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Many civil and mechanical engineering structures can be simplified as double-beam systems, i.e., a primary beam and a secondary beam connected to the primary beam. Many studies have investi...

Friction bounds the lower performance in control applications. Effective product modeling of controlling mechanisms and capturing the nonlinearity imposed by friction always attract the attention of researchers. Present work intends to capture the nonlinear dynamic behavior of a mechanical system with control release operation under boundary friction. The system used for this purpose is a second-order mechanical system comprising of rotary inertia element (lever), linear element (targeted mass), and spring element. The mechanical system chosen bears a resemblance to actual systems with control release like actuators, hydraulically operated copy turning machine, flight control mechanism, and robotics. The system dynamics have been captured under the light of two friction models viz. LuGre model and Dahl model. The performance of the system under these two friction models is ascertained for different times taken by the mass to settle, post and pre-zero-crossing time taken by target mass, maximum amplitude, time-period, and amplitude decay. The present work is capable of providing guidelines to simulate systems with control release under friction.

Research evidence abounds on the effectiveness of micropillar-based microelectromechanical systems for the detection of a wide variety of ultrasmall biological objects for clinical and non-clinical applications. However, the standard micropillar-based sensing platforms rely on a single-column micropillar with a spot at the tip for binding of objects. Although this long-standing form has shown immense potential, performance improvement is hindered by the fundamental limits enforced by physical laws. Moreover, the single-column micropillar has a lower sensing area and is ill-suited for a simultaneous differential sensing of chemical/biological objects of different mass. Here, we report a new set of nature-inspired, branched micropillar-based sensing resonators to address the highlighted issues. The characteristics of the newly proposed branched micropillars are comprehensively examined with three payloads (Bartonella Bacilliformis, Escherichia coli, and Micro magnetic beads). Anchored on the capability of continuum theoretical framework, the mathematical model of the micropillar is formulated through the synthesis of the modified couple stress, the Rayleigh-Love, and the Timoshenko theories. The finite element method is employed to shed light on the variability of the structures' resonant response under performance reduction factors (payload's rotary inertia, damaged substrate, and density of a surrounding fluid). The results obtained indicate superior performance indicators for the triply-branched micropillar: enhanced response sensitivity for multiple payloads and less susceptibility to deterioration in resonant frequencies due to fluid immersion.

Purpose In this paper, the important aspects of vibration analysis of carbon nanotubes (CNTs) as nano-resonators are studied. This study has covered the important nonlinear phenomena such as jump super-harmonic and chaotic behavior. CNT is modeled by using the modified nonlocal theory (MNT). Design/methodology/approach In previous research studies, the effects of CNT’s rotary inertia, stiffness and shear modulus of the medium were neglected. So by considering these terms in MNT, a comprehensive model of vibrational behavior of carbon nanotube as a nanosensor is presented. The nanotube is modeled as a nonlocal nonlinear beam. The first eigenmode of an undamped simply supported beam is used to extract the nonlinear equation of CNT. Harmonic balance method is used to solve the equation, while to study its super-harmonic behavior, higher-order harmonic terms were used. Findings In light of frequency response equation, jump phenomenon and chaotic behavior of the nanotube with respect to the amplitude of excitation are investigated. Also in each section of the study, the effects of elastic medium and nonlocal parameters on the vibration behavior of nanotube are investigated. Furthermore, parts of the results in linear and nonlinear cases were compared with results of other references. Originality/value The present modification of the nonlocal theory is so important and useful for accurate investigation of the vibrational behavior of nano structures such as a nano-resonator.

This paper presents an analytical study on the dynamic instability of castellated columns subjected to axial excitation loading. By assuming the instability modes, the kinetic energy and strain energy of the columns and the loss of the potential of the axially applied load are evaluated, from which the mass matrix, stiffness matrix, and geometric stiffness matrix of the system are derived. These matrices are then used for deriving dynamic equations and carrying out the analysis of dynamic instability of castellated columns by using Bolotin’s method. The analytical expression for determining the critical excitation frequency of the columns is derived, which takes account for not only the shear influence of web openings but also the rotary inertia effect on the transverse vibration of the columns. Numerical examples are also provided for illustrating the dynamic instability behaviour of castellated columns when subjected to axial excitation loading. The results show that the consideration of the shear effect in castellated columns results in a shaft of the dynamic instability zone to low frequency side and a reduction of the width of the dynamic instability zone. The shear effect on the dynamic instability zone becomes more significant in the short column than in the long column, and in the wide flange column than in the narrow flange column.

