing robotic gait rehabilitation devices. The latest advancements in the mechanical design, types of control and actuation are also covered. The study comprehends discussions on robotic rehabilitation devices developed both for the training on treadmill and over-ground training. The assist-as-needed strategy for the gait training is particularly emphasized while reviewing various control strategies applied to these robotic devices. This study further reviews experimental investigations and clinical assessments of different control strategies and mechanism designs of robotic gait rehabilitation devices using experimental and clinical trials. [ABSTRACT FROM AUTHOR]

An attempt is made in this article to analyse the large-amplitude local dynamics of nanofluid-conveying nanotubes with geometrical imperfections. Each element of the nanotube can have displacements along both longitudinal and transverse directions. A nonlinear damping model is also taken into account utilising the Kelvin-Voigt approach. The stress nonlocality and strain gradient influences are modelled using an advanced scale-dependent theory. Moreover, the Beskok-Karniadakis approach is applied for relative motions at the nanotube wall. To present the coupled motion equations of the coupled nanotube, Hamilton's approach is used. Moreover, to develop a reliable solution procedure, Galerkin's method along with continuation technique is utilised. The effects of nonlinear damping, geometrical imperfection, being at nanoscales, fluid velocity and relative motion at the wall on the large-amplitude local dynamics are investigated. [ABSTRACT FROM AUTHOR]

The coupled nonlinear mechanical behavior of nonlocal strain gradient nanotubes subject to distributed excitation forcing is investigated for the first time. Both longitudinal displacements and transverse deflection are taken into consideration in both the continuum-based formulation and the numerical solution. The influences of being at the nanoscale level are modeled with the use of the nonlocal strain gradient theory. The coupled large amplitude motion characteristics are extracted via Galerkin's approach and a continuation method. The influences of scale coefficients, the slenderness ratio, and the force amplitude of the external forcing on the motion are examined. [ABSTRACT FROM AUTHOR]

In this article, the nonlinear parametric response of viscoelastic nanotubes conveying pulsatile flow is investigated. A two-parameter scale-dependent elasticity-based model is developed within the framework of a nonlocal theory with strain gradient influences. To model the effects of fluid molecules, which slip on the internal nanotube wall, on the parametric response, Karniadakis–Beskok approach is used. Viscoelastic effects are also described via Kelvin–Voigt scheme. Hamilton law, Galerkin and continuation techniques are, respectively, utilized in this analysis for obtaining, discretising and solving nonlinear coupled equations. Both subcritical and supercritical nonlinear parametric responses are examined considering various parameters such as the speed variation amplitude and frequency. The viscoelastic nanotube conveying pulsatile flow exhibits a hardening nonlinearity in the subcritical regime while it displays a softening nonlinearity in the supercritical regime. [ABSTRACT FROM AUTHOR]

An advanced nonlinear continuum model is presented to analyse the super and subcritical nonlinear behaviour of nanotubes. The nanoscale system is used to convey fluid flow at nanoscale levels. Due to the restrictions of one-parameter size-dependent models, a more comprehensive nonlinear coupled model containing two different size parameters is introduced using the nonlocal strain gradient theory (NSGT). Both axial and transverse inertial terms are taken into consideration, leading to more accurate results for nanotubes conveying fluid. In addition, since the mean free path of molecules is not negligible compared to the diameter of the tube at nanoscales, the Beskok–Karniadakis approach is implemented. The NSGT, Galerkin's technique and continuation method are finally employed to derive, discretise and solve the coupled nonlinear equations, respectively. The frequency–amplitude response, modal interactions and the possibility of energy transfer between modes are examined in both supercritical and subcritical flow regimes. [ABSTRACT FROM AUTHOR]

This article deals with developing a coupled scale-dependent model to explore the nonlinear bifurcation response of initially imperfect nanotubes conveying nanofluid flow taking into consideration the influences of nonlinear viscoelasticity. Furthermore, the influences of both centrifugal and Coriolis forces are considered. The Beskok–Karniadakis model is employed to capture the influences of slip at the interface between the imperfect viscoelastic nanotube and the nanofluid. A refined combination of nonlocal and strain gradient elasticities is employed for taking into consideration size influences. After formulating the kinetic energy, elastic energy, viscous work and external work, the nonlinear coupled equations are derived for the nanofluid-conveying nanosystem, which simultaneously vibrates along the transverse and longitudinal directions. The nonlinear dynamical characteristics are calculated via utilising a Galerkin procedure and a direct-time-integration technique. It is found that chaotic regions can be removed by imposing a proper geometric imperfection. [ABSTRACT FROM AUTHOR]

