Multi-moving Loads Induced Vibration of FG Sandwich Beams Resting on Pasternak Elastic Foundation

Wachirawit  SONGSUWAN; Monsak  PIMSARN; Nuttawit  WATTANASAKULPONG

doi:10.48048/wjst.2021.9260

Authors

Wachirawit SONGSUWAN Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
Monsak PIMSARN Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
Nuttawit WATTANASAKULPONG School of Engineering and Technology, Walailak University, Nakhon Si Thammarat 80160, Thailand

DOI:

https://doi.org/10.48048/wjst.2021.9260

Keywords:

FG sandwich beam, Free vibration, Forced vibration, Multi-moving loads, Elastic foundation

Abstract

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange’s equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams’ deflection results under a number of moving loads.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

JR Vinson. The Behavior of Sandwich Structures of Isotropic and Composite Materials. Technomic Publication, Pennsylvania, USA, 1999.

TP Vo, HT Thai, TK Nguyen, A Maheri and J Lee. Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Eng. Struc. 2014; 64, 12-22.

TK Nguyen, TTP Nguyen, TP Vo and HT Thai. Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Compos. Part B 2015; 76, 273-85.

TP Vo, HT Thai, TK Nguyen, F Inam and J Lee. A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Compos. Struc. 2015; 119, 1-12.

TP Vo, HT Thai, TK Nguyen, F Inam and J Lee. Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Compos. Part B 2015; 68, 59-74.

P Tossapanon and N Wattanasakulpong. Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation. Compos. Struc. 2016; 142, 215-25

C L Trinh, TP Vo, AI Osofero and J Lee. Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach. Compos. Struc. 2016; 156, 263-75.

TQ Bui, A Khosravifard, Ch Zhang, MR Hematiyan and MV Golub. Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method. Eng. Struc. 2013; 47, 90-104.

AM Zenkour. A comprehensive analysis of functionally graded sandwich plates: Part 1-deflection and stresses. Int. J. Solids Struct. 2005; 42, 5224-42.

AM Zenkour. A comprehensive analysis functionally graded sandwich plates: Part 2-Buckling and free vibration. Int. J. Solids Struct. 2005; 42, 5243-58.

AMA Neves, AJM Ferreira, E Carrera, M Cinefra, RMN Jorge and CMM Soares. Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects. Adv. Eng. Soft. 2012; 52, 30-43.

Q Li, VP Iu and KP Kou. Three-dimensional vibration analysis of functionally graded material sandwich plates. J. Sound Vib. 2008; 311, 498-515.

M Kashtalyan and M Menshykova. Three-dimensional elasticity solutions for sandwich panels with a functionally graded core. Compu. Struc. 2009; 87, 36-43.

S Natarajan and G Manickam. Bending and vibration of functionally graded material sandwich plates using an accurate theory. Fin. Ele. Ana. Des. 2012; 57, 32-42.

O Rahmani, SMR Khalili, K Malekzadeh and H Hadavinia. Free vibration analysis of sandwich structures with a flexible functionally graded syntactic core. Compu. Struc. 2009; 91, 229-35.

M Liu, Y Cheng and J Liu. High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexible core. Compos. Part B 2015; 72, 97-107.

AH Sofiyev. The vibration and buckling of sandwich cylindrical shells covered by different coating subjected to the hydrostatic pressure. Compos. Struc. 2014; 117, 124-34.

AH Sofiyev. Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells. Compos. Part B 2015; 77, 349-62.

M Şimşek and T Kocatürk. Free and forced vibration of a functionally graded beam subjected to a concentrated moving load. Compos. Struc. 2009; 90, 465-73.

M Şimşek. Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load. Compos. Struc. 2010; 92, 2532-46.

M Şimşek, T Kocatürk and ŞD Akbaş. Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load. Compos. Struc. 2012; 94, 2358-64.

M Şimşek. Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions. Compos. Struc. 2015; 133, 968-78.

D Hao and C Wei. Dynamic characteristic analysis of bi-directional functionally graded Timoshenko beams. Compos. Struc. 2016; 141, 253-63.

SMR Khalili, AA Jafari and SA Eftekhari. A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads. Compos. Struc. 2010; 92, 2497-511.

SA Eftekhari and AA Jafari. A mixed method for free and forced vibration of rectangular plates. Appl. Math. Model. 2012; 36, 2814-31.

Y Wang and D Wu. Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load. Acta Astronautica 2016; 127, 171-81.

C Tao, YM Fu and HL Dai. Nonlinear dynamic analysis of fiber metal laminated beams subjected to moving loads in thermal environment. Compos. Struc. 2016; 140, 410-6.

T Yan, S Kitipornchai, J Yang and XQ He. Dynamic behaviour of edge-cracked shear deformable functionally graded beams on elastic foundation under a moving load. Compos. Struc. 2011; 93, 2992-3001.

HP Lee. The dynamic response of a Timoshenko beam subjected to a moving mass. J. Sound Vib. 1996; 198, 249-56.

E Esmailzadeh and M Ghorashi. Vibration analysis of a Timoshenko beam subjected to a travelling mass. J. Sound Vib. 1997; 199, 615-28.

MA Mahmoud and MAA Zaid. Dynamic response of a beam with crack subject to a moving mass. J. Sound Vib. 2002; 256, 591-603.

K Kiani, A Nikkhoo and B Mehri. Prediction capabilities of classical and shear deformable beam models excited by a moving mass. J. Sound Vib. 2009; 320, 632-48.

M Şimşek. Vibration analysis of a functionally graded beam under a moving mass by using different beam theories. Compos. Struc. 2010; 92, 904-17.

M Şimşek. Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory. Int. J. Eng. Sci. 2010; 48, 1721-32.

Y Wang, K Xie and T Fu. Vibration analysis of functionally graded graphene oxide‑reinforced composite beams using a new Ritz‑solution shape function. J Braz. Soc. Mech. Sci. Eng. 2020; 42, 180.

Y Wang, K Xie. T Fu and C Shi. Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses. Compos. Struc. 2019; 209, 928-39.

Y Wang, A Zhou, T Fu and W Zhang. Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass. Int. J. Mech. Mater. Des. 2019; 16, 519-40.

M Şimşek. Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory. Compos. Struc. 2019; 224, 111041.

MAR Loja and JI Barbosa. In-plane functionally graded plates: A study on the free vibration and dynamic instability behaviours. Compos. Struc. 2020; 237, 111905.

YL Lei, K Gao, X Wang and J Yang. Dynamic behaviors of single- and multi-span functionally graded porous beams with flexible boundary constraints. Appl. Math. Model. 2020; 83, 754-76.

M Şimşek and M Al-shujairi. Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads. Compos. Part B 2017; 108, 18-34.