Showing papers on "Rotary inertia published in 2022"

Static, stability and dynamic characteristics of asymmetric bi-directional functionally graded sandwich tapered elastic arches in thermo-mechanical environments

Abstract: This research paper investigates the in-plane static, stability and dynamic characteristics of tapered Timoshenko bi-directional functionally graded (BDFG) sandwich curved elastic arches (symmetric and asymmetric) in thermo-mechanical environments using the differential quadrature element method (DQEM). Physical properties such as Young's modulus , the mass density, Poisson's ratio and the thermal expansion coefficient are defined to vary both with respect to temperature and position while shear deformation , axial deformation , and rotary inertia effects are incorporated in the analysis. Different types of arches namely circular, parabolic, catenary, elliptic and sinusoidal models are modelled by having non-uniform cross-section and the BDFG properties. General functions are used to vary the physical properties through the thickness and length of the curved. Incorporating the influence of having a thermal environment for simplified models, the current methodology for studying such structures is verified by comparing the results with previously published literature and finite element software simulations. The effect of the temperature rise, physical properties variation and geometrical parameters (such as the ratio of thickness to length, the opening angle and non-uniform cross-section) on the static deformation, buckling load and free vibration characteristics of BDFG arches with metal/ceramics in the inner surface and ceramics/metal in the outer surface of the arch is investigated. In addition, the mechanical behaviour of sandwich arches for various combinations such as homogeneous or FG for outer skins and the inner core is presented under thermo-mechanical loadings.

Size-dependent vibration of laminated functionally graded curved beams covered with piezoelectric layers

Abstract: Abstract The nonlocal piezoelectric theory and first-order shear deformation theory are combined to study the nano-scale effect on the free vibration of a laminated functionally graded curved nano-beam covered with piezoelectric layers. The first-order shear deformation theory is introduced to consider the shear deformation and rotary inertia effects resulting from the torsional and flexural deformations. The effective elastic properties of the elastic nano-layers are estimated by using the Cox model. The governing equations are derived by employing Hamilton’s principle, and the efficient differential quadrature method is used to solve the discretized equations. Through numerical examples, it is found that the effects of beam thickness, volume fraction of fibers, curve parameter and boundary conditions on the natural frequencies are quite related to the nonlocal coefficient of curved beam. The vibration characters of curved nano-beam are discussed in detail.

Active flutter control of delaminated composite plate using active fiber composite patches

Abstract: The effect of delamination on flutter characteristics of delaminated plate and control of flutter velocity is presented in this paper. The structural model of the smart delaminated plate is constructed using a 3D degenerated element, where the shear deformation and rotary inertia are considered based on the Reissner–Mindlin assumptions. Using the modal output of the structural model through a direct matrix abstraction program (DMAP), aerodynamic forces are generated from MSC.Nastran. Further flutter analysis is carried out using the pk-method in the MATLAB environment. This MSC.Nastran coupled FE model is thoroughly validated with various examples of dynamic and aeroelastic analysis. The effect of delamination location and interface on flutter characteristics of laminated plate with various boundary conditions are investigated first, and an attempt is made to enhance flutter velocity of the delaminated plate through active control technique.

Parametric resonance of shear deformable nanotubes: A novel higher-order model incorporating nonlinearity from both curvature and inertia

Abstract: The research on nonlinear parametric resonance is of significance in the application of nanotubes in nanoelectromechanical systems . To capture the nonlinear behaviors of the nanotube in an accurate way, a size-dependent nonlinear model fully considering the transverse shear deformation , the nonlinearity from curvature and inertia is proposed for the first time. Specifically, the size-dependency is modeled by the nonlocal strain gradient theory coupled with surface effect. By introducing the accurate curvature, Zhang Fu's higher-order beam theory is developed to establish the refined displacement field. Besides, the axial nonlinear inertial force caused by transverse vibration is derived by introducing the hypothesis of “non-extensible beam”. The two-step perturbation-incremental harmonic balance method (TSP-IHBM) is developed to obtain both the stability boundary and bifurcation diagram . The accuracy is confirmed through convergence analysis and the validation by Runge Kutta method . Results provide four bifurcation topologies with different stiffness parameters and reveal the relationships between the stability boundary and the bifurcation diagram. It is found that the inertia nonlinearity may change the bifurcation diagram from stiffness hardening characteristics to softening characteristics. Also, parameter analysis provides the influence law of different size-dependent effects on the stability boundary and bifurcation diagram. • Propose size-dependent model fully considering nonlinear inertia and curvature. • Develop TSP-IHBM to obtain both stability boundary and bifurcation diagram. • Establish higher order shear deformation model coupling size-dependent effects. • Nonlinear inertia has great effects on response but little on stability boundary. • The effects of size-dependence may change the topology of bifurcation diagram.