This paper analyses the coupled dynamics of nonuniform deformable axially functionally graded (AFG) viscoelastic microbeams with special consideration to a Kelvin–Voigt type viscosity in the FGM system. When modelling AFG viscoelastic systems, linear assumptions are commonly utilised to simplify numerical or analytical calculations. Another important factor which is usually neglected in the literature on AFG systems is to ignore in-plane/axial displacements/inertia. Viscosity between infinitesimal elements of AFG systems is also usually neglected to simplify calculations. This paper is the first to analyse the viscosity on the dynamical behaviour of AFG microbeams with the help of the Kelvin–Voigt method of viscosity, and the Euler–Bernoulli beam theory. The size dependence in the model and numerical simulations is incorporated via the modified version of the couple stress theory. Viscous stress-components of the Kelvin–Voigt model incorporated via their negative work contribution. The use of an energy balance generates the continuous model of the AFG system in the longitudinal as well as transverse directions. There are both nonlinear and linear couplings between elastically generated and viscous related terms. The nonuniform shape of the microbeam is incorporated via an axial-coordinate-dependent width. A truncation/discretisation for the coupled nonlinear model is performed using Galerkin's method. The couplings between the dynamics of the AFG viscoelastic microbeam is examined through analysing the influence of various microsystem parameters (e.g. gradient index, viscosity coefficient, and the taper ratio of the microbeam). [ABSTRACT FROM AUTHOR]

In this paper, the pulsatile coupled vibrations of a viscoelastic microtube conveying pulsatile fluid is examined for the first time. The problem is grouped into the class of parametrically excited, internally damped, gyroscopic where both Coriolis and parametric forces are present in the presence of viscosity. The Kelvin–Voigt approach of the viscosity, the Euler–Bernoulli for the deformation, the modified couple stress theory for the small size, and Hamilton's principle for deriving differential equations are used. Parametric frequency–response curves are obtained in the vicinity of the parametric resonance near the critical speed for both subcritical and supercritical regimes. The effect of the flow pulsation on the oscillations is investigated. [ABSTRACT FROM AUTHOR]

The large-amplitude vibrations of axially functionally graded (AFG) microcantilevers is investigated for the first time. Due to a harmonic base-displacement, the AFG microcantilever undergoes large time-varying deformations; the small-size influences are incorporated using the modified couple stress theory (MCST) and the large-amplitude vibrations is moderated. Exponential distributions along the length are considered for material properties. Hamilton's work/energy principle is used to balance the energies of the oscillating AFG microcantilever. The harmonic base-displacement is included via a relative motion rule. A truncation is conducted and a large-dimensional multi DOF system is obtained for an AFG microcantilever under inextensibility. A continuation method is utilised and frequency and base-displacement diagrams are obtained for different material gradient indices and the spatial variation of the material properties. [ABSTRACT FROM AUTHOR]

An investigation is performed on the viscoelastic nonlinear vibrations of functionally graded imperfect Timoshenko beams. The internal viscosity is incorporated using the Kelvin–Voigt scheme. Beam's centerline stretching is the cause of geometric nonlinearities. Material property distributions follow the Mori–Tanaka model. Shear deformation and rotary inertia are incorporated using the Timoshenko theory. A slight curvature is included to account for a geometric imperfection. The coupled axial/transverse/rotational motion model is developed using Hamilton's energy/work/energy loss. Galerkin's method is used, without neglecting the longitudinal inertia/displacement, and a large dimensional discretized/truncated model is obtained. Numerical integrations, using a continuation-based technique, are employed for force/frequency diagrams. Viscosity, material gradient index, and imperfection effects on the system vibrations are investigated. [ABSTRACT FROM AUTHOR]

A nonlinear viscoelastic model is developed for the dynamics of nanotubes conveying fluid. The influences of strain gradients and stress nonlocality are incorporated via a nonlocal strain gradient theory (NSGT). Since at nanoscales, the assumptions of no-slip boundary conditions are not valid, the Beskok–Karniadakis theory is used to overcome this problem. The coupled nonlinear differential equations are derived via performing an energy/work balance. The derived equations along the transverse and axial axes are simultaneously solved to obtain the nonlinear frequency response. For this purpose, Galerkin's technique together with a continuation method are utilized. The frequency response is investigated in both subcritical and supercritical flow regimes. [ABSTRACT FROM AUTHOR]

