The Deflection of Rotating Composite Tapered Beams with an Elastically Restrained Root in Hygrothermal Environment

2019 ◽  
Vol 74 (10) ◽  
pp. 849-859
Author(s):  
B.C. Lin ◽  
Y. Qin ◽  
Y.H. Li ◽  
J. Yang
Keyword(s):  
Temperature Variation ◽  
Differential Quadrature Method ◽  
Orientation Angle ◽  
Power Series Solution ◽  
Static Deflection ◽  
Moisture Concentration ◽  
Rotating Speed ◽  
Centrifugal Stiffening ◽  
Hygrothermal Environment ◽  
Elastically Restrained

AbstractThis article aims to study the static deflection of a rotating composite Timoshenko beam subjected to the laterally distributed load and restrained by the elastic root and affected by the various cross-section, installation mode, and hygrothermal environment. The governing equation is established according to the force equilibrium condition and solved by a semianalytical power series solution. To verify the correctness, the results of differential quadrature method are introduced to make a comparison. Then, several parameters that can affect the static deflection of the beam, such as the rotating speed, temperature variation, elastic root, and so on, are investigated. Results indicate that (1) pitch angle, rotating speed, and hub radius can result in the centrifugal stiffening effect; (2) setting angle, fibre orientation angle, taper ratio, and elastic root affect the static deflection by changing the rigidity of the rotating composite tapered beam; and (3) temperature variation and moisture concentration can cause the expansion deformation and the change of material properties.

Nonlinear forced vibration of rotating composite laminated cylindrical shells under hygrothermal environment

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiao Li ◽  
Wentao Jiang ◽  
Xiaochao Chen ◽  
Zhihong Zhou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Multiple Scales ◽  
Cylindrical Shells ◽  
Nonlinear Partial Differential Equations ◽  
Dynamic Responses ◽  
Partial Differential ◽  
Moisture Concentration ◽  
Hygrothermal Environment ◽  
Laminated Cylindrical Shells

Abstract This work aims to study nonlinear vibration of rotating composite laminated cylindrical shells under hygrothermal environment and radial harmonic excitation. Based on Love’s nonlinear shell theory, and considering the effects of rotation-induced initial hoop tension, centrifugal and Coriolis forces, the nonlinear partial differential equations of the shells are derived by Hamilton’s principle, in which the constitutive relation and material properties of the shells are both hygrothermal-dependent. Then, the Galerkin approach is applied to discrete the nonlinear partial differential equations, and the multiple scales method is adopted to obtain an analytical solution on the dynamic response of the nonlinear shells under primary resonances of forward and backward traveling wave, respectively. The stability of the solution is determined by using the Routh–Hurwitz criterion. Some interesting results on amplitude–frequency relations and nonlinear dynamic responses of the shells are proposed. Special attention is given to the combined effects of temperature and moisture concentration on nonlinear resonance behavior of the shells.

Bending Vibrations of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root

1994 ◽  
Vol 61 (4) ◽  
pp. 949-955 ◽  
Author(s):  
Sen Yung Lee ◽  
Shueei Muh Lin
Keyword(s):  
Differential Equations ◽  
Coupling Effect ◽  
Fundamental Solutions ◽  
Variable Coefficients ◽  
Bending Vibrations ◽  
Rotating Speed ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Elastically Restrained ◽  
Angle Of Rotation

Without considering the Coriolis force, the governing differential equations for the pure bending vibrations of a rotating nonuniform Timoshenko beam are derived. The two coupled differential equations are reduced into two complete fourth-order differential equations with variable coefficients in the flexural displacement and in the angle of rotation due to bending, respectively. The explicit relation between the flexural displacement and the angle of rotation due to bending is established. The frequency equations of the beam with a general elastically restrained root are derived and expressed in terms of the four normalized fundamental solutions of the associated governing differential equations. Consequently, if the geometric and material properties of the beam are in polynomial forms, then the exact solution for the problem can be obtained. Finally, the limiting cases are examined. The influence of the coupling effect of the rotating speed and the mass moment of inertia, the setting angle, the rotating speed and taper ratio on the natural frequencies, and the phenomenon of divergence instability (tension buckling) are investigated.

