Nonlinear vibration of unsymmetrical laminated composite beam on elastic foundation

I. Pakar,M. Bayat,L. Cveticanin 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.4

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

Vibration analysis of high nonlinear oscillators using accurate approximate methods

Pakar, I.,Bayat, M. Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.46 No.1

In this paper, two new methods called Improved Amplitude-Frequency Formulation (IAFF) and Energy Balance Method (EBM) are applied to solve high nonlinear oscillators. Two cases are given to illustrate the effectiveness and the convenience of these methods. The results of Improved Amplitude-Frequency Formulation are compared with those of EBM. The comparison of the results obtained using these methods reveal that IAFF and EBM are very accurate and can therefore be found widely applicable in engineering and other science. Finally, to demonstrate the validity of the proposed methods, the response of the oscillators, which were obtained from analytical solutions, have been shown graphically and compared with each other.

Vibration analysis of high nonlinear oscillators using accurate approximate methods

I. Pakar,M. Bayat 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.46 No.1

In this paper, two new methods called Improved Amplitude-Frequency Formulation (IAFF) and Energy Balance Method (EBM) are applied to solve high nonlinear oscillators. Two cases are given to illustrate the effectiveness and the convenience of these methods. The results of Improved Amplitude-Frequency Formulation are compared with those of EBM. The comparison of the results obtained using these methods reveal that IAFF and EBM are very accurate and can therefore be found widely applicable in engineering and other science. Finally, to demonstrate the validity of the proposed methods, the response of the oscillators, which were obtained from analytical solutions, have been shown graphically and compared with each other.

Vibration of electrostatically actuated microbeam by means of homotopy perturbation method

M. Bayat,I. Pakar,A. Emadi 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.6

In this paper, it has been attempted to present a powerful analytical approach called Homotopy Perturbation Method (HPM). Free vibration of an electrostatically actuated microbeam is considered to study analytically. The effect of important parameters on the response of the system is considered. Some comparisons are presented to verify the results with other researcher’s results and numerical solutions. It has been indicated that HPM could be easily extend to any nonlinear equation. We try to provide an easy method to achieve high accurate solution which valid for whole domain.

Vibration of electrostatically actuated microbeam by means of homotopy perturbation method

Bayat, M.,Pakar, I.,Emadi, A. Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.6

In this paper, it has been attempted to present a powerful analytical approach called Homotopy Perturbation Method (HPM). Free vibration of an electrostatically actuated microbeam is considered to study analytically. The effect of important parameters on the response of the system is considered. Some comparisons are presented to verify the results with other researcher's results and numerical solutions. It has been indicated that HPM could be easily extend to any nonlinear equation. We try to provide an easy method to achieve high accurate solution which valid for whole domain.

Mathematical solution for nonlinear vibration equations using variational approach

M. Bayat,I. Pakar 국제구조공학회 2015 Smart Structures and Systems, An International Jou Vol.15 No.5

In this paper, we have applied a new class of approximate analytical methods called Variational Approach (VA) for high nonlinear vibration equations. Three examples have been introduced and discussed. The effects of important parameters on the response of the problems have been considered. Runge-Kutta’s algorithm has been used to prepare numerical solutions. The results of variational approach are compared with energy balance method and numerical and exact solutions. It has been established that the method is an easy mathematical tool for solving conservative nonlinear problems. The method doesn’t need small perturbation and with only one iteration achieve us to a high accurate solution.

Structural health monitoring through nonlinear frequency-based approaches for conservative vibratory systems

M. Bayat,I. Pakar,H.R. Ahmadi,M. Cao,A.H. Alavi 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.73 No.3

This paper proposes a new approximate analytical solution for highly nonlinear vibration of mechanical systems called Hamiltonian Approach (HA) that can be widely use for structural health monitoring systems. The complete procedure of the HA approach is studied, and the precise application of the presented approach is surveyed by two familiar nonlinear partial differential problems. The nonlinear frequency of the considered systems is obtained. The results of the HA are verified with the numerical solution using Runge-Kutta’s [RK] algorithm. It is established the only one iteration of the HA leads us to the high accurateness of the solution.

Accurate analytical solution for nonlinear free vibration of beams

M. Bayat,I. Pakar 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.43 No.3

In this study, Hamiltonian Approach (HA) is applied to analysis the nonlinear free vibration of beams. Two well-known examples are illustrated to show the efficiency of this method. One of them deals with the Nonlinear vibration of an electrostatically actuated microbeam and the other is the nonlinear vibrations of tapered beams. This new approach prepares us to achieve the beam’s natural frequencies and mode shapes easily and a rapidly convergent sequence is obtained during the solution. The effects of the small parameters on the frequency of the beams are discussed. Some comparisons are conducted between the results obtained by the Hamiltonian Approach (HA) and numerical solutions using to illustrate the effectiveness and convenience of the proposed methods.

Accurate analytical solution for nonlinear free vibration of beams

Bayat, M.,Pakar, I. Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.43 No.3

In this study, Hamiltonian Approach (HA) is applied to analysis the nonlinear free vibration of beams. Two well-known examples are illustrated to show the efficiency of this method. One of them deals with the Nonlinear vibration of an electrostatically actuated microbeam and the other is the nonlinear vibrations of tapered beams. This new approach prepares us to achieve the beam's natural frequencies and mode shapes easily and a rapidly convergent sequence is obtained during the solution. The effects of the small parameters on the frequency of the beams are discussed. Some comparisons are conducted between the results obtained by the Hamiltonian Approach (HA) and numerical solutions using to illustrate the effectiveness and convenience of the proposed methods.

Numerical study on the performance of corrugated steel shear walls

Edalati, S.A.,Yadollahi, Y.,Pakar, I.,Emadi, A.,Bayat, M. Techno-Press 2014 Wind and Structures, An International Journal (WAS Vol.19 No.4

This paper examines the nonlinear behaviour of corrugated steel plate shear walls under lateral pushover load. One of the innovations in these types of walls which have used in recent years is the use of the corrugated steel shear walls rather un-stiffness plates. In the last decades many experimental studies have been done on the on the corrugated steel shear walls. A finite element analysis that includes both material and geometric nonlinearities is employed for the investigation. A comparison is made between the behaviour of steel shear walls with sinusoidal corrugated plate and trapezoidal corrugated plate. The effects of parameters such as the thickness of the corrugated plate, the corrugation depth in the corrugated plates and the corrugation length of the infill of the corrugated plates, are investigated. The results of this study have demonstrated that in the wall with constant dimensions, the trapezoidal plates have higher energy dissipation, ductility and ultimate bearing than sinusoidal waves, while decreasing the steel material consumption.