• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.802-807
• /
• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

• Structural Engineering and Mechanics
• /
• v.54 no.3
• /
• pp.419-432
• /
• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11a
• /
• pp.394.1-394
• /
• 2002

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. (omitted)

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.1
• /
• pp.66-73
• /
• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

• Journal of KSNVE
• /
• v.9 no.4
• /
• pp.828-834
• /
• 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.

• Journal of the Korean Society for Advanced Composite Structures
• /
• v.3 no.4
• /
• pp.38-44
• /
• 2012

This paper presents experimental studies aiming at evaluation of structural behaviors of RC (Reinforced Concrete) beams externally strengthened with taper ended CFRPs(Carbon Fiber Reinforced Polymers). Experiments are performed with RC beams having different numbers of CFRP layers and length of each layer. The beams are subjected to four point-bending with simply supported condition. Test results of taper ended CFRPs and non-tapered CFRPs are compared and the better strengthening effect is observed from tapered ended CFRPs.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2005.04a
• /
• pp.79-86
• /
• 2005

This paper deals with the static optimal shapes of simple beams which are subjected to a vertical point load. The area and second moment of inertia of the regular polygon cross-section of the tapered beams are determined, which have always same volume and same length for the parabolic taper. The differential equation governing the elastic curve is derived using the small deflection theory and solved numerically. By using the numerical results of deflections, rotations and bending stresses of such beams, the optimal shapes, namely, optimal section ratios, of the beams subjected to a single point load according to variation of load position parameters are determined and presented in the figures. Examples of the static optimal shapes for beams with a single load and multiple loads are reported. The design process of this study can be used directly for the minimum weight design of simple beams.

• Journal of Korean Society of Steel Construction
• /
• v.18 no.3
• /
• pp.321-329
• /
• 2006

The use of tapered structural members was first proposed by Ami rikian for the economical use of materials.Generaly, tapered members are used in single-story structures with one or more bays and in cantilevered sections of ate architectural representation. If only focused on the section performance, however, the width-to-thickness ratio or t apered ratio can exced regulations. Such a case requires a study on the behavior of tapered members. To investigate the plastic and local buckling behavior of web-tapered beams, seven steel beams were the tapered ratio and the width-to-thicknes ratio. The results of maximum strength, strength deterioration, and stiffnes deterioration were compared.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1995.04a
• /
• pp.18-21
• /
• 1995

A numerical method is presented to obtain natural frequencies and mode shapes of the arbitrary tapered beams with static deflections due to arbitrary distributed dead loads. The differential equation governing the free vibration is derived and solved numerically. In the numerical example, the linearly tapered beams and both the triangular and sinusoidal distributed dead loads are chosen. The lowest three natural frequencies are reported and typical mode shapes are presented in the figure.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.34 no.1
• /
• pp.57-65
• /
• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.