In spite of the current use in modern civil engineering of straight structural components made of reinforced concrete, such as beams and slabs, arches still remain quite often adopted in architectural design, due to their interesting mechanical and esthetical properties. Therefore, practical analytical and numerical tools should be available in order to allow designers to ensure the resistance and stability of this type of structures, especially in the dynamic regime and when point masses are added. The sixth degree differential equation of motion of inextensible arches is known to be quite difficult to deal with and is not applicable to the case examined here of arches with added point masses [1]. The procedure adopted in this article consisted on finding relatively easy particular solutions of this equation satisfying the end conditions and using them as trial functions in the Rayleigh-Ritz formulations of the practical cases of interest. Circular arches of different opening angles are examined here under the classical hypotheses: (1) the effect of shear deformation and rotary inertia are neglected (2) the arch axis is inextensible (3) the dimensions of the cross-section are small in comparisons with the radius;(4) the cross-section is uniform. Three different kinds of end conditions are considered: simply supported-simply supported (SS), clamped-simply supported (CS) and clamped-clamped (CC). The Rayleigh-Ritz method allowed in each case to determine, via an algebraic solution of the associated eigenvalue problem, the first seven mode shapes and natural frequencies of arches with different values of the opening angle. The comparison with the results available in the bibliography was satisfactory and the mode shapes were plotted. The second part of this work was devoted to arches with added concentrated masses: likewise, the numerical values found for the natural frequencies compare quite well with the few references available and the mode shapes are plotted showing the effects of the opening angle, the mass and the positions of the added point masses.

Purpose The purpose of this paper is to propose and analyze the free vibration response of the spatial curved beams with variable curvature, torsion and cross section, in which all the effects of rotary inertia, shear and axial deformations can be considered. Design/methodology/approach The governing equations for free vibration response of the spatial curved beams are derived in matrix formats, considering the variable curvature, torsion and cross section. Frobenius’ scheme and the dynamic stiffness method are applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. Findings To assess the validity of the proposed solution, a convergence study is carried out on a cylindrical helical spring with a variable circular cross section, and a comparison is made with the finite element method (FEM) results in ABAQUS. Further, the present model is used for reciprocal spiral rods with variable circular cross section in different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the results provide a relatively accurate solution. Originality/value The numerical results show that only a limited number of terms are needed in series solutions and in the Taylor expansion series to ensure an accurate solution. In addition, with a simple modification, the present formulation is easy to extend to analyze a more complicated model by combining with finite element solutions or analyze the transient responses and stochastic responses of spatial curved beams by Laplace transformation or Fourier transformation.

This paper aims to propose an analytical solution for dynamic analysis of the hetero junction carbon nanotubes (HJCNTs)-based mass nanosensors using a nonlocal strain gradient Timoshenko beam model. To have a more precise nanosensor, it is necessary to have deep information about the vibration characteristics of the nanostructure. So, two main goals are followed in this paper. At first, the vibration of HJCNTs with general (elastic) boundary conditions and without attached mass are studied using a proposed analytical solution. Afterward, the HJCNT is applied as a cantilever mass sensor for sensing light as well as heavy masses attached to its tip. For the large and heavy masses, the rotary inertia of the attached mass is also considered in the analysis. The governing differential equations are derived based on the Hamilton's principle and solved by an analytical method, which is based on the modified Fourier series. The weighted residual method is employed for obtaining the variationally consistent boundary conditions using the known equations of motion of the structure. The field quantities are obtained in the closed forms. The convergence and accuracy of the proposed solution are validated through some special cases available in the literature. The effects of small scale parameters and the elastic boundaries on the frequency and mode shapes of HJCNTs are studied. Moreover, the factors that affect the frequency shift of HJCNT-mass sensor are discussed. The obtained results introduce HJCNTs as new mass nanosensors that can operate more efficiently than uniform CNTs. This paper can be greatly useful in designing HJCNT-mass sensors and may serve as a benchmark for the future research in this field.

