Novel phenomena on snap-through and nonlinear vibrations of bistable ACPCL cantilever shell under combined external and parametric excitations for wind turbine blade, theory and experiment

A comparative analysis of the dynamic stability of cylindrical and conical shells with the same geometric and mechanical characteristics under periodic uniformly distributed axial compression was presented. The study of the stability of steady periodic vibrations of thin elastic shells was based on the joint use of the method of curvilinear grids, the projection method and the parameter continuation method combined with the Newton–Kantorovich method. Geometrically nonlinear relations of the thin elastic shells theory are formulated on the basis of the vector approximation of the displacements function in the general curvilinear coordinate system in tensor form and satisfy the Kirchhoff-Love hypothesis. The discretization of the differential equations of the steady forced vibrations in the direction of the generating shells using the method of curvilinear grids was carried out. The components of the elements displacement vectors of the shells middle surface in the circular directionare approximated by trigonometric series. Reduction of the number of generalized coordinates of the discrete dynamic model of shells steady forced vibrations was performed by the Bubnov-Galerkin basis reduction method. A transition from vector ordinary differential equations to a nonlinear system of algebraic equations was made. The construction of a mathematical model of the dynamic stability of steady forced nonlinear vibrations of thin elastic shells was performed according to Floquet's theory using the projection method. The criterion for the loss of stability was the equality to zero of the determinant of the matrix of linearized equations of steady forced nonlinear vibrations of shells according to the Lyapunov theorem. A comparative analysis of frequencies and modes of natural vibrations of cylindrical and conical shells with the same geometric and mechanical characteristics and boundary conditions was performed. Nonlinear steady vibrations of the shells due to periodic axial compression were studied. The critical values of the dynamic load and the corresponding forms of loss of shell stability in the range of lower frequencies of their natural vibrations were obtained.

Nonlinear vibrations of FG cylindrical shells subjected to parametric and external excitations

To identify the vibration characteristics and potential vibration control of different fiber reinforced polymer (FRP) cables for long-span cable-stayed bridges, the critical resonant responses of these cables under indirect excitations including external and parametric excitations are studied in this paper. Based on theoretical equations, the primary resonant responses of different cables under indirect excitations were first calculated and compared, afterwards the influence of cable length and design stress to the resonant responses and the importance of external and parametric excitations were further studied. Analysis of results show that all of the FRP cables measuring 575 m in length possess lower resonant responses compared with steel cables, while the hybrid FRP cable with smart dampers exhibits even lower responses than the other FRP cables. Moreover, the external excitation induced resonance will become critical for some kinds of FRP cables with increasing cable length. A method on adjusting design stresses mitigates this critical resonance and benefits vibration control of FRP cables. In addition, parametric excitation plays a more important role in resonant responses for short-length cables in comparison to external excitation, whereas both parametric and external excitations are critically important for long-length cables.

Nonlinear forced vibrations of functionally graded three-phase composite cylindrical shell subjected to aerodynamic forces, external excitations and hygrothermal environment

This literature review focuses mainly on geometrically nonlinear (finite amplitude) free and forced vibrations of circular cylindrical shells and panels, with and without fluid-structure interaction. Work on shells and curved panels of different geometries is but briefly discussed. In addition, studies dealing with particular dynamical problems involving finite deformations, eg, dynamic buckling, stability, and flutter of shells coupled to flowing fluids, are also discussed. This review is structured as follows: after a short introduction on some of the fundamentals of geometrically nonlinear theory of shells, vibrations of shells and panels in vacuo are discussed. Free and forced vibrations under radial harmonic excitation (Section 2.2), parametric excitation (axial tension or compression and pressure-induced excitations) (Section 2.3), and response to radial transient loads (Section 2.4) are reviewed separately. Studies on shells and panels in contact with dense fluids (liquids) follow; some of these studies present very interesting results using methods also suitable for shells and panels in vacuo. Then, in Section 4, shells and panels in contact with light fluids (gases) are treated, including the problem of stability (divergence and flutter) of circular cylindrical panels and shells coupled to flowing fluid. For shells coupled to flowing fluid, only the case of axial flow is reviewed in this paper. Finally, papers dealing with experiments are reviewed in Section 5. There are 356 references cited in this article.

Non-linear structural vibrations under combined parametric and external excitations

A numerical study of a dry friction oscillator with parametric and external excitations

A study on aerodynamic sound from an externally excited flexible structure in flow

Nonlinear vibrations of fluid-conveying FG cylindrical shells with piezoelectric actuator layer and subjected to external and piezoelectric parametric excitations

The nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with initial imperfection exposed to axial parametric and external excitation in the thermal environment is presented in this paper using a semi-analytical method. The distribution of temperature and material constitutive of the stiffeners along the direction of thickness is assumed. The cylindrical shell consists of three layers, the interior and exterior layer is respectively rich metal and ceramic, and the middle layer is functionally graded material (FGM). Using the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the nonlinear vibration problem has been solved. Then, utilizing the multiple scales method, the nonlinear vibration behavior of the system is examined. The resonant case, including internal parametric resonance among three modes and subharmonic resonance of order one-half, is considered. The results show that although the trend of all figures is approximately like together, but the maximum amplitude vibration of the internal SSMFG cylindrical shell with the angle of stiffeners and the external SSMFG cylindrical shell with the angle of stiffeners is more than others.

Nonlinear Interactions: Analytical, Computational, and Experimental Methods

This investigation focuses on the nonlinear dynamic behaviors in the transverse vibration of an axially accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincare map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable relationship between the dual-frequency excitations.

Parametric resonance in cylindrical shells: a case study in the nonlinear vibration of structural shells

A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.

Potential well evolution and metastable dynamics of bistable asymmetric laminated composite square shallow shell under external and parametric excitations