The three-dimensional free vibration and time response of rotating functionally graded (FG) cantilevered beams are studied. Material properties assumed to change gradually through both the width thickness in power-law form. second-kind Lagrange’s equations used conjunction with Ritz method derive comprehensive coupling dynamic for axial, chordwise, flapwise motions. trial functions deformations taken as products Chebyshev polynomials corresponding boundary functions. Nonlinear considered...

The free vibration of rotating tapered Timoshenko beams (TBs) made the axially functionally graded materials (FGMs) is studied. Chebyshev polynomials multiplied by boundary functions are selected as admissible in Ritz minimization procedure, which called Chebyshev–Ritz method. As such, geometric conditions satisfied, while numerical robustness guaranteed through use polynomials. approach provides an upper bound exact frequencies. effectiveness method confirmed convergence and comparison...

The modal analysis of rotating cantilevered rectangular Mindlin plates with variable thickness is studied. Ritz method used to derive the governing eigenfrequency equation by minimizing energy functional plate. admissible functions are taken as a product Chebyshev polynomials multiplied boundary functions, which enable displacements and rotational angles satisfy geometric conditions guarantee numerical robustness, while approach provides upper bound exact frequencies. effectiveness present...

The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework Euler-Bernoulli and Timoshenko beam theories. thickness-wise material gradient variation nanobeam considered. By introducing a second-order axial shortening term into displacement field, governing equations motion present new model are derived by Hamilton’s principle. differential solved through Galerkin method. models validated...

Shape memory polymers (SMPs) and shape polymer composites have drawn considerable attention in recent years for their effects. A unified modeling approach is proposed to describe thermomechanical behaviors effects of thermally activated amorphous SMPs SMP-based syntactic foam by using the generalized finite deformation multiple relaxation viscoelastic theory coupled with time–temperature superposition property. In this paper, thermoviscoelastic parameters are determined from a single dynamic...

Modal analysis of rotating tapered cantilevered Timoshenko beams undergoing in-plane vibration is investigated. The coupling effect axial motion and transverse considered. Kane dynamic method applied to deriving the governing eigenvalue equations. displacement rotational angle components are approximately described by products Chebyshev polynomials corresponding boundary functions. guarantee numerical robustness while functions satisfaction geometric conditions. excellent convergence present...

AbstractThe modal analysis of rotating axially functionally graded tapered Euler–Bernoulli beams with various boundary conditions is studied. The Chebyshev polynomials multiplied by functions are chosen as the admissible in Ritz minimisation procedure, which called Chebyshev–Ritz method. guarantee numerical robustness while satisfy geometric and approach provides upper bound exact frequencies. effectiveness method verified through convergence comparative studies. effects hub radius ratio,...

Through the Timoshenko beam theory (TBT), 3D dynamics of a rotary functional gradient (FG) cantilever are investigated. Material capabilities alter continuously throughout thickness obeying power law. It is assumed that Poisson’s ratio does not change. Based on von Kármán nonlinearity, governing equation determined through Hamilton principle, which includes Coriolis effects. The couplings among axial, flapwise and chordwise deformations caused by usage functionally graded materials (FGMs)...

This paper uses high-order approximate coupling (HOAC) dynamics equations for the hub–beam system with segmented active constrained layer damping treatment (SACLD). To improve characteristics of traditional (ACLD), viscoelastic layer, and piezoelectric constraining are cut at same position. The structure enhanced by increasing shear strain layer. finite element method is used to discretize SACLD beam. discontinuity beam element-to-element displacement achieves notch. Based on theory...

The dynamic properties of the micro beam are obviously different from those traditional macro due to size effect material on a scale. rigid-flexible coupling analysis an internal attached rotating hub is studied in this paper. Based accurate description non-linear deformation flexible beam, first-order approximation model derived couple stress theory and Hamilton theory, taking second-order quantity axial displacement caused by transverse into account. simplified which neglects presented....

Rotating hub-flexible rod system is a typical rigid-flexible coupling dynamic mechanism, which has wide range of industrial applications. In this paper, comprehensive nonlinear dynamical model rotating rod-concentrated mass considering effect established to study its properties. By employing the Hamilton principle and classical beam theory, set differential equations motion are derived including couplings elastic deformation rigid rotation hub. The additional centrifugal force, tangential...