Cut-outs are the integral parts of laminated plate components in a variety of civil, aerospace and marine engineering applications. Cut-outs alter the dynamic behaviour of the structures by reducing mass and stiffness simultaneously. The glass epoxy laminates are fabricated by resin infusion method through vacuum bagging system in the laboratory. The experimental studies are carried out on composite plates with cut-out positioned at different locations in the laminate. A finite element formulation based on the first-order shear deformation theory is developed in the present study using nine noded isoparametric shallow shell elements. The effects of rotary inertial contribution of mass on the natural frequencies are studied in the present paper. The present finite element formulation is validated by comparing the solutions obtained in terms of natural frequencies with the relevant published results and also experimental data. The correlation between experimental and numerical mode shapes is established by using modal assurance criteria.

An improved mathematical model of a piezoelectric vibrating gyroscope is constructed with the effects of electromechanical coupling and rotary inertia taken into account. The gyroscope consists of a cantilever beam with tip mass attached to its free end. The piezoelectric materials are adhered to the four surfaces of the rectangular beam. By using two Euler angles and extended Hamilton’s principle, the electromechanical coupled partial differential equations governing the flexural-flexural motions of the piezoelectric gyroscope are obtained. The accuracy and effectiveness of the comprehensive mathematical model are validated by the existing models in literature. The necessity of taking rotary inertia into account is discussed. The natural frequencies of the rotating piezoelectric beam in both drive and sense directions have been investigated by considering the effects of the tip mass, angular speed, and external impedance. The dynamic behaviors of the piezoelectric gyroscope with different parameters, such as the tip mass, the lengths of piezoelectric materials and beam, and the external impedance, have been studied. In particular, the optimal combination of the external excitation frequency and the external impedance for the best calibration curve of the piezoelectric gyroscope is identified. Finally, the dynamic performance of the piezoelectric gyroscope under varying boundary conditions has been investigated for the potential practical applications.

This paper presents a new hybrid analytical/numerical systematic approach for continuous modeling of wave propagation in planar structural systems. To do so, a structure is considered as a number of waveguide elements that are connected to each other through different types of discontinuities. The wave propagation in waveguides is modeled using advanced Timoshenko beam theory to account for the rotary inertia, which provides accurate results for high-frequency excitations. The refraction matrices for different types of discontinuities such as change of material and cross section, various types of boundary conditions, and two- and three-member joints are presented using the existing literature, and the refraction matrices for a right-angled four-member joint is derived analytically for the first time. To provide a robust methodology for the analysis of large structural systems, a general new assembly procedure is introduced that is capable of assembling all of the propagation and refraction matrices in a single global system matrix. To insure the validity of the proposed methodology, detailed numerical examples are provided and their results are verified with finite element numerical method.

In this study, the nonlinear vibration and stability of a simply supported axially moving Rayleigh viscoelastic beam equipped with an intermediate nonlinear support are investigated. The type of considered nonlinearity is geometric and is due to the axial stretching. The Kelvin–Voigt model is used to regard the beam internal damping. The Hamilton’s principle is employed to derive the governing equations and corresponding boundary conditions. The multiple scales method is applied to the dimensionless form of the governing equations and the nonlinear frequencies, time response of the system for two cases of the axial velocity fluctuation frequency are obtained. The stability of the system is investigated via solvability condition and Routh–Hurwitz criterion. Some case studies are accomplished to demonstrate the effect of rotary inertia, axial velocity and parameters of intermediate support on the system response, critical velocity and the system stability. Furthermore, the variation of the first two resonance frequencies with respect to mean axial velocities for different locations of the intermediate support are investigated. It is found that by moving the intermediate support from one end of the beam to its midpoint, the region in which the first mode undergoes static instability, shrinks. Moreover, although rotary inertia impressively decreases the natural frequencies, intermediate support has the dominant effect on increasing the natural frequencies.

