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    • Using a Piecewise Linear Spring to Approximate an Essentially Nonlinear Spring: Design and Validation

    Haining Li,Kefu Liu,Jian Deng

    TRANSACTIONS OF THE CANADIAN SOCIETY FOR MECHANICAL ENGINEERING（2025）

    Lakehead Univ

    Cited 0|Views3
    Abstract
    This study develops a procedure for designing a piecewise linear spring (PLS) to approximate an essentially nonlinear spring (ENS). The PLS is constructed with a cantilever beam constrained by a pair of single- or double-stop blocks. The design begins by determining the restoring force of the desired ENS using the equivalent stiffness which quantifies the characteristics of a cubic polynomial. Then, based on the force-deflection model of a cantilever beam with an overhang, the configuration parameters for single- and double-stop blocks are determined through a least squares optimization. The numerical simulation demonstrates that the PLS with double-stop blocks approximates the desired ENS behaviors better in terms of the restoring force, potential energy, and instantaneous frequency transition. An experiment apparatus with four tunable stop blocks is developed to validate the numerical simulation results. The static experimental tests verify the accuracy of the analytical model. The dynamic experimental tests show that within the achievable range of displacement, the PLSs behave similarly to the ENS. However, the maximum displacement is smaller than the designed one due to an insufficient exciting force. To address this issue, the desired displacement range is reduced by half. With the redesigned PLSs, the improved experimental results are obtained.
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    Key words
    essentially nonlinear spring,piecewise linear spring,equivalent stiffness,restoring force,design optimization
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