Dynamic response of a non-classically damped beam with general boundary conditions subjected to a moving mass-spring-damper system

This paper presents the transverse vibration of Bernoulli-Euler homogeneous isotropic damped beams with general boundary conditions. The beams are assumed to be subjected to a load moving at a uniform velocity. The damping characteristics of the beams are described in terms of fractional derivatives of arbitrary orders. In the analysis where initial conditions are assumed to be homogeneous, the Laplace transform cooperates with the decomposition method to obtain the analytical solution of the investigated problems. Subsequently, curves are plotted to show the dynamic response of different beams under different sets of parameters including different orders of fractional derivatives. The curves reveal that the dynamic response increases as the order of fractional derivative increases. Furthermore, as the order of the fractional derivative increases the peak of the dynamic deflection shifts to the right, this yields that the smaller the order of the fractional derivative, the more oscillations the beam suffers. The results obtained in this paper closely match the results of papers in the literature review.

Download Full-text

Dynamic Response of a Spinning Timoshenko Beam With General Boundary Conditions and Subjected to a Moving Load

Journal of Applied Mechanics ◽

10.1115/1.2901390 ◽

1994 ◽

Vol 61 (1) ◽

pp. 152-160 ◽

Cited By ~ 32

Author(s):

J. W.-Z. Zu ◽

R. P. S. Han

Keyword(s):

Dynamic Response ◽

Boundary Conditions ◽

Timoshenko Beam ◽

Moving Load ◽

Original System ◽

Adjoint System ◽

General Boundary ◽

General Boundary Conditions ◽

Adjoint Systems ◽

Analysis Technique

The dynamic response of a spinning Timoshenko beam with general boundary conditions and subjected to a moving load is solved analytically for the first time. Solution of the problem is achieved by formulating the spinning Timoshenko beams as a non-self-adjoint system. To compute the system dynamic response using the modal analysis technique, it is necessary to determine the eigenquantities of both the original and adjoint systems. In order to fix the adjoint eigenvectors relative to the eigenvectors of the original system, the biorthonormality conditions are invoked. Responses for the four classical boundary conditions which do not involve rigidbody motions are illustrated. To ensure the validity of the method, these results are compared with those from Euler-Bernoulli and Rayieigh beam theories. Numerical simulations are performed to study the influence of the four boundary conditions on selected system parameters.

Download Full-text

Dynamic and Sound Radiation Characteristics of Rectangular Thin Plates with General Boundary Conditions

Curved and Layered Structures ◽

10.1515/cls-2019-0010 ◽

2019 ◽

Vol 6 (1) ◽

pp. 117-131

Author(s):

Yuan Du ◽

Haichao Li ◽

Qingtao Gong ◽

Fuzhen Pang ◽

Liping Sun

Keyword(s):

Dynamic Response ◽

Boundary Conditions ◽

Ritz Method ◽

Sound Radiation ◽

Current Method ◽

Thin Plates ◽

General Boundary ◽

General Boundary Conditions ◽

Radiation Characteristics ◽

Aspect Ratios

AbstractBased on the classical Kirchhoff hypothesis, the dynamic response and sound radiation of rectangular thin plates with general boundary conditions are studied. The transverse displacements of plate are represented by a double Fourier cosine series and three supplementary functions. The potential discontinuity associated with the original governing equation can be transferred to auxiliary series functions. All kinds of boundary conditions can be easily achieved by varying stiffness value of springs on each edge. The natural frequencies and vibration response of the plates are obtained by means of the Rayleigh–Ritz method. Sound radiation characteristics of the plate are derived using Rayleigh integral formula. Current method works well when handling dynamic response and sound radiation of plates with general boundary conditions. The accuracy and reliability of current method are confirmed by comparing with related literature and FEM. The non-dimensional frequency parameters of the rectangular plates with different boundary conditions and aspect ratios are presented in the paper, which may be useful for future researchers.Meanwhile, some interesting points are foundwhen analyzing acoustic radiation characteristics of plates.

Download Full-text