• Title/Summary/Keyword: Euler Parameter

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Nonlinear dynamic responses of cracked atomic force microscopes

  • Alimoradzadeh, M.;Akbas, S.D.
    • Structural Engineering and Mechanics
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    • v.82 no.6
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    • pp.747-756
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    • 2022
  • This study presents the nonlinear free and forced vibrations of a cracked atomic force microscopy (AFM) cantilever by using the modified couple stress. The cracked section of the AFM cantilever is considered and modeled as rotational spring. In the frame work of Euler-Bernoulli beam theory, Von-Karman type of geometric nonlinear equation and the modified couple stress theory, the nonlinear equation of motion for the cracked AFM is derived by Hamilton's principle and then discretized by using the Galerkin's method. The semi-inverse method is utilized for analysis nonlinear free oscillation of the system. Then the method of multiple scale is employed to investigate primary resonance of the system. Some numerical examples are presented to illustrate the effects of some parameters such as depth of the crack, length scale parameter, Tip-Mass, the magnitude and the location of the external excitation force on the nonlinear free and forced vibration behavior of the system.

A new solution for dynamic response of FG nonlocal beam under moving harmonic load

  • Hosseini, S.A.H.;Rahmani, O.;Bayat, S.
    • Steel and Composite Structures
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    • v.43 no.2
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    • pp.185-200
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    • 2022
  • A Closed-form solution for dynamic response of a functionally graded (FG) nonlocal nanobeam due to action of moving harmonic load is presented in this paper. Due to analyzing in small scale, a nonlocal elasticity theory is utilized. The governing equation and boundary conditions are derived based on the Euler-Bernoulli beam theory and Hamilton's principle. The material properties vary through the thickness direction. The harmonic moving load is modeled by Delta function and the FG nanobeam is simply supported. Using the Laplace transform the dynamic response is obtained. The effect of important parameters such as excitation frequency, the velocity of the moving load, the power index law of FG material and the nonlocal parameter is analyzed. To validate, the results were compared with previous literature, which showed an excellent agreement.

Buckling and bending analyses of a sandwich beam based on nonlocal stress-strain elasticity theory with porous core and functionally graded facesheets

  • Mehdi, Mohammadimehr
    • Advances in materials Research
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    • v.11 no.4
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    • pp.279-298
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    • 2022
  • In this paper, the important novelty and the defining a physical phenomenon of the resent research is the development of nonlocal stress and strain parameters on the porous sandwich beam with functionally graded materials in the top and bottom face sheets.Also, various beam models including Euler-Bernoulli, Reddy and the generalized formulation of two-variable beam theories are obtained in this research. According to a nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Thus, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It can be seen that the critical buckling load and transverse deflection of sandwich beam by considering both nonlocal stress-strain parameters is higher than the nonlocal stress parameter. On the other hands, it is noted that by considering the nonlocal stress-strain parameters simultaneously becomes the actual case.

Thermoelastic damping in generalized simply supported piezo-thermo-elastic nanobeam

  • Kaur, Iqbal;Lata, Parveen;Singh, Kulvinder
    • Structural Engineering and Mechanics
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    • v.81 no.1
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    • pp.29-37
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    • 2022
  • The present paper deals with the application of one dimensional piezoelectric materials in particular piezo-thermoelastic nanobeam. The generalized piezo-thermo-elastic theory with two temperature and Euler Bernoulli theory with small scale effects using nonlocal Eringen's theory have been used to form the mathematical model. The ends of nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non-dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping and frequency shift. Effect of frequency and nonlocal parameter on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with the different theories of thermoelasticity.

COMPUTATIONAL METHOD FOR SINGULARLY PERTURBED PARABOLIC REACTION-DIFFUSION EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

  • GELU, FASIKA WONDIMU;DURESSA, GEMECHIS FILE
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.25-45
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    • 2022
  • In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

Estimation algorithms of the model parameters of robotic manipulators

  • Ha, In-Joong;Ko, Myoung-Sam;Kwon, Seok-Ki
    • 제어로봇시스템학회:학술대회논문집
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    • 1987.10a
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    • pp.932-938
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    • 1987
  • The dynamic equations of robotic manipulators can be derived from either Newton-Euler equation or Lagrangian equation. Model parameters which appear in the resulting dynamic equation are the nonlinear functions of both the inertial parameters and the geometric parameters of robotic manipulators. The identification of the model parameters is important for advanced robot control. In the previous methods for the identification of the model parameters, the geometric parameters are required to be predetermined, or the robotic manipulators are required to follow some special motions. In this paper, we propose an approach to the identification of the model parameters, in which prior knowledge of the geometric parameters is not necessary. We show that the estimation equation for the model parameters can be formulated in an upper block triangular form. Utilizing the special structures, we obtain a simplified least-square estimation algorithm for the model parameter identification. To illustrate the practical use of our method, a 4DOF SCARA robot is examined.

