Application of Laplace iteration method to study of nonlinear vibration of laminated composite plates

Masroori, A.; Mahmoodi, Ehsan

doi:10.1590/s1679-78252013000400007

Cited by 8 publications

(3 citation statements)

References 11 publications

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“…To obtain the analytic solution for these equations is not an easy task. Various solving methods for the two mass systems with two degrees of freedom [3][4][5][6][7][8][9] are developed (see [10]): the energy balance method [11], the He's frequency-amplitude procedure [12], the He's variation approach [13], the higher order Hamiltonian approach [14] etc. For all of them it is common that the result is unable to give an exact reprea e-mail: cpinter.livia@uni-obuda.hu (corresponding author) sentation in the complex plane of the dynamic balance between inertia, stiffness, damping and external forces [15].…”

Section: Introductionmentioning

confidence: 99%

Rotating vector solving method applied for nonlinear oscillator

Cvetićanin

Suchy

Bíró

et al. 2021

Eur. Phys. J. Spec. Top.

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Significant number of procedures for solving of the finite degree-of-freedom forced nonlinear oscillator are developed. For all of them it is common that they are based on the exact solution of the corresponding linear oscillator. For technical reasons, the aim of this paper is to develop a simpler solving procedure. The rotating vector method, developed for the linear oscillator, is adopted for solving of the nonlinear finite degree-of-freedom oscillator. The solution is assumed in the form of trigonometric functions. Assuming that the nonlinearity is small all terms of the series expansion of the function higher than the first are omitted. The rotating vectors for each mass are presented in the complex plane. In the paper, the suggested rotating vector procedure is applied for solving of a three-degree-of-freedom periodically excited oscillator. The influence of the nonlinear stiffness of the flexible elastic beam, excited with a periodical force, on the resonant properties of the system in whole is investigated. It is obtained that the influence of nonlinearity on the amplitude and phase of vibration is more significant for smaller values of the excitation frequency than for higher ones.

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Section: Introductionmentioning

confidence: 99%

Rotating vector solving method applied for nonlinear oscillator

Cvetićanin

Suchy

Bíró

et al. 2021

Eur. Phys. J. Spec. Top.

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“…Mochida et al (2012) studied free vibration response of doubly curved shallow shells using approximate Galerkin method. Classical theory of elasticity and von-Karman's non-linear deformation theory were used by Rafieipour et al (2013) to investigate free vibration analyses of laminated composite plates.…”

Section: Introductionmentioning

confidence: 99%

Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores

Fard

Livani

Ghasemi

2014

Lat. Am. j. solids struct.

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This paper dealt with free vibration analysis of thick double curved composite sandwich panels with simply supported or fully clamped boundary conditions based on a new improved higher order sandwich panel theory. The formulation used the first order shear deformation theory for composite face sheets and polynomial description for the displacement field in the core layer which was based on the displacement field of Frostig's second model. The fully dynamic effects of the core layer and face sheets were also considered in this study. Using the Hamilton's principle, the governing equations were derived. Moreover, effects of some important parameters like that of boundary conditions, thickness ratio of the core to panel, radii curvatures and composite lay-up sequences were investigated on free vibration response of the panel. The results were validated by those published in the literature and with the FE results obtained by ABAQUS software. It was shown that thicker panels with a thicker core provided greater resistance to resonant vibrations. Also, effect of increasing the core thickness in general was significant decreased fundamental natural frequency values. KeywordsFree vibration, Double curved sandwich panel, Boundary conditions, Improved higher order sandwich panel theory.Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores INTRODUCTIONStructural efficiency is an important attribute for aircraft structures. A higher order theory approach, used by Kant and Patil (1991), replaced sandwich structure with an equivalent higher order shear deformable structure, which lacked the ability to determine local buckling modes and imperfection effects on the overall behavior. Using the three-dimensional elasticity equations, Bhimaraddi (1993) studied the static response of orthotropic doubly curved shallow shells. He assumed that the ratio of the shell thickness to its middle surface radius is negligible as compared to unity. The high- er order sandwich panel theory was developed by Frostig et al. (1994Frostig et al. ( , 2004, who considered two types of computational models in order to express governing equations of the core layer. The second model assumed a polynomial description of the displacement fields in the core that was based on displacement fields of the first model. Their theory did not impose any restrictions on distribution of the deformation through thickness of the core. Singh (1999) studied free vibration of the open deep sandwich shells made of thin layers and a moderately thick core. Rayleigh-Ritz method was also used to obtain natural frequencies. The improved higher order sandwich plate theory (IHSAPT), applying the first-order shear deformation theory for the face sheets, was introduced by Malekzadeh et al. (2005Malekzadeh et al. ( , 2006.