This is the first paper which investigates the nonlinear forced dynamic response of shear deformable functionally graded (SDFG) microscale beams with viscoelastic properties. A third-order model of shear deformations, which satisfies both the lower and upper boundary conditions, is utilised. The influences of viscoelastic properties are incorporated via the Kelvin-Voigt scheme. Furthermore, the influences of being at a miniature scale are captured via a modified couple stress theory (MCST). The material distribution of the microsystem is modelled via application of the Mori-Tanaka approach. Nonlinear three-dimensional coupled equations, which govern the size-dependent motions of the SDFG microbeam, are derived and then numerically solved. The present results show that for large coupled motions, the nonlinearity caused by viscosity plays a crucial role in the dynamics of SDFG microbeams. [ABSTRACT FROM AUTHOR]

The formulations for the modified couple stress theory (MCST) are consistently derived in general orthogonal curvilinear coordinate systems. In particular, the expressions for the rotation vector, higher-order strain, and stress tensors, i.e., the rotation gradient tensor and the deviatoric part of the symmetric couple stress tensor, and the classical strain and stress tensors are derived for an arbitrary orthogonal curvilinear coordinate system. Additionally, using the theory of surfaces, the formulations for the MCST are derived for general doubly curved coordinates, which are more convenient to use for shells of arbitrary curvature. The expressions for special cases, i.e., cylindrical and spherical shells, are obtained. The MCST expressions derived in this study are comprehensive and generally and can be used for consistent utilisation of the MCST in any orthogonal curvilinear coordinate system. [ABSTRACT FROM AUTHOR]

Viscosity effects on the mechanical behaviour of functionally graded (FG) Timoshenko microbeams are investigated; the model possesses both linear nonlinear viscous terms. The Mori-Tanaka homogenisation method is used for the continuous variations of the material properties of the microsystem along the thickness; the Kelvin-Voigt scheme is employed for the internal damping; the shear deformation and rotary inertia are modelled for the viscoelastic microbeam via the Timoshenko theory; the modified couple stress theory is used for size influences. An energy loss/balance via Hamilton's principle is used for obtaining the equations of motion. Galerkin's approach together with a continuation method is employed for the mechanical responses. The simultaneous effects of viscosity, being small, and FG materials on the mechanical behaviour are investigated. [ABSTRACT FROM AUTHOR]

This paper addresses the nonlinear resonant dynamics of axially functionally graded (AFG) tapered beams subjected to initial geometric imperfections, based on the Timoshenko beam theory. A rigorous coupled axial–transverse–rotational nonlinear model is developed taking into account the geometric nonlinearities due to the large deformations coupled with an initial imperfection along the length of the beam as well as nonlinear expressions accounting for nonuniform tapered geometry and mechanical properties. The Hamilton's energy principle is used to balance the kinetic and potential energies of the AFG imperfect tapered Timoshenko beam with the work done by damping and the external excitation load. This results in a set of strongly nonlinear partial differential equations (PDEs). The Galerkin decomposition scheme involving an adequate number of both symmetric and asymmetric modes is utilized to reduce the PDEs to a set of nonlinear ordinary differential equations. A well-optimized numerical scheme is developed to handle the high-dimensional discretized model. [ABSTRACT FROM AUTHOR]

The stability and bifurcations of viscoelastic microcantilevers is investigated via the Kelvin-Voigt scheme and the modified couple stress (MCS) theory. All the nonlinearities due to large deformations (due to the movement of the free end) are taken into account. The viscous segments of the deviatoric segment of the symmetric couple stress tensor and the stress tensor itself are considered. The energy loss due to viscosity is balanced with the energy input to the microcantilever. The equations for the transverse and axial motions are obtained and the inextensibility condition is applied, yielding an integro-partial-differential equation with inertial and stiffness nonlinearities. A continuation method is used for numerical solutions, with highlighting the viscosity effect on the large-amplitude motions. [ABSTRACT FROM AUTHOR]

Modal interactions and internal energy transfers are investigated in the large-amplitude oscillations of a functionally graded microcantilever with an intermediate spring-support. Based on the Mori–Tanaka homogenization technique and the modified couple stress theory, the energy terms of the functionally graded microsystem (kinetic and size-dependent potential energies) are developed and dynamically balanced. Large-amplitude deformations, due to having one end free, are modeled taking into account curvature-related nonlinearities and assuming an inextensibility condition. The continuous model of the functionally graded microsystem is reduced, by means of the Galerkin method, yielding an inertial- and stiffness-wise nonlinear model. Numerical simulations on this highly nonlinear reduced-order model of the functionally graded microcantilever are performed using a continuation method; a possible case of modal interactions is determined by obtaining the natural frequencies of the microsystem. The nonlinear oscillations of the microcantilever are examined, and it is shown how the energy fed to the functionally graded microsystem (from the base excitation) is transferred between different modes of oscillation. [ABSTRACT FROM AUTHOR]