Porosity-dependent free vibration and transient responses of functionally graded composite plates employing higher order thickness stretching model

Abstract: Tailoring the mechanical properties in hybrid materials, like functionally graded materials (FGMs), has become more pragmatic with the recent progress in material manufacturing and design. The porosities in FGMs, which develop during the manufacturing process, may become detrimental to armored plates or bulletproof designs. On the other hand, gradient-porosity distributions may have broad advantages in the design of lightweight and variable-stiffness aircraft components. The present study investigates the free vibration and transient responses of porosity-gradient FGM plates. A higher order theory, which considers the transverse shear and normal deformation, warping of the transverse cross-section, and higher order rotary inertia, is utilized for the first time to model the deformation of the porous FGM plate. The advantages of this model are (i) higher order kinematic terms for membrane and bending deformations due to the coupled membrane-bending behavior of FGMs in addition to the thickness-stretching effects, and (ii) the flexibility of applying external loads at different points along the thickness direction of the FGM plate. An analytical solution technique, popularly known as Navier’s approach, is adopted for the spatial solutions, and Newmark’s average acceleration method is utilized for the temporal solutions. The influence of the geometrical and porosity parameters on the structure’s vibration response is studied. Natural frequencies are affected significantly with uniform porosity distribution, while graded porosities can tweak vibration response in a small range but with better control. In the absence of the elasticity solutions, the present results may be considered the possible benchmark solutions for comparison of the other two-dimensional (2D) kinematic models.

Critical velocities and displacements of anisotropic tubes under a moving pressure

Abstract: Critical velocities and middle-surface displacements of anisotropic axisymmetric cylindrical shells (tubes) under a uniform internal pressure moving at a constant velocity are derived in closed-form expressions by using the Love–Kirchhoff thin shell theory incorporating the rotary inertia and material anisotropy. The formulation is based on the general three-dimensional constitutive relations for orthotropic elastic materials and provides a unified treatment of orthotropic, transversely isotropic, cubic and isotropic tubes, which can represent various composite and metallic tubes. Closed-form formulas are first obtained for the general case with both the rotary inertia and radial stress effects, which are then reduced to the special cases without the rotary inertia effect and/or radial stress effect. It is shown that when the rotary inertia effect is suppressed and the radial normal stress is neglected, the newly derived formulas for the critical velocities of orthotropic and isotropic tubes recover the two existing ones for thin tubes as special cases. An example for an isotropic tube is provided to illustrate the new formulas, which give the values of the critical velocity and dynamic amplification factor that agree well with those obtained experimentally and computationally by others.

Vibration characteristic analysis of tunnel structure buried in elastic foundation based on dynamic stiffness matrix

Abstract: In this study, the free vibration characteristics of a non-circular tunnel buried in a Winkler foundation are first investigated based on a dynamic stiffness approach and the Wittrick–Williams algorithm. The non-circular tunnel was modeled as a shell composed of multipartial circular cylinders based on the first shear deformation Flügge shell theory, by which the effects of shear deformation and moment of inertia were considered. The transfer function of the state variable was derived, and the elementary dynamic stiffness matrices were formulated based on this transfer function. Similar to the finite element method, the global dynamic stiffness matrix was established by assembling each elementary dynamic stiffness matrix. By solving the global dynamic stiffness matrix using the Wittrick–Williams algorithm, the natural frequencies and the corresponding mode shapes were determined. Subsequently, the calculated results were compared with literature and finite element analysis results, thus validating the accuracy and reliability of the proposed method. A parametric analysis was conducted to investigate the effects of the cross-section, stiffness coefficient, thickness, and length of the tunnel composed of multipartial circular cylinders. It was concluded that among the four types of cross-sections, the free vibration characteristics of the shells with close isoperimetric radii are similar. The natural frequencies of the shells buried in a moderately stiff Winkler foundation increase rapidly with its stiffness coefficient, whereas those of the shells buried in softer and stiffer foundations remain practically constant. The increase in shell thickness progressively increases the natural frequencies. In contrast, the natural frequencies decrease sharply with the increase in shell length; they first decrease to the lowest limits and subsequently remain unaltered. Thus, the free vibration characteristics of an actual tunnel structure resting on a Winkler foundation can be obtained by conducting the free vibration analysis on a sufficiently long shell segment, which is of major significance in the dynamic design of tunnel structures.

