Design of passive suspension system with non-linear springs using B-spline collocation method

The issue of vibration isolation challenges engineers' designs across the engineering spectrum. From an engineering standpoint, vibration control impacts the fields of transportation, manufacturing, construction and mechanical design. Dynamic systems produce vibrations for various reasons i.e. rotating unbalanced masses (high speed turbines); inertia of reciprocating components (internal combustion engines); irregular rolling contact (automobiles) or induced eddy current (locomotives) vibrations. In most cases, vibrations cause only physical discomfort and/or loss of accuracy. But in extreme cases, transmitted forces may cause a body to undergo high amplitude resonant vibrations, leading to high cyclic stresses and imminent fatigue failure resulting in a catastrophic occurrence and possible loss of life. Therefore, isolating the vibration's source from other system components becomes essential. Deploying a parallel underdamped spring-damper arrangement achieves this required isolation by suspending the component's mass.;The frequency response function (FRF) of a second order under-damped suspension model suggests that for a given excitation frequency, suspensions with lower natural frequencies benefits vibration isolation. Lowering the natural frequency requires springs with low stiffness. Using soft springs is not always plausible as it significantly reduces the suspension's load carrying capacity. Therefore, in order to improve vibration isolation, the initial displacement requires high stiffness suspension followed by low stiffness beyond the required load carrying capacity. This initial high stiffness enables the suspension to sustain high loads, whereas the softspring behavior improves the suspension's vibration isolation.;Current research explores improving vibration isolation with a suspension system which uses non-linear spring stiffness. It proposes a suspension mechanism with compliant cantilevered beams used as springs. The suspension spring is mathematically modeled using the Euler-Bernoulli equation for bending of beams to create a non-linear governing equation. The resulting governing equation provides a numerical solution to develop a force versus deflection plot.;The analysis reveals that two distinct regions come under consideration when evaluating suspension: stiff-spring and soft-spring. The ensuing dynamic analysis leads to a frequency response function (FRF) of a spring-mass-damper system which emulates the suspension's operating condition. It reveals that vibration isolation manifests significant improvement when the suspension operates in the soft-spring region as compared to a linear spring arrangement. A numerical technique called B-spline collocation approximates the non-linear governing equation's solution. A prototype of the suspension system is manufactured and tested for static and dynamic characteristics. The analytical and experimental results are found to be in agreement.