Dynamics of Viscoelastic Plate With Curved Boundaries of Arbitrary Shape

1978 ◽  
Vol 45 (3) ◽  
pp. 629-635 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
Free Vibration ◽  
Transient Response ◽  
Forced Vibration ◽  
Arbitrary Shape ◽  
Impact Load ◽  
Viscoelastic Plate ◽  
Dynamic Loads ◽  
Curved Boundaries ◽  
Vibration Problems ◽  
General Dynamic

This paper is concerned with vibration and transient response problems of viscoelastic plates with curved boundaries of arbitrary shape subjected to general dynamic loads. The results for free and forced vibration problems are given in generalized forms for arbitrary-shaped viscoelastic plates. As examples of this problem, the free vibration of a circular clamped viscoelastic plate with an eccentric hole and the dynamic response of a circular solid viscoelastic plate subjected to an eccentric annular impact load are discussed. Numerical calculations are carried out for both the problem, and experimental results are also obtained as an additional check of this study.

scholarly journals Application of Laplace Transform to the Free Vibration of Continuous Beams

2017 ◽  
Vol 63 (1) ◽  
pp. 163-180 ◽  
Author(s):  
H.B. Wen ◽  
T. Zeng ◽  
G.Z. Hu
Keyword(s):  
Free Vibration ◽  
Laplace Transform ◽  
Reaction Force ◽  
Bending Moment ◽  
Frequency Equation ◽  
Simplified Model ◽  
Continuous Beam ◽  
Transform Method ◽  
Continuous Beams ◽  
Vibration Problems

AbstractLaplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

The Lift Force on a Cylinder Vibrating in a Current

1990 ◽  
Vol 112 (4) ◽  
pp. 297-303 ◽  
Author(s):  
G. Moe ◽  
Z.-J. Wu
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Cross Flow ◽  
Reference Frequency ◽  
Average Force ◽  
Vibrational Response ◽  
Uniform Current ◽  
Extensive Program ◽  
Vibration Tests ◽  
Lock In

This paper reports an extensive program of forced and free vibration tests on a single circular cylinder moving mainly perpendicularly to a uniform current. For both free and forced vibration tests, two cases were investigated: one in which the cylinder was restrained in the in-line direction and the other in which it was supported on suitable springs. The cross-flow vibrational response and hydrodynamic forces on the cylinder were measured. Large variations of motion frequency in the “lock-in” range were found from the free vibration tests. This leads to two different definitions of reduced velocity, namely, a so-called nominal reduced velocity based on one reference frequency and the true reduced velocity based on the actual vibration frequency. When different results are compared, the true reduced velocity should be used. The forced vibration tests showed, as may be expected, that the transverse force in the “lock-in” range on the average will add energy to the cylinder at moderate motion amplitudes and subtract energy at large amplitudes. Some conditions resulting in a steady-state vibration of a flexibly mounted cylinder were analyzed. The actual force traces also show very large and apparently random deviations from the average force amplitude. The results from the forced and the free vibration tests are consistent with each other if the true reduced velocity and reduced amplitude are the same.

Static Deflection and Free Vibration of Nonprismatic Beam Structures Solved by DQEM Using EDQ

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Equilibrium Equation ◽  
Static Deflection ◽  
Beam Structures ◽  
Prismatic Beam ◽  
Vibration Problems ◽  
Analysis Models ◽  
Element Boundary

Abstract The development of (DQEM) analysis models of static deformation and free vibration problems of generic non-prismatic beam structures was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the buckling equilibrium equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. They prove that the DQEM efficient.

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

Case Studies of Forced Vibration Problems of a Rotor

2019 ◽  
pp. 167-216
Author(s):  
Osami Matsushita ◽  
Masato Tanaka ◽  
Masao Kobayashi ◽  
Patrick Keogh ◽  
Hiroshi Kanki
Keyword(s):  
Case Studies ◽  
Forced Vibration ◽  
Vibration Problems
Sign in / Sign up

Export Citation Format

Share Document