Vibration Analysis and Control of a Rotating Flexible Arm With ACLD Treatment

2002 ◽  
Author(s):  
E. H. K. Fung ◽  
D. T. W. Yau
Keyword(s):  
Vibration Suppression ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Gravitational Effect ◽  
Transverse Displacement ◽  
Complex Eigenvalue ◽  
Constrained Layer Damping ◽  
Rotating Speed ◽  
Centrifugal Stiffening ◽  
And Control

In this paper, the vibration behavior and control of a clamped-free rotating flexible cantilever arm with fully covered Active Constrained Layer Damping (ACLD) treatment is investigated. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The stress-strain relationship for the viscoelastic material (VEM) is described by a complex shear modulus while the shear deformations in the two piezoelectric layers are neglected. Hamilton’s principle in conjunction with finite element method (FEM) is used to derive the nonlinear coupled differential equations of motion and the associated boundary conditions that describe the rigid hub angle rotation, the arm transverse displacement and the axial deformations of the three-layer composite. This refined model takes into account the effects of centrifugal stiffening due to the rotation of the beam and the potential energies of the VEM due to extension and bending. Active controllers are designed with PD for the piezo-sensor and actuator. The vibration frequencies and damping factors of the closed-loop beam/ACLD system are obtained after solving the characteristic complex eigenvalue problem numerically. The effects of different rotating speed, thickness ratio and loss factor of the VEM as well as different controller gain on the damped frequency and damping ratio are presented. The results of this study will be useful in the design of adaptive and smart structures for vibration suppression and control in rotating structures such as rotorcraft blades or robotic arms.

scholarly journals Dynamic Analysis of a Tapered Composite Thin-Walled Rotating Shaft Embedded with SMA Wires Using the Generalized Differential Quadrature Method

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Weiyan Zhong ◽  
Feng Gao ◽  
Yongsheng Ren ◽  
Xiaoxiao Wu ◽  
Hongcan Ma
Keyword(s):  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Governing Equations ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Generalized Differential Quadrature Method ◽  
Thin Walled ◽  
Generalized Differential

A dynamical model is developed for the tapered composite thin-walled rotating shaft with shape memory alloy (SMA) wires embedded in. The SMA wires are embedded at an interlayer of the shaft and arranged along the conical surface of the tapered composite shaft. Recovery stresses generated during the phase transformation are calculated based on one-dimensional Brinson’s model. The governing equations are obtained based on a refined variational asymptotic method (VAM) and Hamilton’s principle. The partial differential equations of motion are reduced to the ordinary differential governing equations by using the generalized differential quadrature method (GDQM). Numerical results of natural frequencies and critical speeds are obtained. The effects of the fraction of SMA wires, the initial strain of SMA wires, temperature, ply angle, taper ratio, boundary conditions, and rotating speed on the frequency characteristics are investigated.

Elastic Buckling Strength of Restrained Orthotropic Web Plates

2004 ◽  
Vol 261-263 ◽  
pp. 615-620
Author(s):  
Jae Ho Jung ◽  
Soon Jong Yoon ◽  
S.K. You
Keyword(s):  
Local Buckling ◽  
Solution Technique ◽  
Power Series Solution ◽  
Flexural Members ◽  
Buckling Strength ◽  
Longitudinal Edge ◽  
Flexural Member ◽  
Degree Of Restraint ◽  
Elastically Restrained ◽  
Web Plates

In this paper, the buckling behavior of elastically restrained orthotropic web plates is investigated. In general, the pultruded FRP structural member is composed of flat plate elements and each plate element is elastically restrained against rotation by adjacent plate components. For finding the local buckling strength of composite flexural member considering the elastic restraint at the juncture of plate components, the orthotropic web plate is modeled as an elastically restrained orthotropic plate under linearly distributed in-plane forces. For the derivation of buckling equation, the power series solution technique is employed. For the plate having different mechanical properties, the parametric studies are conducted by varying the degree of restraint along the longitudinal edge under compression. By using the results obtained, simplified form of equation is also developed so that the practicing engineers can evaluate the buckling stress of such a plate for the preliminary design of FRP flexural members.

A power series solution for rotating nonuniform Euler–Bernoulli cantilever beams

2017 ◽  
Vol 24 (17) ◽  
pp. 3855-3864 ◽  
Author(s):  
Desmond Adair ◽  
Martin Jaeger
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Mode Shapes ◽  
Power Series Solution ◽  
Cantilever Beams ◽  
Power Series Method ◽  
Novel Approach ◽  
Matrix Differential ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.

Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

2021 ◽  
pp. 146442072098689
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam
Keyword(s):  
Natural Frequency ◽  
Virtual Work ◽  
Ritz Method ◽  
Functionally Graded ◽  
Elliptical Plate ◽  
Moisture Concentration ◽  
Boundary Constraints ◽  
Pasternak Elastic Foundation ◽  
Edge Conditions ◽  
Hygrothermal Environment

In the present work, effect of hygrothermal environment on vibration and buckling behavior of embedded functionally graded elliptical plate under uniform in plane compression is studied. The properties of elliptical plate vary in transverse direction following power law. The functionally graded elliptical plate is considered to be resting on the Winkler–Pasternak elastic foundation. The governing equations are derived using the principle of virtual work and solved by employing the Rayleigh–Ritz method. The algebraic polynomials are employed to satisfy the different boundary constraints. The advantage of the presented mathematical model over the previously reported methods is that it eliminates the constraints regarding edge conditions, and it is simple and computationally fast. The inclusive results depicting the effect of various parameters namely, material property exponents, foundation parameters, aspect ratio on mechanical and thermomechanical buckling, and natural frequency of embedded functionally graded elliptical plate in a hygrothermal environment are reported after the test of convergence and extensive comparisons. The study shows that increase in foundation moduli lead to an increase in natural frequency and buckling parameter. Furthermore, it is noticed that the temperature and moisture concentration remarkably affect the buckling and vibration behavior of functionally graded elliptical plate.

