Abstract
This study intends to introduce the novel and efficient exact equivalent function (EF) for well-known deadzone nonlinearity. To indicate the effectiveness of this EF, the nonlinear vibration of cantilever beam in presence of deadzone nonlinear boundary condition is studied. The powerful analytical method, called He's Parameter Expanding Method (HPEM) is used to obtain the exact solution of dynamic behavior of mentioned system. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution. Comparison of the obtained solutions using numerical method shows the soundness of this analytical EF.
Highlights
The nonlinear free vibration of beams is of considerable interest to engineers and has been much studied
The results presented in this paper reveal that the method is very effective and convenient for nonlinear oscillators for which the highly nonlinear boundary condition exists
In this study deadzone discontinuous nonlinearity has been considered as a boundary condition of a cantilever beam and redefined exactly using the basic continuous functions
Summary
The nonlinear free vibration of beams is of considerable interest to engineers and has been much studied. The sources of nonlinearity of vibration systems are generally considered as due to the following aspects: (1) the physical nonlinearity, (2) the geometric nonlinearity and, (3) the nonlinearity of boundary conditions As it is reported in many research papers, the deadzone nonlinearity is an on-differentiable function. This input characteristic is ubiquitous in a wide range of mechanical and electrical components such as valves, gear vibration, DC servo motors, and other devices. Approximation of this nonlinear condition to obtain analytical solution of behavior of mentioned systems is always the major difficulty of engineer’s computations. Chengwu and Rajendra [7] used the arctangent function to approximate
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