Lateral vibration of a composite stepped beam consisted of SMA helical spring based on equivalent Euler–Bernoulli beam theory

The dynamic characteristics of the shape memory alloy (SMA) helical spring proposed to be used in the semi-active suspension platform (e.g. the optic disk drive) are considered in this study. The component mounted on the platform generates periodic oscillation due to parametric excitation, such as rotation of an eccentric mass. In this way, the induced vibration of the platform could load the suspension spring in both axial and lateral directions. Besides its tunable dynamic characteristics by phase transformation, the SMA helical spring providing both axial and lateral flexibilities is applicable in this regards. In this paper, the spring constant of the helical spring in transverse deformation was first derived by employing the first theorem of Castiglianoʹs. The derived spring constant was then used to define the equivalent flexural stiffness of the spring. Consequently, the natural frequency of a stepped composite beam with the assembly of SMA spring and other beam-like component was derived by transfer matrix method. The calculated natural frequencies of the stepped beam were compared with the experimental measurements. It is found that the formulation well predicted the natural frequency of the SMA spring both in martensite and austenite phases, respectively. The tunable characteristics of the SMA helical spring in lateral vibration were also demonstrated.