In this paper, the vibration analysis of a Silicon Biological Nano-sensor (SBNS) with full coverage of Myosin as biologically adsorbent layer is investigated based on modified nonlocal Euler–Bernoulli beam model. This SBNS works based on calculating the shift of resonant frequency in the presence of Myosin layer and adsorbed viruses and bacteria. For this end, the effects of surface stresses, nonlocal parameter, and rotary inertia as well as the mass and stiffness of the adsorbent layer are taken into account, which can play a major role in changing the resonant frequency and the precision of SBNSs at nano-scale. The results illustrate that the effects of adsorbent layer, surface stresses, nonlocal parameter and rotary inertia may reduce resonant frequency of SBNS, which is significant especially at nano-scale. Finally, for the purpose of verification assessment, the numerical results were compared with the results of other studies and showed complete agreement. The present study can provide helpful insights for the design and characterization of accurate biological Nano-sensors.

This paper investigates the dynamic behavior of uniform Rayleigh beam resting on Pasternak foundation and subjected to exponentially varying magnitude moving the load. The solution techniques are based on finite Fourier sine transformed Laplace transformation and convolution theorem. The results show that for a fixed value of axial force, damping coefficient and rotatory inertia, increases in shear modulus and foundation modulus reduces the response amplitude of the dynamical system. It was also found that increases in axial force, rotary inertia, and damping coefficient for fixed values of shear modulus and foundation modulus lead to decreases in the deflection profile of the Rayleigh beam resting on Pasternak foundation. Finally, it was found that the effect of shear modulus is more noticeable that of the foundation modulus.

Micro-milling is one of the micro-manufacturing techniques used for creating micro-scale features. In this article, a size-dependent formulation based on the strain gradient elasticity theory is developed to analyze the micro milling tool vibration. A new cutting forces formulation in rotating frame is presented in this paper. Considering structural nonlinearities , gyroscopic moment, rotary inertia , process damping and size effect, nonlinear equations of tool motion are derived using non-classical Timoshenko beam theory and Hamilton's principal. Partial differential governing equations of the tool are converted to ordinkary differential equations by using assumed modes method. Then the method of multiple scales is used to obtain the analytical solution for tool vibrations. The proposed approach is applied to investigate the chatter instability observed in micro-milling operations. To verify the presented model, simulated stability lobe diagrams are compared with the results obtained from experimental tests and literature. According to the results, neglecting size effect, gyroscopic and rotary terms in the tool model causes significant errors in prediction of the chatter in micro-milling process.

In spite of gaining practical importance of functionally graded (FG) shafts, stability analysis of such FG rotor-bearing system has not been reported yet. This paper presents the development of a finite element (FE) procedure and code for stability analysis of cracked FG rotor-bearing system under thermal environment. Two-noded Timoshenko beam elements are used to model the FG shaft considering the effects of gyroscopic moments, translational and rotary inertia, bending and shear deformation and material damping. Zirconia (ZrO2) and stainless steel (SS) are considered as constituents of the radially graded FG shaft with temperature dependent material properties. Considering breathing crack behaviour, local flexibility coefficients (LFCs) are derived using the Paris's equation and the Castigliano's theorem. Results show that while the depth, orientation and locations of cracks, thermal gradient and material damping affect the stability threshold speed, it is important to choose the material gradient index judiciously. Thus, even when surface cracks appear on the FG shaft, threshold speed could still be in the desired range, which is important for damage tolerant design in high temperature applications.

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the effects of the Winkler coefficient, Pasternak coefficient and damping coefficient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary differential equations with variable coefficients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verified through two numerical examples. The influences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with different taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.