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“…In general, it is not easy to obtain analytical solutions to a dynamical magneto-thermo-viscoelastic problem in anisotropic materials. therefore, an important number of engineering and mathematical papers devoted to the numerical solution have studied the overall behavior of such materials (Oden and Armstrong, 1971;Ting and Chen, 1982;Dargush and Banerjee, 1991;Misra, et al, 1992;Chen, et al, 2009;Tsai, 2009;Xing and Makinouchi, 2002;El-Naggar, et al, 2002Abd-Alla, et al, 2003, 2008Wu and Chu, 2004;Baksi, et al, 2006;Hosseini, et al, 2007;Huang and Rosakis, 2007;Fahmy, 2008Fahmy, , 2009Fahmy and El-Shahat, 2008;Feng, et al, 2008;Othman and Song, 2008;Damanpack, et al (2013);Rafieipour, et al (2013)). …”

Section: Introductionmentioning

confidence: 99%

A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures

Fahmy

2014

Lat. Am. j. solids struct.

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A numerical computer model, based on the dual reciprocity boundary element method (DRBEM) for studying the generalized magneto-thermo-visco-elastic stress waves in a rotating functionally graded anisotropic thin film/substrate structure under pulsed laser irradiation is established. An implicit-implicit staggered algorithm was proposed and implemented for use with the DRBEM to get the solution for the temperature, displacement components and thermal stress components through the structure thickness. A comparison of the results for different theories is presented in the presence and absence of rotation. Some numerical results that demonstrate the validity of the proposed method are also presented. Key wordsMagneto-Thermoviscoelasticity; Rotation; Functionally graded materials; Anisotropic; Dual Reciprocity Boundary Element Method; Distribution.A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures 1 INTRODUCTION Biot (1956) introduced the theory of coupled thermoelasticity to overcome the first shortcoming in the theory of uncoupled thermoelasticity introduced by Duhamel (1837) and Neuman (1885) where it predicts two phenomena not compatible with physical observations. First, the equation of heat conduction of this theory does not contain any elastic terms. Second, the heat equation is of a parabolic type, predicting infinite speeds of propagation for heat waves. Later on, generalized theories of thermoelasticity were introduced in order to eliminate the shortcomings of the uncoupled thermoelasticity. Lord and Shulman (1967) developed the theory of coupled thermoelasticity with one relaxation time by constructing a new law of heat conduction to replace the classical Fourier's law. This law contains the heat flux vector as well as its time derivative. It contains also new constant that acts as relaxation time. Since the heat equation of this theory is of the wave-type, it automatically ensures finite speeds of propagation for heat and elastic waves. Green and Lindsay (1972) cluded a temperature rate among the constitutive variables to develop a temperature-ratedependent thermoelasticity that does not violate the classical Fourier's law of heat conduction when the body under consideration has a center of symmetry; this theory also predicts a finite speed of heat propagation. This theory is known as the theory of thermoelasticity with two relaxation times. According to these theories, heat propagation should be viewed as a wave phenomenon rather than diffusion one Relevant theoretical developments on the subject were made by Naghdi (1992, 1993) they developed three models for generalized thermoelasticity of homogeneous isotropic materials which are labeled as model I, II and III. These theories of thermoelasticity LS, GL and GN theories are known as the generalized theories of thermoelasticity with finite thermal wave speed. In general, it is not easy to obtain analytical solutions to a dynamical magneto-...

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Application of Laplace iteration method to study of nonlinear vibration of laminated composite plates

Cited by 8 publications

References 11 publications

Rotating vector solving method applied for nonlinear oscillator

Rotating vector solving method applied for nonlinear oscillator

Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores

A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures

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