# T. H. Young

## Publications

##### 3 Free Vibration and Buckling of Rectangular Plates under Nonuniform In-Plane Edge Shear Loads

**Authors:**
T. H. Young,
Y. J. Tsai

**Abstract:**

A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work. The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

**Keywords:**
stress analysis,
free vibration,
plate buckling,
nonuniform in-plane edge shear

##### 2 Dynamic Stability of Axially Moving Viscoelastic Plates under Non-Uniform In-Plane Edge Excitations

**Authors:**
T. H. Young,
S. J. Huang,
Y. S. Chiu

**Abstract:**

**Keywords:**
axially moving viscoelastic plate,
dynamic stability,
in-plane periodic
excitation,
non-uniformly distributed edge tension

##### 1 In-Plane Responses of Axially Moving Plates Subjected to Arbitrary Edge Excitations

**Authors:**
T. H. Young,
Y. S. Ciou

**Abstract:**

The free and forced in-plane vibrations of axially moving plates are investigated in this work. The plate possesses an internal damping of which the constitutive relation obeys the Kelvin-Voigt model, and the excitations are arbitrarily distributed on two opposite edges. First, the equations of motion and the boundary conditions of the axially moving plate are derived. Then, the extended Ritz method is used to obtain discretized system equations. Finally, numerical results for the natural frequencies and the mode shapes of the in-plane vibration and the in-plane response of the moving plate subjected to arbitrary edge excitations are presented. It is observed that the symmetry class of the mode shapes of the in-plane vibration disperses gradually as the moving speed gets higher, and the u- and v-components of the mode shapes belong to different symmetry class. In addition, large response amplitudes having shapes similar to the mode shapes of the plate can be excited by the edge excitations at the resonant frequencies and with the same symmetry class of distribution as the u-components.

**Keywords:**
Arbitrary edge excitations,
axially moving plates,
in-plane vibration,
extended Ritz method

## Abstracts

##### 2 Free Vibration and Buckling of Rectangular Plates under Nonuniform In-Plane Edge Shear Loads

**Authors:**
T. H. Young,
Y. J. Tsai

**Abstract:**

**Keywords:**
stress analysis,
free vibration,
plate buckling,
nonuniform in-plane edge shear

##### 1 Dynamic Stability of Axially Moving Viscoelastic Plates under Nonuniform in-Plane Edge Excitations

**Authors:**
T. H. Young,
S. J. Huang,
Y. S. Chiu

**Abstract:**

**Keywords:**
axially moving viscoelastic plate,
in-plane periodic excitation,
nonuniformly distributed edge tension,
dynamic stability