Abstract
Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system.
Highlights
A tilted support spring nonlinear system usually shows excellent energy absorption performance and was used to protect precise instruments since 1960s
The model of the tilted support spring nonlinear system with critical components is shown in Figure 1, where m1 and m2 denote the mass of critical components and the main body; k1 and c1 are the linear elastic coefficient and the damping coefficient between critical components and the main body; k2 and c2 are the linear elastic coefficient and the damping coefficient of the tilted support spring nonlinear system; l0 and φ0 are the length and the support angle of the four tilted support springs before they are compressed, respectively
Βü0, where T = 1/ω2 is taken as the period parameter; τ = t/T is the dimensionless time parameter; τ0 = t0/T is the dimensionless pulse duration parameter; λ1 = ω1/ω2 is the frequency parameter ratio of the system; λ2 = m1/m2 is the mass ratio of the system; β = T2/l0 is defined as a characteristic parameter of the system; ς1 = c1/2√k1m1 is the damping ratio between critical components and the main body; ς2 = c2/2√2k2m2 is the damping ratio of the tilted support spring nonlinear system; βü0m is the dimensionless peak pulse acceleration, respectively
Summary
A tilted support spring nonlinear system usually shows excellent energy absorption performance and was used to protect precise instruments since 1960s. Assuming the damage of products occurs firstly at the so-called critical components, the damage boundary surface concept was proposed and applied to typical nonlinear systems by Wang [9, 10]. This damage boundary surface concept leads to a noticeable reduction of disparity between the theoretical findings and the real-test results. Wang [13, 14] gained the model of a suspension packaging system under a rectangular pulse and further discussed the effects of the angle and the damping ratio on the shock response spectra, the acceleration response, and the damage boundary surface. The results provide theoretical foundations for the design of the tilted support spring nonlinear system
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