Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

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Introduction To Perturbation Techniques

1 Introduction: Linear Atomic Chains- 2 Two- and Three-Dimensional Lattices- 3 Properties of the Phonon Gas- 4 Stress and Strain- 5 Elasticity Relations- 6 Static Deformations of Solids- 7 Dynamical Behavior of Solids- 8 Dissipation and Noise in Mechanical Systems- 9 Experimental Nanostructures- 10 Nanostructure Fabrication I- 11 Nanostructure Fabrication II- A Mathematical Tools- A1 Scalars, Vectors, Tensors- A11 Vectors- A12 Tensors- A2 Eigenvectors and Eigenvalues- A3 The Dirac Delta Function- B Compatibility Relations for Stress and Strain- C Notation

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1768678

Foundations of Nanomechanics: From Solid-State Theory to Device Applications

Vibrations of straight and curved composite beams: A review

Rotating composite beams and blades have a wide range of applications in various engineering structures such as wind turbines, industrial fans, and steam turbines. Therefore, proper understanding of such structures is of a great importance. As a result, the behavior of rotating composite beam structures has received a lot of attention. This paper presents a comprehensive review of scholarly articles about rotating composite beams as published in the past decades. The review addresses analytical, semi-analytical and numerical studies dealing with dynamical problems involving adaptive/smart/intelligent materials (e.g. piezoelectric materials, electrorheological fluids, shape memory alloys, etc.), damping and vibration control, advanced composite materials (e.g. functionally graded materials and nanocomposites), complicating effects and loadings (e.g. added mass, tapered beams, initial curve and twist, etc.), and experimental methods. Moreover, the influence of Vlasov or restrained warping, out-of-plane warping, transverse shear, arbitrary cross-sectional geometry, trapeze phenomena, swept tip, size-dependent effect, as well as other areas that have been considered in research, are reviewed in depth. The review concludes with a presentation of the remaining challenges and future research needs.

Dynamics, vibration and control of rotating composite beams and blades: A critical review

A numerical study of free and forced vibration of composite sandwich beam with viscoelastic core

The free non-linear vibration of a rotating beam has been considered in this paper. The von Karman strain–displacement relations are implemented. Non-linear equations of motion are obtained by Hamilton’s principle. Results are obtained by applying the method of multiple scales to a set of discretized ordinary differential equations which obtained by using the Galerkin discretization method. This set contains coupling between transverse and axial displacements as quadratic and cubic geometric non-linearities. Non-linear normal modes and non-linear natural frequencies with or without internal resonance are observed. In the internal resonance case, the internal resonance between two transverse modes and between one transverse and one axial mode are explored. Obtained results in this study are compared with those obtained from literature. The stability and some dynamic characteristics of the non-linear normal modes such as the phase portrait, Poincare section and power spectrum diagrams have been inspected. It is shown that, for the first internal resonance case, the beam has one stable or degenerate uncoupled mode and either: (a) one stable coupled mode, (b) one unstable coupled mode, (c) two stable and one unstable coupled modes, (d) three stable coupled modes, and (e) one stable coupled mode. On the other hand, for the second internal resonance case, the beam has one stable or unstable or degenerate uncoupled mode and either: (a) two stable coupled modes, (b) two unstable coupled modes, and (c) one stable coupled mode depending on the parameters.

Non-linear modal analysis of a rotating beam

A geometrically exact mechanical model for the overall dynamics of elastic isotropic rotating blades is proposed. The mechanical formulation is based on the special Cosserat theory of rods which includes all geometric terms in the kinematics and in the balance laws without any restriction on the geometry of deformation besides the enforcement of the local rigidity of the blade cross sections. All apparent forces acting on the blade moving in a rotating frame are accounted for in exact form. The role of internal kinematic constraints such as the unshearability of the slender blades is discussed. The Taylor expansion of the governing equations obtained via an Updated Lagrangian formulation is then employed to obtain the linearized perturbed form about the prestressed configuration under the centrifugal forces. By applying the Galerkin approach to the linearized equations of motion, the linear eigenvalue problem is solved to yield the frequencies and mode shapes. In particular, the natural frequencies of unshearable blades including coupling between flapping, lagging, axial and torsional components are investigated. The angular speeds at which internal resonances may arise due to specific ratios between the frequencies of different modes are determined thus shedding light onto the overall modal couplings in rotating beam structures depending on the angular speed regime. The companion paper (part 2) discusses the nonlinear modes of vibration away from internal resonances.

A geometrically exact approach to the overall dynamics of elastic rotating blades—part 1: linear modal properties

Nonlinear free vibration analysis of rotating composite Timoshenko beams

Current research deals with thermal buckling of rotating carbon nanotube reinforced composite (CNTRC) beams Material properties of the composite beam are assumed to be temperature dependent Also volume fraction of CNT may change across the beam thickness which results in a functionally graded media Beam is subjected to uniform temperature rise and constant angular rotating speed The governing equations of the composite beam are obtained using the Timoshenko beam theory and von Karman type of kinematic assumptions Material properties of the composite media are estimated using a refined rule of mixtures approach The obtained governing equations of the composite beam are linearized to study the pre-buckling deformations and conditions for the occurrence of classical bifurcation buckling are analysed After that, using the adjacent equilibrium criterion, the stability equations governing the onset of buckling are obtained These equations are solved by means of the generalized differential quadratures method Numerical results are given to analyse the conditions of thermo-inertial buckling for rotating FG-CNTRC beams with different boundary conditions, various volume fractions and graded patterns for CNTs and different geometrical parameters It is shown that beams with intermediate volume fraction of CNTs do not have necessarily intermediate critical buckling temperature Also for certain conditions of boundary conditions, rotation may increase the critical buckling temperature of the beam

Hadi Arvin

Papers

A numerical study of free and forced vibration of composite sandwich beam with viscoelastic core

Non-linear modal analysis of a rotating beam

A geometrically exact approach to the overall dynamics of elastic rotating blades—part 1: linear modal properties

Nonlinear free vibration analysis of rotating composite Timoshenko beams

Interactive thermal and inertial buckling of rotating temperature-dependent FG-CNT reinforced composite beams