In the present paper, the prevention of a probable instability after a sudden change in deformation of thin shallow cylindrical composite panels under impulse loads is pursued using embedded super-elastic SMA wires. A novel and practical framework is proposed to analyze these panels according to the precisely determined super-elastic function of the shape memory alloys. The suggested phase transformation algorithm can deal with the existing deficiencies in the modeling of the super-elastic behaviors. The governing equations of motion are obtained based on a matrix form of the energy equilibrium, using Sanders’ shell theory, and including the in-plane and rotary inertia effects. The resulting nonlinear finite element formulation is programmed in FORTRAN language to solve the time-dependent equations by the Newmark-beta numerical time-integration approach. The Budiansky-Roth criterion is used to determine the stability thresholds of the structures by detecting the abrupt and unexpected deformations under the suddenly imposed transverse concentrated load. Effects of imposing loads with different time durations, types, and characteristics, various amounts of the pre-tension, different viscous damping and volume fractions of the SMA are examined in order to determine the dynamic instability strength of the hybrid composite cylindrical shells and the resulting deformations in a fully non-linear solution. The large magnitudes of the pre-tension loads can change the instability performance of the structures under even small loads. In this study, the viscous damping of the host composite panels is ignored in comparison to the energy absorption due to the hysteresis loops of the stress-strain transformation diagrams of the SMA wires.

The homoclinic phenomena and chaotic motions of the forced double layered nanoplates (DLNP) are investigated. By the nonlocal theory, the nonlinear equations of motion of DLNP subjected to transverse harmonic excitation are established. The buckled DLNP considered herein means that the parameter regime of the first mode are always unstable. It should be emphasized that the homoclinic Melnikov function is related to the nonlinear term which is affected by the boundary conditions. Hence two different boundary conditions, i.e. simply supported with movable and immovable edges are compared herein. The extended Melnikov method is employed to discuss the homoclinic phenomena and chaotic motions of the DLNP system. The criteria for the homoclinic motions of the four buckling cases are established. Then the results by the above global perturbation analyses are verified by the numerical integration evidences including Lyapunov exponential spectrums, Fourier spectrums and Poincare sections. The influences of the structural parameters such as small scale effect and boundary conditions on the homoclinic behaviors are mainly discussed. From the results, the most remarkable fact can be seen that the rotary inertia term could break the symplectic symmetry of the unperturbed vibration system. The parametric regime where the chaotic motion may appear shrink with the increase of the nonlinear term r1, which means chaotic motion more likely appear for immovable edges than those with movable edges. Parametric regime where the transverse homoclinic phenomenon appears will decrease with the increase of the small scale parameter. And the homoclinic phenomena more likely appear in higher mode vibration.

Energy methods such as Energy Flow and Statistical Energy Analyses have been popularly used to predict the medium to high frequency vibro-acoustic response of several structures. In these energy methods, usually the common simple structural theories are used for simplicity. Since, the effects of shear deformation and rotary inertia at high frequency regions are unavoidable, it is necessary to determine the validity of these theories in each frequency domain. This paper aims to propose a method for defining a criteria to select a proper structural theory based on the order of shear deformation and rotary inertia to be used in vibration analyses. Several common as well as higher-order beam theories are chosen as test examples to derive and compare the key wave parameters to evaluate the effects of shear deformation and rotary inertia for wave propagation in near-field and far-field regions. Based on the results, a new classification of the frequency range is introduced for selecting an appropriate beam theory and commensurate method for wave propagation and vibration analyses. The same method can be used for other structures to define a proper structural theory based on shear deformation and rotary inertia terms for low to high frequency vibration analyses.

Wave propagation problem is solved in smart laminated carbon nanotube (CNT)-reinforced composite cylindrical shells coupled with piezoelectric layers on the top and bottom surfaces in hygrothermal environments for the first time. The motion equations are derived based on the first-order shear deformation shell theory considering the transverse shear effects and rotary inertia. The hygrothermal effects are also included in the mathematical modeling and the effective material properties of a CNT-reinforced composite shell are estimated through the Mori-Tanaka micromechanical model. Dispersion solutions are obtained by solving an eigenvalue problem. Parametric studies are carried out to investigate the effects of temperature/moisture variation, CNT volume fraction and orientation, piezoelectricity, shell geometry, stacking sequence, and material properties of the host substrate laminated composite shell at different axial and circumferential wave numbers. The results show that the temperature/moisture variation influences moderately on the dispersion solutions of smart laminated CNT-reinforced composite shells. The presented methodology and results can be used in wave propagation analysis of smart laminated CNT-reinforced composite shells affected by hygrothermal environmental conditions.

