• Geomechanics and Engineering
• /
• v.16 no.2
• /
• pp.141-150
• /
• 2018

In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

• Structural Engineering and Mechanics
• /
• v.80 no.6
• /
• pp.657-668
• /
• 2021

In this study, a relationship between the resonance frequency ratio and Poisson's ratio was proposed that can be used to directly determine the elastic constants. Using this relationship, the frequency ratio between the 1st bending mode and 2nd bending mode for any rectangular Timoshenko beam can be directly estimated and used to determine the elastic constants efficiently. The exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The highest percent difference for the frequency ratio between the theoretical values and the estimated values for all the beam dimensions studied was less than 0.02%. The proposed equations were used to obtain the elastic constants of beams with different material properties and dimensions using the first two measured transverse bending frequencies. Results show that using the equations proposed in this study, the Young's modulus and Poisson's ratio of rectangular Timoshenko beams can be determined more efficiently and accurately than those obtained from industry standards such as ASTM E1876-15 without the need to test the torsional vibration.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.4
• /
• pp.365-373
• /
• 2011

This paper presents the dynamic response and the vibration characteristics for a rail-track supported by discrete springs and dampers. Recently, automatic conveyer system, rail-track, rack-master system demand the soundproof facilities and vibration suppression measures in order to satisfy the strict environmental standards. The equations of motions of the dynamic characteristics for a vibration suppression rail-track under a traveling mass were derived by Galerkin's mode summation method considering gravity, centrifugal force, Coriolis force, inertia force of the moving mass, transverse inertia of the rail-track. Also, numerical results were calculated by Runge-Kutta integration method. In order to investigate vibration characteristics and dynamic responses, modal testing and measurement of the responses of the rail-track were performed. Through the experiment and numerical simulations, numerical results have a good agreement with experimental ones.

• Structural Engineering and Mechanics
• /
• v.35 no.2
• /
• pp.217-240
• /
• 2010

A semi-analytical method is presented for accurately prediction of the free vibration behavior of generally laminated composite plates with arbitrary boundary conditions. The method employs the technique of separation of spatial variables within Hamilton's principle to obtain the equations of motion, including two systems of coupled ordinary homogeneous differential equations. Subsequently, by applying the laminate constitutive relations into the resulting equations two sets of coupled ordinary differential equations with constant coefficients, in terms of displacements, are achieved. The obtained differential equations are solved for the natural frequencies and corresponding mode shapes, with the use of the exact state-space approach. The formulation is exploited in the framework of the first-order shear deformation theory to incorporate the effects of transverse shear deformation and rotary inertia. The efficiency and accuracy of the present method are demonstrated by obtaining solutions to a wide range of problems and comparing them with finite element analysis and previously published results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2006.05a
• /
• pp.1218-1222
• /
• 2006

The bolts fixing the valve cover to the engine were often reported to be failed in a wheel loader model. Recently this failures were continually repeated in the specified equipment. In order to identify the fatigue fractures of the bolts, various vibration tests were carried out. From these tests, it was found out that the failure was due to the resonance between the excitation force of engine and the transverse mode of engine valve cover. So, the several modifications for the bolts were considered to avoid the resonance. Finally, the bolt failure problem was clearly resolved.

• Structural Engineering and Mechanics
• /
• v.10 no.1
• /
• pp.81-92
• /
• 2000

This study is an investigation of the effect of cracks on the dynamical characteristics of a cantilever beam, having multiple open-edge transverse cracks. The flexibilities due to crack have been identified for several crack depths and locations. In the study the finite element method and component mode synthesis methods are used. Coupling the components is performed by a flexibility matrix taking into account the interaction forces. Each component is modelled by cantilever beam finite elements with two nodes and three degrees of freedom at each node. The results obtained lead to conclusion that, by using the drop in the natural frequencies and the change in the mode shapes, the presence and nature of cracks in a structure can be detected. There is some counter-evidence, however, that the effects due to multiple cracks may interact to make detection more difficult than for isolated cracks.

• Proceedings of the KIEE Conference
• /
• 2005.07c
• /
• pp.1951-1953
• /
• 2005

This paper present a new disk-type piezoelectric transformer. The input side of the transformer has a crescent-shaped electrode and the output side has a focused poling direction. The piezoelectric transformers operated in each transformer's resonance vibration mode. The electrodes and poling directions on commercially available piezoelectric ceramic disks were designed so that the planar or shear mode coupling factor $(k_p,\;k_{15})$ becomes effective rather than the transverse mode coupling factor ($k_{31}$). A single layer prototype transformer, 26[mm] in diameter and $1.5{\sim}4.0[mm]$ thick, was fabricated, such as step-up ratio, power transformation efficiency and temperature were measured.

• Structural Engineering and Mechanics
• /
• v.15 no.1
• /
• pp.115-134
• /
• 2003

The Ting Kau Bridge in Hong Kong is a cable-stayed bridge comprising two main spans and two side spans. The bridge deck is supported by three towers, an end pier and an abutment. Each of the three towers consists of a single reinforced concrete mast which reduces its section in steps, and it is strengthened by transverse cables and struts in the transverse vertical plane. The bridge deck is supported by four inclined planes of cables emanating from anchorages at the tower tops. In view of the threat from typhoons, the dynamic behaviour of long-span cable-supported bridges in the region is always an important consideration in their design. This paper is devoted to the ambient vibration measurements of the bridge for evaluation of dynamic characteristics including the natural frequencies and mode shapes. It also describes the modelling of the bridge. A few finite element models are developed and calibrated to match with the field data and the results of subsequent structural health monitoring of the bridge.

• Proceedings of the KSME Conference
• /
• 2000.04a
• /
• pp.596-601
• /
• 2000

The paper presents free vibration and stability analyses of a non-uniform Timoshenko beam resting on a two-parameter elastic soil. The soil parameters can vary along the spat and is assumed to be two-parameter model including the effects of both transverse shear deformation and elastic foundation Governing equations related to the vibration and the stability of the beam are derived from Hamilton's principle, and the resulting eigen-value problems can be solved to give natural frequencies and critical force by finite element method. Numerical results for both vibration and stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies, mode shapes and critical forces are investigated for various thickness ratios, shear foundation parameter, Winkler foundation parameter and boundary conditions of tapered Timoshenko beams.

• Advances in nano research
• /
• v.4 no.1
• /
• pp.31-44
• /
• 2016

This article is concerned with the free vibration problem for chiral double-walled carbon nanotube (DWCNTs) modelled using the non-local elasticity theory and Euler Bernoulli beam model. According to the governing equations of non-local Euler Bernoulli beam theory and the boundary conditions, the analytical solution is derived and two branches of transverse wave propagating are obtained. The numerical results obtained provide better representations of the vibration behaviour of double-walled carbon nanotube, where the aspect ratio of the (DWCNTs), the vibrational mode number, the small-scale coefficient and chirality of double-walled carbon nanotube on the frequency ratio (${\chi}^N$) of the (DWCNTs) are significant. In this work, the numerical results obtained can be used to predict and prevent the phenomenon of resonance for the forced vibration analyses of double -walled carbon nanotubes.