Lumped parameter models representing impedance functions at the end of a finite beam on a viscoelastic medium

This study presents a lumped parameter model that represents impedance functions at the end of a finite flexural beam on a viscoelastic medium. This model comprises units arranged in series, each of which consists of a spring, a dashpot, and a so-called ''gyro-mass element.'' A formula is presented for determining the properties of the elements in the units. The impedance function simulated by the proposed model shows good agreement with the rigorous impedance function. A significant reduction in the degrees of freedom is a major advantage of this model for solving recent vibration problems.

[1]  Izuru Takewaki,et al.  Efficient analysis of pile-group effect on seismic stiffness and strength design of buildings , 2005 .

[2]  Lu Sun,et al.  Steady-State Dynamic Response of a Bernoulli–Euler Beam on a Viscoelastic Foundation Subject to a Platoon of Moving Dynamic Loads , 2008 .

[3]  S. Farghaly,et al.  An exact frequency equation for an axially loaded beam-mass-spring system resting on a Winkler elastic foundation , 1995 .

[4]  Ricardo Dobry,et al.  Horizontal Response of Piles in Layered Soils , 1984 .

[5]  George Gazetas,et al.  Lateral Vibration and Internal Forces of Grouped Piles in Layered Soil , 1999 .

[6]  Wen-Hwa Wu,et al.  Systematic lumped‐parameter models for foundations based on polynomial‐fraction approximation , 2002 .

[7]  Ding Zhou,et al.  Dynamic characteristics of a beam and distributed spring-mass system , 2006 .

[8]  Oskar Mahrenholtz,et al.  Beam on viscoelastic foundation: an extension of Winkler’s model , 2009 .

[9]  R. Blevins,et al.  Formulas for natural frequency and mode shape , 1984 .

[10]  J. Enrique Luco,et al.  Discrete models for vertical vibrations of surface and embedded foundations , 1990 .

[11]  Masato Saitoh,et al.  Simple Model of Frequency-Dependent Impedance Functions in Soil-Structure Interaction Using Frequency-Independent Elements , 2007 .

[12]  Farhang Daneshmand,et al.  VIBRATION AND INSTABILITY ANALYSIS OF CARBON NANOTUBES CONVEYING FLUID AND RESTING ON A LINEAR VISCOELASTIC WINKLER FOUNDATION , 2010 .

[13]  Lars Vabbersgaard Andersen,et al.  Assessment of lumped-parameter models for rigid footings , 2010 .

[14]  Jan Drewes Achenbach,et al.  Dynamic Response of Beam on Viscoelastic Subgrade , 1965 .

[15]  John P. Wolf,et al.  Spring‐dashpot‐mass models for foundation vibrations , 1997 .

[16]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[17]  Ling Zhang,et al.  Deformation analysis of geocell reinforcement using Winkler model , 2009 .

[18]  Masato Saitoh,et al.  Lumped parameter models representing impedance functions at the interface of a rod on a viscoelastic medium , 2011 .

[19]  George Gazetas,et al.  Soil-pile-bridge seismic interaction : Kinematic and inertial effects. Part I: Soft soil , 1997 .

[20]  Lu Sun,et al.  A CLOSED-FORM SOLUTION OF A BERNOULLI-EULER BEAM ON A VISCOELASTIC FOUNDATION UNDER HARMONIC LINE LOADS , 2001 .

[21]  Milos Novak,et al.  Dynamic Stiffness and Damping of Piles , 1974 .

[22]  Lu Sun,et al.  A closed-form solution of beam on viscoelastic subgrade subjected to moving loads , 2002 .

[23]  Ricardo Dobry,et al.  Simple Radiation Damping Model for Piles and Footings , 1984 .

[24]  B. R. Becker,et al.  Dynamic Response of Beams on Elastic Foundation , 1992 .

[25]  John P. Wolf,et al.  Foundation Vibration Analysis Using Simple Physical Models , 1994 .