In this article, a high-fidelity structural optimization framework is developed by combining the high-accuracy of finite element method with iterative improvement capability of metaheuristic algorithms. Rotary inertia and transverse shear deformation are included in the finite element model by considering first-order shear deformation theory (FSDT). Three powerful nature-inspired metaheuristic algorithms viz. genetic algorithm (GA) in its classical form, a particle swarm optimization (PSO) variant and a cuckoo search (CS) variant are used. Advanced memetic attributes are incorporated in the PSO and CS to form their respective variants—repulsive particle swarm optimization with local search and chaotic perturbation (RPSOLC) and CHP co-evolutionary host–parasite (CHP). Extensive numerical simulations are carried out to validate these approaches by comparing with existing literature. A comprehensive set of benchmark solutions on certain new problems are also reported. Statistical tests and keen assessment of the predicted results show CHP comprehensively outperforms RPSOLC and GA, while RPSOLC has marginal superiority over GA.

Natural frequencies of circular deep arches made of functionally graded materials (FGMs) with general boundary conditions are obtained in this research based on the unconstrained higher-order shear deformation theory taking into account the depth change, complete effects of shear deformation, and rotary inertia. The material properties are assumed to vary continuously through the thickness direction of the arch. Displacement field within the arch is obtained through expansion up to an arbitrary order. Governing differential equations of the in-plane vibration are derived using Hamilton's principle. These equations are solved numerically utilizing the differential quadrature method (DQM) formulation. In order to illustrate the validity and accuracy of the presented results, results are compared with the available data in the open literature. Afterwards, novel numerical results are given for free vibration behaviour of the FGM deep arches with various boundary conditions.

Wave propagation behavior in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented, straight carbon nanotubes (CNTs) is analytically investigated for the first time via the first-order shear deformation shell theory including the transverse shear effects and rotary inertia. The Mori-Tanaka method is used for micromechanical modeling. Dispersion solutions are computed by solving an eigenvalue problem. The effects of CNT orientation, CNT volume fraction, and shell geometry on the dispersion solutions are examined. Various orientations of CNTs lead to different dispersion behaviors; the variation of wave phase velocities is more significant at lower axial wave numbers; and the effects of CNT volume fraction and shell geometry on wave dispersion behaviors are more obvious at higher circumferential wave numbers. The presented model and analytical results of this study can be utilized in the wave propagation analysis of piezoelectric shells reinforced with CNTs for the design of new smart structures used in structural health monitoring and/or energy harvesting applications.

A novel semi-active controller with adaptable parameters is developed to suppress the forced-vibration of a functionally graded material Timoshenko rotating beam with unknown parameters. The control algorithm is provided with a frequency estimator in order to identify the unknown frequency of the external excitations. The simplicity of the adaptive algorithm and efficient performance through a wide range of frequencies, are the advantages of the presented controller. Consecutive calculations allow the control parameters to be adjusted when the excitation frequency changes abruptly. The effects of hub radius, transverse shear deformation , and rotary inertia and tip masses are taken into account and the finite element method is utilized to discretize the dynamic model. The results demonstrate that the control algorithm is able to reduce the nonlinear vibration of the rotating beam at different nodes along its length when the frequency of the excitations changes. The controller is also effective when the rotational speed of the hub changes gradually over time.

In the aerospace and automotive applications driveshafts are manufactured using fiber reinforced composite materials. Compared to a conventional metallic driveshaft, a composite driveshaft gives higher natural frequencies and critical speeds, and lower vibration. They are also lightweight structures, especially when they are tapered. The design of the driveshaft is based on its fundamental natural frequency, and tapering the driveshaft can substantially improve the value of this natural frequency. In this study, the vibration analysis of the tapered composite driveshaft is carried out using the hierarchical finite element formulation, and for this purpose, the Timoshenko beam theory is used. In addition, the effects of rotary inertia, transverse shear deformation, gyroscopic force, axial load, coupling due to the lamination of composite layers, and taper angle are incorporated in the hierarchical finite element model. The potential energy and the kinetic energy of the tapered composite shaft are obtained, and then the equations of motion are developed using Lagrange’s equation. The finite element solution is validated using the approximate solution based on the Rayleigh-Ritz method. A comprehensive parametric study is conducted based on the hierarchical finite element formulation.