A viscoelastic model for the nonlinear analysis of the coupled transverse, longitudinal, and rotational oscillations of an imperfect shear deformable microbeam is developed, for the first time, based on the modified couple stress theory. An energy dissipation mechanism is developed via use of the Kelvin–Voigt internal energy dissipation mechanism. For the stress and deviatoric part of the symmetric couple stress tensors, the viscous components along with the corresponding work terms are obtained. The size-dependent elastic energy along with the kinetic energy of the viscoelastic microsystem is formulated in terms of the displacement field together with system geometric and physical parameters. The internal energy dissipation is developed via the work done by the viscous components of the stress and the deviatoric part of the symmetric couple stress tensors by means of the Kelvin–Voigt mechanism. These work and energy terms are inserted into Hamilton’s principle together with the work due to an external force in order to obtain three viscoelastically coupled equations governing the transverse, longitudinal, and rotational motions with cubic and quadratic nonlinear terms. A high-dimensional Galerkin approximation method is applied for all the three equations, yielding three sets of second-order coupled ordinary differential equations with cubic and quadratic nonlinearities. Upon application of a transformation, a continuation technique along with the backward differentiation formula (BDF) is employed in order to obtain the time-variant response of the system subject to a harmonic load. Special attention is paid to the effect of the Kelvin–Voigt type viscoelasticity on the system response in the presence of the length-scale parameter. [ABSTRACT FROM AUTHOR]

A coupled parametric–transverse nonlinearly broadband energy harvester utilizing mechanical stoppers has been designed, fabricated, experimentally tested, and in some cases theoretically verified. An energy harvester with coupled parametric and transverse cantilever beams with additional tip-masses was excited using an electrodynamic shaker. A piezoelectric bimorph has been attached to each cantilever beam; when the excitation frequency was in the vicinity of the parametric or transverse resonances, the mechanical strain developed in the piezo-bimorphs was converted into electrical energy across a purely resistive ac load. For the cases involving no stoppers, a weak softening-type nonlinear frequency–voltage behavior was observed for the parametrically excited cantilever beam; however, with the addition of mechanical stoppers, both the transverse and parametrically excited cantilever beams displayed a strong hardening-type nonlinear frequency–voltage behavior. The stoppers substantially increased the operating bandwidth for both the parametric and transversely excited cantilever beams compared to the case without stoppers. For the theoretical investigations, a good agreement for both the fundamental frequencies and frequency–response curves was obtained. It is shown that by coupling transverse and parametric cantilevers with mechanical stoppers, the nonlinear energy harvested by the system takes place over a much broader frequency-bandwidth when compared to the singular transverse cantilever mechanism (by about 163.5%). [ABSTRACT FROM AUTHOR]

The nonlinear dynamical characteristics of a doubly curved shallow microshell are investigated thoroughly. A consistent nonlinear model for the microshell is developed on the basis of the modified couple stress theory (MCST) in an orthogonal curvilinear coordinate system. In particular, based on Donnell’s nonlinear theory, the expressions for the strain and the symmetric rotation gradient tensors are obtained in the framework of MCST, which are then used to derive the potential energy of the microshell. The analytical geometrically nonlinear equations of motion of the doubly microshell are obtained for in-plane displacements as well as the out-of-plane one. These equations of partial differential type are reduced to a large set of ordinary differential equations making use of a two-dimensional Galerkin scheme. Extensive numerical simulations are conducted to obtain the nonlinear resonant response of the system for various principal radii of curvature and to examine the effect of modal interactions and the length-scale parameter. [ABSTRACT FROM AUTHOR]

This paper analyses the coupled resonant motion of three-layered shear-deformable microbeams. On the basis of the modified couple stress theory, while both the rotational and translational motions are considered, the size-dependent potential energy of the three-layered microsystems is developed based on a continuous variation of the displacement field through the thickness and constitutive relations. The kinetic energy is also developed in terms of the continuous displacement field. The works done by the external dynamic load and the viscous damping are obtained in terms of the displacement field and microsystem parameters. A dynamic balance is applied to the works of external force and damping of the three-layered microbeam and its kinetic energy and size-dependent potential energy. The nonlinear continuous models for the longitudinal, transverse, and rotational motions are then reduced via use of a weighted-residual method. Numerical simulations upon the reduced-order models for the translational and rotational motions are performed for the three-layered microbeam via use of Houbolt’s finite difference scheme together with Newton-Raphson method. The size-dependent nonlinear coupled resonant responses of the three-layered microsystem are obtained and presented in the form of frequency-responses and force-responses. The effects of three-layered microsystem parameters such as the thickness and material percentage of each layer on the microsystem motion are examined. [ABSTRACT FROM AUTHOR]