Further insights into the timoshenko-ehrenfest beam theory

Abstract: In this paper, the theory of a Timoshenko-Ehrenfest beam is revisited and given a new perspective with particular emphasis on the relative significances of the parameters underlying the theory. The investigation is intended to broaden the scope and applicability of the theory. It has been shown that the two parameters that characterise the Timoshenko-Ehrenfest beam theory, namely the rotary inertia and the shear deformation, can be related and hence they can be combined into one parameter when predicting the beam's free vibration behaviour. A theoretical proof is given that explains why the effect of the shear deformation on the free vibration behaviour of a Timoshenko-Ehrenfest beam for any boundary condition will be always more pronounced than that of the rotary inertia. The range of applicability of the Timoshenko-Ehrenfest beam theory for realistic problems is demonstrated by a set of new curves, which provide considerable insights into the theory.

Whirl dynamics of an axially functionally graded liquid-filled rotor considering shear deformation and rotary inertia

Abstract: In this study, whirl characteristics and stability of an axially functionally graded (AFG) liquid-filled rotor are investigated. The rotor is modeled based on the spinning Timoshenko beam theory. The governing equations for flexural vibration are derived via Hamilton’s principle. For pinned–pinned AFG liquid-filled rotor, the analytical solutions are derived for both the exact whirl frequency equation and the stability model. To validate the present formulations, comparative studies by numerical solutions available in the literature are conducted. Some numerical examples are performed to investigate the effects of gradient parameter, mass ratio, cavity ratio, rotary inertia, and shear deformation on the whirl speed, the critical spinning speed, and the stability of the AFG liquid-filled rotor system. The results show that these parameters have noticeable influences on dynamic behavior and stability of the rotor system. In particular, the rotary inertia and shear deformation play an important role in the stability analysis for different length rotors.

Thermal buckling analysis of a saturated porous thick nanobeam with arbitrary boundary conditions

Abstract: Abstract This manuscript aims to research the thermal buckling of saturated thick (Timoshenko) nanobeams under different boundary conditions using Fourier sine and cosine series for the first time. The equation of motion and related boundary conditions are derived by using the kinematic relations of shear deformation (Timoshenko beam) theory to contain the shear effect. Consequently, the rotary inertia and transverse shear strain are considered through the mathematical analysis. Fourier sine and cosine series are used to compute the critical buckling temperature of the thick saturated nanobeam with deformable boundaries. To check the validity of the presented method, the developed Fourier series method with Stokes’ transformation is applied to validate the thermal buckling of rigidly supported thick nanobeam by giving the proper values to spring parameters. In particular, the presented analytical procedure can also be degenerated to the thin Euler-Bernoulli nanobeam by assigning proper value to shear correction factor. Influence of the deformable boundary conditions, small scale parameter and the saturated parameter (porosity coefficient) on the thermal buckling temperature are discussed in detail. The theoretical models and eigen-value formulation presented herein should also be served to solve the thermal stability response of different micro sized-structures with various temperature effects and supporting conditions.

Nonlocal Timoshenko modeling effectiveness for carbon nanotube-based mass sensors