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A unified consistent couple stress beam theory for functionally graded microscale beams

  • Chih-Ping Wu;Zhen Huang
    • Steel and Composite Structures
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    • v.51 no.2
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    • pp.103-116
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    • 2024
  • Based on the consistent couple stress theory (CCST), we develop a unified formulation for analyzing the static bending and free vibration behaviors of functionally graded (FG) microscale beams (MBs). The strong forms of the CCST-based Euler-Bernoulli, Timoshenko, and Reddy beam theories, as well as the CCST-based sinusoidal, exponential, and hyperbolic shear deformation beam theories, can be obtained by assigning some specific shape functions of the shear deformations varying through the thickness direction of the FGMBs in the unified formulation. The above theories are thus included as special cases of the unified CCST. A comparative study between the results obtained using a variety of CCST-based beam theories and those obtained using their modified couple stress theory-based counterparts is carried out. The impacts of some essential factors on the deformation, stress, and natural frequency parameters of the FGMBs are examined, including the material length-scale parameter, the aspect ratio, and the material-property gradient index.

Vibration of piezo-magneto-thermoelastic FG nanobeam submerged in fluid with variable nonlocal parameter

  • Selvamani Rajendran;Rubine Loganathan;Murat Yaylaci;Ecren Uzun Yaylaci;Mehmet Emin Ozdemir
    • Advances in nano research
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    • v.16 no.5
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    • pp.489-500
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    • 2024
  • This paper studies the free vibration analysis of the piezo-magneto-thermo-elastic FG nanobeam submerged in a fluid environment. The problem governed by the partial differential equations is determined by refined higher-order State Space Strain Gradient Theory (SSSGT). Hamilton's principle is applied to discretize the differential equation and transform it into a coupled Euler-Lagrange equation. Furthermore, the equations are solved analytically using Navier's solution technique to form stiffness, damping, and mass matrices. Also, the effects of nonlocal ceramic and metal parts over various parameters such as temperature, Magnetic potential and electric voltage on the free vibration are interpreted graphically. A comparison with existing published findings is performed to showcase the precision of the results.

A FLOW AND PRESSURE DISTRIBUTION OF APR+ REACTOR UNDER THE 4-PUMP RUNNING CONDITIONS WITH A BALANCED FLOW RATE

  • Euh, D.J.;Kim, K.H.;Youn, Y.J.;Bae, J.H.;Chu, I.C.;Kim, J.T.;Kang, H.S.;Choi, H.S.;Lee, S.T.;Kwon, T.S.
    • Nuclear Engineering and Technology
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    • v.44 no.7
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    • pp.735-744
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    • 2012
  • In order to quantify the flow distribution characteristics of APR+ reactor, a test was performed on a test facility, ACOP ($\underline{A}$PR+ $\underline{C}$ore Flow & $\underline{P}$ressure Test Facility), having a length scale of 1/5 referring to the prototype plant. The major parameters are core inlet flow and outlet pressure distribution and sectional pressure drops along the major flow path inside reactor vessel. To preserve the flow characteristics of prototype plant, the test facility was designed based on a preservation of major flow path geometry. An Euler number is considered as primary dimensionless parameter, which is conserved with a 1/40.9 of Reynolds number scaling ratio. ACOP simplifies each fuel assembly into a hydraulic simulator having the same axial flow resistance and lateral cross flow characteristics. In order to supply boundary condition to estimate thermal margins of the reactor, the distribution of inlet core flow and core exit pressure were measured in each of 257 fuel assembly simulators. In total, 584 points of static pressure and differential pressures were measured with a limited number of differential pressure transmitters by developing a sequential operation system of valves. In the current study, reactor flow characteristics under the balanced four-cold leg flow conditions at each of the cold legs were quantified, which is a part of the test matrix composing the APR+ flow distribution test program. The final identification of the reactor flow distribution was obtained by ensemble averaging 15 independent test data. The details of the design of the test facility, experiment, and data analysis are included in the current paper.

Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory

  • Kaghazian, Abbas;Hajnayeb, Ali;Foruzande, Hamidreza
    • Structural Engineering and Mechanics
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    • v.61 no.5
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    • pp.617-624
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    • 2017
  • Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.