A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers

Qing, Guanghui; Xu, Jian; Li, Pei; Qiu, Jiajun

doi:10.1016/j.compstruct.2005.11.002

Cited by 19 publications

(9 citation statements)

References 28 publications

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“…For isotropic, orthotropic, or anisotropic elasticity solids, the modified H-R variational principle in three-dimensional Cartesian coordinate system (see Figure 1) can be expressed as [6,7,11,12,[36][37][38][39][40][41]:…”

Section: Modified H-r Variational Principlementioning

confidence: 99%

B-Spline Wavelet on the Interval Element for the Solution of Hamilton Canonical Equation

Liu

Shi

et al. 2011

Mechanics of Advanced Materials and Structures

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Based on the modified Hellinger-Reissner (H-R) variational principle for the elastic material, the formulation of B-spline wavelet on the interval (BSWI) element of the Hamilton canonical equation was derived through the use of the interpolation scaling function of BSWI. To demonstrate the excellent predictive capability of the formulation, numerical studies were conducted on a thick plate and a three-layer plate with various common boundary conditions. The basic steps from which the formulation of the BSWI element of the Hamilton canonical equation was derived can also be extended to deduce the expressions of other wavelet elements in the Hamiltonian system, such as Daubechies orthogonal wavelet, biorthogonal wavelet based on lifting scheme, and so on.Keywords wavelet-based finite element, B-spline wavelet on the interval, Hamilton canonical equation, semi-analytical solution, Hellinger-Reissner variational principle

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Section: Modified H-r Variational Principlementioning

confidence: 99%

B-Spline Wavelet on the Interval Element for the Solution of Hamilton Canonical Equation

Liu

Shi

et al. 2011

Mechanics of Advanced Materials and Structures

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“…Tiersten [14] demonstrated Hamilton's principle for linear piezoelectric media under different boundary conditions and discussed both homogeneous and inhomogeneous problems. In addition, Qing et al [15] proposed a modified mixed Hellinger-Reissner (H-R) variational principle based on the work of Steele and Kim [16].…”

Section: Introductionmentioning

confidence: 99%

“…Durbin [19] combined a trigonometric series with an inversion series and presented rather smaller results. Qing et al [15] subsequently made comparisons to the inverse algorithms proposed by both Zhao and Durbin and improved Zhao's algorithms by using Subbotin splines. Wang et al [6] improved the calculation efficiency with two novel algorithms and additionally compensated for the deviation node in Qing's algorithms.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Semianalytical Solutions for Piezoelectric Laminates Subjected to Underwater Shocks

Liang

Zhu

et al. 2020

Mathematical Problems in Engineering

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In this study, a piezoelectric laminate is analyzed by applying the Laplace transform and its numerical inversion, Fourier transform, differential quadrature method (DQM), and state space method. Based on the modified variation principle for the piezoelectric laminate, the fundamental equations for dynamic problems are derived. The solutions for the displacement, stress, electric potential, and dielectric displacement are obtained using the proposed method. Durbin’s inversion method for the Laplace transform is adopted. Four boundary conditions are discussed through the DQM. The proposed method is validated by comparing the results with those of the finite element method (FEM). Moreover, this semianalytical method is further extended to describe the dynamic response of piezoelectric laminated plates subjected to underwater shocks by introducing Taylor’s fluid-structure interaction algorithm. Both air-backed and water-backed laminated plates are investigated, and the effect of the fluid is examined. In the time domain, the electric potential and displacements of sample points are calculated under four boundary conditions. The present method is shown to be accurate and can be a useful method to calculate the dynamic response of underwater laminated sensors.

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“…Further, the exact solutions of the static deflections of the functionally graded (FG) structure embedded with piezoelectric fiber reinforced composite (PFRC) material are reported by Ray and Sachade. 26 Similarly, the transient behaviour of the layered smart composite structure investigated by Qing et al 27 via modified mixed variational principle using the propagator matrices method. The flexural vibration of layered cylindrical shell panel with PFRC actuators is analysed by Shen and Yang 28 using HSDT mid-plane kinematics and the geometrical nonlinearity in von Karman sense.…”

Section: Introductionmentioning

confidence: 99%

Numerical and experimental nonlinear dynamic response reduction of smart composite curved structure using collocation and non-collocation configuration

Singh

Hirwani

Panda

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this work, a generic geometrical nonlinear mathematical model of smart composite curved shell panels has been developed for the evaluation of the linear and nonlinear dynamic responses. Further, the dynamic deflections are reduced by employing the piezoelectric material with the parent composite using two different arrangements (sensor and actuator). The current layered structure model is developed based on the higher-order mid-plane kinematics including the stretching effect. The electric potential due to the piezoelectric material included via a quadratic function of thickness for the current combined electro-elastic modeling. The geometrical distortion of the smart shell panel structure accounted via Green-Lagrange strain field including all of the nonlinear higher-order terms. The desired responses are evaluated computationally using an original computer code (MATLAB environment) with the help of the current higher-order model and finite element steps. The nonlinear dynamic deflection values are obtained through the direct iterative method in conjunction with Newmark’s integration. Additionally, the accuracy of the proposed model is demonstrated via comparison study with the available published literature with and without electric field potential. The reduction of response frequencies is also compared with the in-house experimental data. Lastly, few more numerical examples are computed for the various geometrical parameter including the shell configuration and the comprehensive behaviour of the currently developed nonlinear numerical model for the analysis of smart layered structure discussed in details.

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A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers

Cited by 19 publications

References 28 publications

B-Spline Wavelet on the Interval Element for the Solution of Hamilton Canonical Equation

B-Spline Wavelet on the Interval Element for the Solution of Hamilton Canonical Equation

Three-Dimensional Semianalytical Solutions for Piezoelectric Laminates Subjected to Underwater Shocks

Numerical and experimental nonlinear dynamic response reduction of smart composite curved structure using collocation and non-collocation configuration

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