Nonlinear Dynamic Response of Piezoelectric Cylindrical Shell with Delamination under Hygrothermal Conditions

2012 ◽  
Vol 204-208 ◽  
pp. 4698-4701
Author(s):  
Jin Hua Yang ◽  
De Liang Chen
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference Method ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Transverse Motion ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
The Finite Difference Method ◽  
Delamination Length

Abstract. On the basis of the nonlinear plate-shell and piezoelectric theory, the governing equations of motion for axisymmetrical piezoelectric delaminated cylindrical shell under hygrothermal conditions were derived. The governing equation of transverse motion was modified by contact force and thus the penetration between two delaminated layers could be avoided. The whole problem was resolved by using the finite difference method. In calculation examples, the effects of delamination length, depth and amplitude of load on the nonlinear dynamic response of the axisymmetrical piezoelectric delaminated shell under hygrothermal conditions were discussed in detail.

Nonlinear Dynamic Response of Piezoelectric Beam Reinforced with BNNTs under Electro-Thermo-Mechanical Loadings

2014 ◽  
Vol 1065-1069 ◽  
pp. 1083-1086
Author(s):  
Jin Hua Yang ◽  
Wen Liang Fan
Keyword(s):  
Variational Principle ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Constitutive Relations ◽  
Boron Nitride Nanotubes ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
Numerical Examples ◽  
Piezoelectric Beam ◽  
The Finite Difference Method

This paper presents an investigation on the nonlinear dynamic response of piezoelectric beam reinforced with boron nitride nanotubes (BNNTs) under combined electro-thermo-mechanical loadings. By employing nonlinear strain and utilizing piezoelectric theory, the constitutive relations of the piezoelectric beam reinforced with BNNTs are established. Then the dynamic governing equations of the structure are derived through variational principle and resolved by applying the finite difference method. In numerical examples, the effects of geometric nonlinear, voltage etc. on the nonlinear dynamic response of piezoelectric beam reinforced with BNNTs are discussed.

Research on Dynamic Response of Q235 Steel Cylindrical Shell Subjected to Lateral Explosion Loading

2013 ◽  
Vol 631-632 ◽  
pp. 864-869
Author(s):  
Fu Yin Gao ◽  
Yuan Long ◽  
Chong Ji ◽  
Chang Xiao Zhang
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Computer Code ◽  
Nonlinear Dynamic Response ◽  
Q235 Steel ◽  
Explosion Loading ◽  
Experimental Researches ◽  
Oil Gas ◽  
Steel Cylindrical Shell

Experimental researches were presented on dynamic characteristics of Q235 steel cylindrical shell impacted-explosive laterally by 75g cylindrical TNT dynamite at the center．The dynamic response was obtained under different distances with different setting ways of explosive sources．By means of an explicit nonlinear dynamic finite element computer code LS-DYNA，the nonlinear dynamic response process of cylindrical shell subjected to laterally explosion loading were numerically simulated with ALE coupling method. The numerical simulation results were in good agreement with experimental data. The results provided important reference for the blast-resistant properties analysis and safety assessment of oil-gas pipes safety.

The Selection of the Linearized Natural Frequency for the Second-Order Normal Form Method

2011 ◽  
Author(s):  
Zhenfang Xin ◽  
S. A. Neild ◽  
D. J. Wagg
Keyword(s):  
Normal Form ◽  
Dynamic Response ◽  
Natural Frequency ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Second Order ◽  
Nonlinear Dynamic Response ◽  
Weakly Nonlinear ◽  
Selection Of ◽  
Normal Form Technique

The normal form technique is an established method for analysing weakly nonlinear vibrating systems. It involves applying a simplifying nonlinear transform to the first-order representation of the equations of motion. In this paper we consider the normal form technique applied to a forced nonlinear system with the equations of motion expressed in second-order form. Specifically we consider the selection of the linearised natural frequencies on the accuracy of the normal form prediction of sub- and superharmonic responses. Using the second-order formulation offers specific advantages in terms of modeling lightly damped nonlinear dynamic response. In the second-order version of the normal form, one of the approximations made during the process is to assume that the linear natural frequency for each mode may be replaced with the response frequencies. Here we will show that this step, far from reducing the accuracy of the technique, does not affect the accuracy of the predicted response at the forcing frequency and actually improves the predictions of sub and superharmonic responses. To gain insight into why this is the case, we consider the Duffing oscillator. The results show that the second-order approach gives an intuitive model of the nonlinear dynamic response which can be applied to engineering applications with weakly nonlinear characteristics.

Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Intrinsic Curvature ◽  
Nonlinear Dynamic Response ◽  
Helical Springs ◽  
Secondary Resonances ◽  
Element Approach

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation and vice rotation (and displacement) interpolation and, thus, can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed, which captures coupling due to nonzero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate loading amplitudes lead to the presence of secondary resonances (not captured by linearized models), while large loading amplitudes lead to complex dynamics and transverse buckling.

scholarly journals Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Y. X. Hao ◽  
W. Zhang ◽  
X. L. Ji
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Internal Resonance ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Internal Resonances ◽  
Third Order ◽  
Nonlinear Dynamic Response

The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle. Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm. The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.

Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

2010 ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Intrinsic Curvature ◽  
Amplitude Response ◽  
Nonlinear Dynamic Response ◽  
Helical Springs ◽  
Secondary Resonances ◽  
Element Approach

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation vice rotation (and displacement) interpolation, and thus can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed which captures coupling due to non-zero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate amplitude response leads to the presence of secondary resonances not captured by linearized models.

Nonlinear Dynamic Response of Carbon Nanotube Nanocomposite Microbeams

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Marek Cetraro ◽  
Walter Lacarbonara ◽  
Giovanni Formica
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Path Following ◽  
Transversely Isotropic ◽  
Nonlinear Frequency ◽  
Nonlinear Dynamic Response

The nonlinear dynamic response of nanocomposite microcantilevers is investigated. The microbeams are made of a polymeric hosting matrix (e.g., epoxy, polyether ether ketone (PEEK), and polycarbonate) reinforced by longitudinally aligned carbon nanotubes (CNTs). The 3D transversely isotropic elastic constitutive equations for the nanocomposite material are based on the equivalent inclusion theory of Eshelby and the Mori–Tanaka homogenization approach. The beam-generalized stress resultants, obtained in accordance with the Saint-Venant principle, are expressed in terms of the generalized strains making use of the equivalent constitutive laws. These equations depend on both the hosting matrix and CNTs elastic properties as well as on the CNTs volume fraction, geometry, and orientation. The description of the geometry of deformation and the balance equations for the microbeams are based on the geometrically exact Euler–Bernoulli beam theory specialized to incorporate the additional inextensibility constraint due to the relevant boundary conditions of microcantilevers. The obtained equations of motion are discretized via the Galerkin method retaining an arbitrary number of eigenfunctions. A path following algorithm is then employed to obtain the nonlinear frequency response for different excitation levels and for increasing volume fractions of carbon nanotubes. The fold lines delimiting the multistability regions of the frequency responses are also discussed. The volume fraction is shown to play a key role in shifting the linear frequencies of the beam flexural modes to higher values. The CNT volume fraction further shifts the fold lines to higher excitation amplitudes, while it does not affect the backbones of the modes (i.e., oscillation frequency–amplitude curves).

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