Nonlinear vibration and instability of a visco-Pasternak coupled double-DWBNNTs-reinforced microplate system conveying microflow

2015 ◽  
Vol 229 (17) ◽  
pp. 3274-3290 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
H Vossough ◽  
R Kolahchi
Keyword(s):  
Nonlinear Vibration ◽  
Electromechanical Coupling ◽  
Vinylidene Fluoride ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Mechanical Systems ◽  
Orientation Angle ◽  
Boron Nitride Nanotubes ◽  
Small Scale ◽  
Fluid Viscosity

The present article deals with the nonlinear vibration and instability analysis of a bonded double-smart composite microplate system (DSCMPS) conveying microflow based on nonlocal piezoelasticity theory. Two microplates are connected together by visco-Pasternak medium and both of them made of poly-vinylidene fluoride reinforced by double walled boron nitride nanotubes (DWBNNTs). Modified Navier–Stokes relation is used to evaluate fluid–microplate interaction considering the effects of bulk viscosity and slip boundary condition. Energy method and Hamilton's principle are employed to derive motion equations with regard to von Kármán geometric nonlinearity. Also, charge equation is used to consider electromechanical coupling. Due to existence of nonlinear terms, the governing equations are solved with the help of the differential quadrature method (DQM). A detailed parametric study is conducted to elucidate the effects of the flow velocity, fluid viscosity, Knudsen number, type of elastic medium, temperature change, small scale, aspect ratio, volume fraction, and orientation angle of the DWBNNTs on the vibration and instability behaviors of the coupled DSCMPS. This study might be helpful for the design of nano-electro-mechanical systems/ micro-electro-mechanical systems.

Effect of Channel Orientation on the Heat Transfer Coefficient in the Smooth and Dimpled Rotating Rectangular Channels

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Seokbeom Kim ◽  
Eun Yeong Choi ◽  
Jae Su Kwak
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Orientation Angle ◽  
Rotating Speed ◽  
Rectangular Channels ◽  
Smooth Channel ◽  
Channel Orientation ◽  
Transient Liquid Crystal Technique ◽  
The Heat Transfer Coefficient

The detailed distribution of the heat transfer coefficient on rotating smooth and dimpled rectangular channels were measured using the transient liquid crystal technique. The rotating speed of the channel was fixed at 500 rpm and the tested Reynolds number based on the channel hydraulic diameter was 10,000. A stationary surface and two different channel rotating orientations of 90 deg and 120 deg were tested in order to investigate the effects of channel orientation on the distribution of the heat transfer coefficient in smooth and dimpled rotating surfaces. Results show that the heat transfer coefficient on the trailing surface is higher than that on the leading surface. For the 120 deg channel orientation angle cases, a higher heat transfer coefficient was observed near the outer surface. In the dimpled channel, the effect of the Coriolis force induced secondary flow on the heat transfer coefficient was not as significant as that for the smooth channel case.

The Instability and Vibration of Rotating Beams With Arbitrary Pretwist and an Elastically Restrained Root

2000 ◽  
Vol 68 (6) ◽  
pp. 844-853 ◽  
Author(s):  
S. M. Lin
Keyword(s):  
Differential Equations ◽  
Governing Equation ◽  
Transition Matrix ◽  
Coupling Effect ◽  
General System ◽  
Solution Procedure ◽  
Frequency Equation ◽  
Rotating Speed ◽  
Mass Moment ◽  
Elastically Restrained

The governing differential equations and the boundary conditions for the coupled bending-bending-extensional vibration of a rotating nonuniform beam with arbitrary pretwist and an elastically restrained root are derived by Hamilton’s principle. The semianalytical solution procedure for an inextensional beam without taking account of the coriolis forces is derived. The coupled governing differential equations are transformed to be a vector characteristic governing equation. The frequency equation of the system is derived and expressed in terms of the transition matrix of the vector governing equation. A simple and efficient algorithm for determining the transition matrix of the general system with arbitrary pretwist is derived. The divergence in the Frobenius method does not exist in the proposed method. The frequency relations between different systems are revealed. The mechanism of instability is discovered. The influence of the rotatory inertia, the coupling effect of the rotating speed and the mass moment of inertia, the setting angle, the rotating speed and the spring constants on the natural frequencies, and the phenomenon of divergence instability are investigated.

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