The vibration and stability of a simply supported beam are analyzed when the beam has an axially moving motion as well as a spinning motion. When a beam has spinning and axial motions, rotary inertia plays an important role on the lateral vibration. Compared to previous studies, the present study adopts the Rayleigh beam theory and derives more exact kinetic energy and equations of motion. The rotary inertia terms derived by the present study are compared to those of the previous studies. We investigate the natural frequencies between the present and previous studies. In addition, the critical speed and stability boundary for the spinning and moving speeds are also analyzed. It can be observed from the computed natural frequencies and dynamic responses that the present equations of motion are more reliable than the previous equations because the present equations fully consider the rotary inertia terms.

This paper presents the 3D dynamic formulations for a flexible beam sliding through a revolute-prismatic joint. Considering the geometric nonlinearity, the configuration space of the 3D flexible beam is a nonlinear differentiable manifold (). Moreover, the beam manipulated by the revolute-prismatic joint can undergo large overall motion and slide through the joint. Because of the difficulty mentioned above, most studies on these problems focus on 2D cases or are tackled under a small deformation assumption. In this paper, the rotation matrices are parameterized using rotational vectors to describe accurately the spatial configuration of flexible beams. For convenience, to describe the finite deformation of the beams, the material frame is fixed on the revolute-prismatic joint but will change over time. The corotational method is introduced to take the geometric nonlinearity (small strain and large rotation) of the beam into account. In the corotational frame, the strain energy and kinetic energy of the elements are derived with the same shape functions, which are used to describe the local displacements, to maintain the element-independent framework. Then a ‘standard element’ can be embedded within this framework. In order to consider the shear deformation, the flexible beam is discretized using a fixed number of variable-domain interdependent interpolation elements. Rotary inertia is also considered in this paper. The nonlinear equations of motion are derived by using the extended Hamilton's principle and solved by using the Hilber-Hughes-Taylor method and the Newton-Raphson iteration method. Four examples are presented to demonstrate the validity, accuracy and versatility of the present dynamic formulation.

Free and forced vibration analysis of a geometrically rotating shaft supported on ball bearings has been studied using the numerical method and compared with the results obtained experimentally. This study is concerned with vibration analysis of geometrically nonlinear rotating model with a rigid disk. The shaft has been designed under the frame of Euler–Bernoulli beam theory with additional effects such as rotary inertia, gyroscopic effect, higher-order large deformations, and rotor mass unbalance in order to replicate an equivalent practical model of rotor-bearing system. The mathematical expressions have been derived to demonstrate the nonlinear free and forced vibrations of the rotating shaft coupled with rigid disk in two transverse planes. Solutions of the nonlinear equation are being obtained using method of multiple scales as well as numerical methods. Effects of rotor parameters such as bearing stiffness and damping coefficient are examined with help of this nonlinear mathematical model. The obtained results are portrayed for a better understanding free and forced vibration analysis with time response, FFT, phase portrait, and Poincare’s map. The present outcomes enable an understanding on how the system dynamics influenced with the variations in the values of different parameters.

The present study deals with the numerical investigation on the buckling and vibration behaviour of interlayer hybrid fibre metal laminates (HFMLs) subjected to different types of concentrated edge compression and tension loads. The term interlayer hybrid represents carbon and glass fibre laminates are sandwiched in between aluminum face sheets. Totally six different hybrid configurations are taken into consideration separately for cross-ply and angle-ply layup schemes. To serve this purpose a finite element code using MATLAB is developed to examine the effects of hybrid configuration, aspect ratio, fiber orientation, type of loading and boundary conditions have been considered to study the buckling responses of HFMLs. The plate is modelled by using 9-noded heterosis elements by considering the effect of shear deformation and rotary inertia. It is revealed from the investigation that the hybrid configurations and loading conditions significantly affect the buckling and vibration characteristics of HFMLs.

