Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer

Patil, Mukund A.; Kadoli, Ravikiran

doi:10.1016/j.apm.2020.03.035

Cited by 19 publications

(5 citation statements)

References 25 publications

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“…These results are then compared to those obtained in Ref. [45], who limited themselves to the use of the Euler-Bernoulli beam theory. It is important to note that divergences only arise in the higher modes, thereby emphasising certain discrepancies between the numerical results predicted by our present analysis and those obtained earlier.…”

Section: Comparative Analyses and Verification Of Outcomesmentioning

confidence: 96%

Vibration control and analysis of Terfenol‐D functional gradient material beams with porosities: Linear and nonlinear perspectives in thermal environments

Oudra,

Khouddar,

Adri

et al. 2024

Z Angew Math Mech

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This paper investigates the vibration characteristics, both linear and non‐linear, of beams made from functional gradient materials (FGMs) with layers of Terfenol‐D attached to the top and bottom surfaces. Given the porosities that can occur during the manufacture of FGMs, the study examines the vibrational behaviour of beams with porosities. Euler–Bernoulli beam theory and the von‐Kármán non‐linear deformation field are used to formulate a fundamental equation predicting the free dynamic vibration of Terfenol‐D FGM structures with porosities. To complete this analysis, the paper also presents the application of two advanced methods. The first method involves employing the generalised finite element method (GFEM) associated with the reduced quadrature finite element method (RQFEM). GFEM offers a versatile and powerful approach, while RQFEM provides a specific method for studying dynamic phenomena. The second method utilises a semi‐analytical approach, the variational iteration method (VIM), which examines and complements the first method. Furthermore, we have demonstrated substantial alignment between the proposed solution and the results of finite element analysis, as well as with the existing literature, underscoring the effectiveness and accuracy of our analytical approach. The study also explores the influences of material property distribution, thermal loading, and porosity volume fraction on the linear and non‐linear behaviour of Terfenol‐D FGM beams. This comprehensive exploration furnishes valuable information on the intricate interplay of factors affecting vibration dynamics and control mechanisms in these advanced composite structures, offering insightful perspectives into the potential application of Terfenol‐D FGM beams in various fields.

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Section: Comparative Analyses and Verification Of Outcomesmentioning

confidence: 96%

Vibration control and analysis of Terfenol‐D functional gradient material beams with porosities: Linear and nonlinear perspectives in thermal environments

Oudra,

Khouddar,

Adri

et al. 2024

Z Angew Math Mech

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“…Here, authors have applied these four boundary conditions using δ-point approach. The governing equation may be expressed in its corresponding analog form as: The solution technique for similar example is discussed in greater depth in the reference [24]. Table 1.…”

Section: Example: Terfenol-d Layered Functionally Graded Beam With Cl...mentioning

confidence: 99%

“…⇒ bd means domain-domain terms (24) Similarly, one has to prepare the mass and damping sub-matrices also. Next, proceed with the entire process, which will be elaborated upon as follows:…”

mentioning

confidence: 99%

Discussions on application of differential quadrature method for structural free vibration problems

Vanjari,

Patil,

Saraf

et al. 2024

J. Phys.: Conf. Ser.

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A thorough examination of the use of the differential quadrature method has been presented, including an analysis of the weighting coefficient, several methods for implementing the boundary conditions, and the ultimate advantages it offers compared to other numerical techniques. The authors have detailed the technical techniques involved in this study, including the discretization of the computational domain, the generation of mass, damping, and stiffness matrices, and the subsequent partitioning of these matrices into submatrices. Exemplifications have been given for the differential quadrature (DQ) approaches that meet the clamped-spring support boundary requirement. This study on the principles of the differential quadrature technique will provide valuable insights for a research scholar, novice researcher, and academician in the field of computation.

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“…In between the graded composition of aluminum and aluminum oxide Terfenol-D layer is included. The material properties, volume fraction and expression for calculation of properties is given in [31]. Figure 2 shows the layout of FGMT fluid-conveying pipe.…”

Section: Functionally Graded Fluid Conveying Pipementioning

confidence: 99%

Terfenol-D Layer in a Functionally Graded Pipe Transporting Fluid for Free Vibration

Patil¹,

Kadoli²

2023

Pipeline Engineering - Design, Failure, and Management

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Knowledge of natural frequency of pipeline conveying fluid has relevance to designer to avoid failure of pipeline due to resonance. The damping characteristics of pipe material can be increased by using smart materials like magnetostrictive namely, TERFENOL-D. The objective of the present chapter is to investigate vibration and instability characteristics of functionally graded Terfenol-D layered fluid conveying pipe utilizing Terfenol-D layer as an actuator. First, the divergence of fluid conveying pipe is investigated without feedback control gain and thermal loading. Subsequently, the eigenvalue diagrams are studied to examine methodically the vibrational characteristics and possible flutter and bifurcation instabilities eventuate in different vibrational modes. Actuation of Terfenol-D layer shows improved stability condition of fluid conveying pipe with variation in feedback control gain and thermal loading. Differential quadrature and differential transform procedures are used to solve equation of motion of the problem derived based on Euler-Bernoulli beam theory. Finally, the effects of important parameters including the feedback control gain, thermal loading, inner radius of pipe and density of fluid on vibration behavior of fluid conveying pipe, are explored and presented in numerical results.

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Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer

Cited by 19 publications

References 25 publications

Vibration control and analysis of Terfenol‐D functional gradient material beams with porosities: Linear and nonlinear perspectives in thermal environments

Vibration control and analysis of Terfenol‐D functional gradient material beams with porosities: Linear and nonlinear perspectives in thermal environments

Discussions on application of differential quadrature method for structural free vibration problems

Terfenol-D Layer in a Functionally Graded Pipe Transporting Fluid for Free Vibration

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