Abstract: Carbon nanotubes (CNTs) have been considered for a wide range of nanotechnology applications due to their unique mechanical, thermal, and electrical properties. One of the most notable nanotechnology applications is the frequency shift-based carbon nanotube mass sensor, which has motivated the development of reliable reduced-order models. As such, this research effort focuses on a carbon nanotube-based mass sensor that utilizes Timoshenko beam theory to extend the usability of these models to short and stout structures. Additionally, Eringen's nonlocal elasticity is considered to account for certain nanoscale phenomena. To the authors' knowledge, this is the first time a CNT-based mass sensor modeled with the nonlocal Timoshenko beam theory with a complex-shaped deposited particle has been studied. Considering Timoshenko beam theory and Eringen's nonlocal theory, the Hamilton's principle is utilized to derive the governing equations of motion, boundary conditions, and continuity conditions accounting for a single deposited nanoparticle . Then, it is shown that the obtained frequency shift of the sensor is dependent on the rotary inertia , shear effects, nonlocal parameter, and particle mass, geometry, and location. The variation of each of these parameters leads to a holistic characterization of the proposed system. The discrepancies and limits of applicability between Timoshenko and Euler-Bernoulli models are deeply explored and discussed, particularly for short and stout structures. It is shown that the Euler-Bernoulli model leads to an overprediction of the frequency shifts compared to Timoshenko beam theory, especially for higher modes. The nonlocal Timoshenko-based model is valuable because short and stout structures were found to be preferred for mass sensing applications, since they lead to a higher sensitivity. Other researchers can utilize these findings for the design, modeling, and analysis of nanoscale sensors and resonators.

Dynamic stiffness matrix with Timoshenko beam theory and linear frequency solution for use in compliant mechanisms

Abstract: The kinetostatic and dynamic formulation of planar compliant mechanisms is investigated by making use of the dynamic stiffness method based on Timoshenko beam theory. This research is prompted by the significance of considering both the shear deformation and rotary inertia for short and thick flexure beams widely used in compliant mechanisms. We investigate the problem by developing the frequency-dependent dynamic stiffness matrix with the pseudo-static characteristic for a threefold purpose. The first is to show that a closed-form dynamic stiffness matrix of flexure beams in power series of frequency including the shear deformation and rotary inertia is effective that is parameter-insightful and from a computational standpoint concise. Secondly, a programmable stiffness and mass assembling procedure is developed to build the kinetostatic and dynamic model for compliant mechanisms in a general sense. The third target is to accelerate the calculation efficiency of dynamic stiffness model by introducing a linear solution strategy of natural frequencies which is beneficial for parameter optimization iteration. The presented approach is demonstrated by applying to the parameter influence analysis and dimension synthesis of a bridge-type compliant mechanism widely used in micro displacement and/or force amplifications.

Least Square Method for the Identification of Equivalent Inertia Constant

Abstract: This paper proposes a simple yet accurate least square method to identify the equivalent inertia constant of individual inertia providers. The proposed method requires ambient measurements and is based on the well-known classical swing equation of synchronous machines. The proposed method shows a very good accuracy for the inertia identification of the rotational and virtual inertia in different operating conditions, including stationary ones, and can also be used to quantify the inertia support effect of the time-varying adaptive inertia.

The Measurement of Moment of Inertia by Using Three Wire Pendulum

Abstract: Moment of inertia is a physical quantity of great significance for the rotation of objects. This formal laboratory report studies the use of three-wire pendulum to measure the moment of inertia of an object. The main principle is to use the period of the torsional pendulum motion of the object to approximate the moment of inertia by the conservation of mechanical energy. The experiment verifies the feasibility of measuring the moment of inertia by using a three-wire pendulum within the error range. At the same time, the parallel axis theorem is proved experimentally.

Vibration control device having variable moment of inertia by MR fluid inside a flywheel

Abstract: An inertia effect is proportional to acceleration and mass as a negative force, keeps own situation of a body during movement under inertia law. It is obvious that the inertia mass effect is available to decrease own natural frequency and arise anti-resonance which can be shut down vibration in a special case. In previous paper the authors updated a vibration control device which was having variable moment of inertia by Magneto-Rheological fluid inside a flywheel. Ferrite particles of the MR fluid are clustered when magnetic field is applied by 8 electromagnets to the flywheel. It was clear that the inertia mass effect was varied as higher current, and vibration control effect under the earthquake was confirmed numerically and experimentally. If inertia mass effect can be switched depending on anti-resonance, vibration may be able to be suppressed under the earthquake. Recently some researchers focus reinforcement learning to decrease vibration. Therefore, to switch mass inertia effect, reinforcement learning is adopted. In this paper firstly the vibration control device with thin iron plate attached inside the flywheel is updated from prototype in order to get more inertia effect. Secondly, Deep Deterministic Policy Gradient (DDPG) which is a part of reinforcement algorithm is adopted in order to decrease vibration by inertia mass effect, and vibration tests of one degree-of-freedom were carried out.