Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties

Lal, Achchhe; Shegokar, Niranjan L.; Singh, B.N.

doi:10.1016/j.apm.2016.12.004

Cited by 19 publications

(5 citation statements)

References 41 publications

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“…where k is the thermal conductivity. Combined with the thermal boundary conditions and continuity conditions [37], the temperature distribution can be given by…”

Section: Temperature Distributionmentioning

confidence: 99%

Isogeometric Analysis for Active Control of Piezoelectric Functionally Graded Plates in Thermal Environment

Liu

Jiang

et al. 2021

Shock and Vibration

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An isogeometric analysis (IGA) method is proposed for investigating the active shape and vibration control of functionally graded plates (FGPs) with surface-bonded piezoelectric materials in a thermal environment. A simple first-order shear deformation theory (S-FSDT) with four variables is used to describe the displacement field of the plates. To ensure the investigation of smart piezoelectric structure in the thermal environment closer to the actual situation, a modified piezoelectric constitutive equation with consideration of the temperature effect of dielectric and piezoelectric strain coefficients is implemented to replace the traditional linear piezoelectric constitutive equation. Meanwhile, the neutral surface is adopted to avoid the stretching-bending coupling. The accuracy and effectiveness of the proposed S-FSDT-based IGA method are verified by comparing with several existing numerical examples. Then, the static bending and open-loop control of the plates under mechanical and thermal loads are further studied. Finally, the active control including static bending control and vibration control of piezoelectric functionally graded plates (PFGPs) is also investigated by using a displacement-velocity feedback control law.

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“…where k is the thermal conductivity. Combined with the thermal boundary conditions and continuity conditions [37], the temperature distribution can be given by…”

Section: Temperature Distributionmentioning

confidence: 99%

Isogeometric Analysis for Active Control of Piezoelectric Functionally Graded Plates in Thermal Environment

Liu

Jiang

et al. 2021

Shock and Vibration

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show abstract

“…(27) By plugging the expressions of the displacements and slopes in Eqs. (21), (22), and 23into Eq. (27), the kinetic energy is further written as…”

Section: Tmmentioning

confidence: 99%

“…The development of dynamic models for FGM beams has been carried out by numerous scholars from theoretical and finite element modeling backgrounds [16][17][18][19][20][21] . In this regard, Wang and Li [16] investigated the free vibration characteristics of FGM beams using the Levinson beam theory.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the model is applicable to tapered beams with randomly varying cross width. Lal et al [21] studied the second-order statistics by standard deviation and mean of normalized nonlinear transverse dynamic central deflection responses of an un-damped elastically supported FGM beam with surface-bonded piezoelectric layers under the action of a moving load. The effects of temperature increments, volume fraction exponents, moving loads and velocity, nonlinearity, slenderness ratio, and foundation parameters on the FGM beam were reported.…”

Section: Introductionmentioning

confidence: 99%

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Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Việt

Zaki

Wang

2020

Appl. Math. Mech.-Engl. Ed.

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Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on one-dimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either Timoshenko or Euler-Bernoulli beam theories. Then, Hamilton’s principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.

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“…With finite element method, Esen [29] also studied the transient response of a functionally graded Timoshenko beam subjected to an accelerated moving load when thermal effect was considered. Furthermore, Malekzadeh et al [30][31][32][33][34][35][36] extended their research on the transient response of two-dimensional functionally graded micro-beam, fiber metal laminated beam, and piezoelectric functional graded beam with elastic supports when under moving load and thermal effect, and it showed that thermal loading was a very important parameter for safe and sensitive applications.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of the half-space subjected to a moving point load and thermal stress

Zhou¹,

Shui²,

Su³

2022

Phys. Scr.

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Dynamic transient response of the half-space subjected to a moving point load and thermal stress is investigated analytically in this study. By employing the Helmholtz decomposition and introducing a moving coordinate system, the corresponding modified partial differential equations of motion for the transient waves in the half-space are firstly obtained. With one-side and two-side Laplace transformation over the new time and space variables, the second-order partial differential equations of motion in the modified system are then simplified as the ordinary differential equations, whose solutions are thereafter obtained when the boundary condition is satisfied. To get the dynamic response in time domain, the analytical solutions in Laplace domain are inverted using the Cagniard-de Hoop method. Some examples are evaluated and discussed in details for the purpose of examining the effect of the moving load and thermal stress on the transient response of the half-space.

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Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties

Cited by 19 publications

References 41 publications

Isogeometric Analysis for Active Control of Piezoelectric Functionally Graded Plates in Thermal Environment

Isogeometric Analysis for Active Control of Piezoelectric Functionally Graded Plates in Thermal Environment

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Dynamic response of the half-space subjected to a moving point load and thermal stress

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