Large attachments can dramatically affect the dynamic response of an assembled structure. In various industrial sectors, e.g., the automotive, aircraft, and shipbuilding industries, it is often necessary to predict the dynamic response of assembled structures and large attachments in early-stage engineering design. To deal with this, it is often the finite element method (FEM) that is used in the vibrational analysis. Despite the advent of large-scale computer availability, it is still commonplace, and often necessary, to reduce the model-size with large attachments to acceptable levels for computer time-scale or memory-size limitations. This article discusses the simple methodology of replacing large and sometimes complicated attachments by using a simplified boundary condition. This methodology is well-known in certain sectors of computer-aided design, but here we are able to present a comprehensive discussion from laboratory measurements, finite element analysis and a simplified perspective. Given the availability of experimental data, the errors produced by these methodologies may then be determined by a structure that has a strictly defined geometry and known material properties within a certain tolerance. To demonstrate these effects, an experimental modal analysis is performed on a structure consisting of a beam and a large mass attachment, which is then validated by each of the finite element models that include the relevant approximate ideal boundary conditions. Various approximating boundary conditions are investigated, and quantifiable results are discussed. One of the conclusions confirms the recommendation that rotary inertia terms should be included as a boundary condition wherever possible when large attachments are approximated by an offset mass defined at a point.

In recent years, several novel homopolar inductor machine (HIM) topologies, such as rotors with the rectangular, arc-shaped, sinusoidal and triangle rotor slots, are developed. However, the influence of different rotor slots on the performance of HIM is not clear, and there is no basis for selecting rotor slots. Addressing this issue, a comprehensively comparative studies of these topologies with different rotor slot shapes are implemented. Firstly, the topology and operation principle of the HIM are illustrated. Then, the influences of rotor slot shape on the performance including the no-load air gap flux density, back electromotive force, inductance, torque, torque ripple and losses are systematically studied. Moreover, the stress distribution, modal and rotary inertia of rotor with four different rotor slots are analyzed. Based on the above analyses, the HIM with arc-shaped rotor slots is selected and its prototype is developed. Some electromagnetic performance indexes are tested to verify the rationality of analyses. This work clearly points out the advantages and disadvantages of HIMs with different rotor structures, which could be good reference for the selection of rotor slot shape.

The delamination is one of the major modes of failure occurring in the laminated composite due to insufficient bonding between the layers. In this paper, the natural frequencies of delaminated S-glass and E-glass epoxy cantilever composite plates are presented by employing the finite element method (FEM) approach. The rotary inertia and transverse shear deformation are considered in the present study. The effect of parameters such as the location of delamination along the length, across the thickness, the percentage of delamination, and ply-orientation angle on first three natural frequencies of the cantilever plates are presented for S-glass and E-glass epoxy composites. The standard eigenvalue problem is solved to obtain the natural frequencies and corresponding mode shapes. First three mode shape of S-Glass and E-Glass epoxy laminated composites are portrayed corresponding to different ply angle of lamina.

Multi-Megawatt wind turbines have long, slender and heavy blades that can undergo extremely wind loadings. Aeroelastic stability of wind turbine blades is of great importance in both power production and load carrying capacity of structure. This paper investigates the aeroelastic stability of wind turbine blades modeled as thin walled composite box beam, utilizing unsteady incompressible aerodynamics. The structural model incorporates a number of non-classical effects such as transverse shear, warping inhibition, non-uniform torsional model and rotary inertia. The unsteady incompressible aerodynamics based on Wagner’s function is used to determine the aerodynamic loads. Governing differential equations of motion are obtained using Hamilton’s principle and solved using extended Galerkin’s method. The results obtained in this paper, related to clarification of the effects of pretwist, presetting and bending-torsion elastic coupling on the aeroelastic instability boundaries of the thin-walled composite beams. The obtained results are expected to be useful toward obtaining better predictions of the aeroelastic behavior of composite rotating blades.