• 소음진동
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• 제9권4호
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• pp.828-834
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• 1999

The paper describes the vibration and the stability of nonuniform tapered beams resting on two-layered elastic foundations. The two-layered elastic foundations are constructed by discributed Winkler springs and shearing layers as ofen used in oil models. Governing equations are derived from energy experssions using Hamilton's Principle. The associated eigenvalue problems are solved to obtain the free vibration frequencies or the buckling loads. Numerical results for the vibration and the stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies and critical forces are investigated for various thickness ratios, shear foundation parameters, Winkler foundation parameters, and boundary conditions of tapered beams.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.880-885
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• 2007

Diesel engines have been widely used in ships and power plants because of its higher thermal efficiency, mobility and durability compared to other prime movers. Though these merits, diesel engine including main components are sometimes vibrated due to higher combustion pressure in cylinders. Especially torsional, axial and structural vibrations in propulsion shafting may be severely manifested by the malfunction of torsional and axial dampers and misfiring and unbalanced load in cylinder. The structural vibration of main body and turbocharger core hole are also occurred by the loosen top bracing and excess wear-out or failure of turbocharger's bearings. The marine diesel engine should be safely designed from these vibrations. This paper introduces experimental methods to develop the prototype of integrated vibration monitoring system for marine diesel engine.

• Steel and Composite Structures
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• 제15권4호
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• pp.439-449
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• 2013

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

• 소음진동
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• 제8권3호
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• pp.467-476
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• 1998

The free vibration analysis and design optimization of the rotating composite cylindrical shells with a rectangular cutout are investigated by theoretical method. The Love's thin shell theory is used to derive the frequency equation. The theoretical results are obtained by application of the energy method employing the Rayleigh-Ritz procedure. The used circumferential vibration modes are trigonometric functions, the axial modes are the beam modal functions chosen to satisfy the prescribed boundary conditions. To check the validity, the theoretical results are compared with experimental, FEM and other theoretical results.

• Advances in nano research
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• 제15권5호
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• pp.411-422
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• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Interaction and multiscale mechanics
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• 제2권3호
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• pp.223-233
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• 2009

This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• Steel and Composite Structures
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• 제50권1호
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• pp.25-43
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• 2024

In this article, a mathematical model is developed to predict the dynamic behavior of bio-inspired composite beam with helicoidal orientation scheme under variable axial load using a unified higher order shear deformation beam theory. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equation of composite beam is proposed based on plane stress problem. The variable axial load is distributed through the axial direction by constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived in detail by Hamilton's principle. Using the differential quadrature method (DQM), the governing equations, which are integro-differential equations are discretized in spatial direction, then they are transformed into linear eigenvalue problems. The proposed model is verified with previous works available in literatures. Parametric analyses are developed to present the influence of axial load type, orthotropic ratio, slenderness ratio, lamination scheme, and boundary conditions on the natural frequencies of composite beam structures. The present enhanced model can be used especially in designing spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads.

• 산업기술연구
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• 제17권
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• pp.199-204
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• 1997

In this paper, the result of application of vibration method to the orthotropic plates with free edges supported on elastic foundation and with a pair of opposite edges under axial forces is presented. Such plates represent the concrete highway slab and hybrid composite pavement of bridges. The reinforced concrete slab can be assumed as a special orthotropic plate, as a close approximation. The highway slab is supported on elastic foundation, with free boundaries. Sometimes, the pair of edges perpendicular to the traffic direction may be subject to the axial forces. The plate is subject to the concentrated load/loads, in the form of traffic loads, or the test equipments. Finite difference method is used to obtain the deflection influence surfaces needed for vibration analysis. The influence of the modulus of the foundation, the aspect ratio of the plate, and the magnitudes of the axial forces and the concentrated attached mass on the plate, under the natural frequency is thoroughly studied.

• 한국산업융합학회 논문집
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• 제2권1호
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• pp.53-59
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• 1999

Input shaping technique has been used as a simple method of controlling vibration. With the conventional methods previously proposed by several authors, the frequency range that shows a good performance is restricted. When the designed frequency being different from the natural frequency of a system, the performance of control degrades remarkably. This paper introduced a new technique that uses digital IIR filter to control vibration. This technique has robustness for changing of parameter. In order to prove this we applied input shaping method to 2 axial overhead crane.