the various types of isolators in existence can be grouped into passive isolators or active isolators . passive isolators are devices with fixed system parameters that need to be tailored toward a specific application . their design is thus determined by the dynamic mass to be supported , the type of dynamic disturbance , e . g ., shock , random sinusoidal vibration ; the frequency spectrum of the disturbance ; the environmental conditions , e . g ., temperature , humidity , atmospheric pressure , altitude ; the available sway space and the desired level of attenuation . passive isolators which have been used to reduce the forces transmitted from a vibration source to the environment are support mounts for manufacturing equipment such as presses and engine mounts in automobiles and other means of transportation . passive isolators prevent fragile objects from damage or from being affected by surrounding events , e . g ., semiconductor and optical manufacturing equipment , high precision measurement devices or simple shipping container isolators . these passive devices are typically relatively affordable , but less versatile when compared with active isolators . active isolators are essentially feedback control devices . the general function carried out by active isolators is to sense a disturbance and cancel or dampen the resulting motion by actively controlled actuation that is analogous but opposite in phase to the disturbance . while such active isolators often allow for favorable attenuation results they also exhibit a number of shortcomings the most significant being , high energy consumption for generating the continuous actuation . in one embodiment , the present invention provides an adaptive shock and vibration attenuation device with significant advantages over conventional isolators that are currently commercially available . the adaptive isolators of the present invention are able to operate in shock or vibration mode and provide optimized protection to excitations of varying characteristics such as duration , amplitude , force and frequency . adaptive shock and vibration attenuation is implemented by passive shock or vibration mounts that allow the adjustment of their dynamic characteristics in response to changes in the excitation conditions . dynamic characteristics include stiffness and damping . in one embodiment , the mount stiffness is varied by combining a passive mount with highly nonlinear force - deflection characteristics with an electromagnetic actuator or other means . alternatively , in other embodiments , the damping may be varied by adjusting or regulating the coulomb friction or by varying the viscous damping through temperature control of the damping medium . these adjustments of the mount characteristics result in the shifting of the operating point or natural frequency . non - invasive , non - contact sensors are used together with hardware or software - based signal processing to identify the excitation displacement or force signal and to generate the appropriate adjustments of the mount characteristics . the present invention combines elements of both passive and active isolation where the circular natural frequency , ù n , of the system can be adaptively controlled in response to changes in excitation conditions . the approach is based on an underlying passive isolator with progressive ( hard spring ) or degressive ( soft spring ) stiffness characteristics , whose operating point along the force - deflection curve can be adaptively controlled . a convenient means for achieving shift is the application of an actuator force . since the circular natural frequency ( ù n ) of the isolator system is proportional to the square root of the stiffness , k , a high degree of nonlinearity in the load - deflection curve is desired in order to achieve maximum changes in the natural circular frequency of the isolator with minimal actuator force and within minimal sway space . a shift in the operating point may be accomplished through electromagnetic forces or other means . a change in the system &# 39 ; s circular natural frequency , ù n , may be achieved through controlled variation of the stiffness , k , or the damping ratio ( æ ). an adaptive attenuation device of the invention performs the following main functions : sensing of the impending vibration or shock signal , discerning the character and parameters of the signal , deriving a set of system parameters that optimize the attenuation performance of the isolator and employing the integrated actuator to adjust the system parameters accordingly . in contrast to purely active isolators , the adaptive isolators of the present invention provide basic attenuation even in the case of malfunction of the active components . active isolators require a constant supply of energy for the actuation in order to achieve total cancellation of the dynamic disturbance , while the present invention will use actuation only in short periods of special dynamic events such as temporary resonance and shocks . the devices of the present invention also provide adaptivity or a general ability to react to changing conditions . adaptive capabilities of these devices include , but are not limited to changes in the frequency or amplitude of dynamic disturbance , e . g ., varying operating speed of a sheet metal transfer press based on the product , powering up / down of manufacturing equipment through resonance ; supported dynamic mass , e . g ., varying payload in a shipping container ; the environmental conditions , e . g ., temperature changes due to external factors or due to heat generation during equipment operation ; and the passive damping properties , e . g ., property changes of rubber compounds in elastomeric isolation mounts by aging or due to exposure to chemical agents . the present invention provides adaptive isolators which are simpler and less expensive than the conventional active isolators . adaptive isolators are more reliable , lighter , require less power for actuation , and offer basic passive protection even in the case of malfunctioning of the adaptive controller . the present invention is further illustrated by the following , non - limiting mathematical system models . the governing equations for harmonic force and motion excitation become differential equations with coefficients k and c that depend on a control parameter p ( e . g . actuator force ): m  x ¨ + c  ( p )  x . + k  ( p )  x = f 0  cos  ( ω   t ) ω n = 1 m  k m  x ¨ + c  ( p )  x . + k  ( p )  x = c  ( p )  y . + k  ( p )  y y = y 0  cos  ( ω   t ) the behavior of the elastomeric material of the underlying passive mounts can be characterized by the mooney - rivlin strain energy function w written in the form : w = ∑ n k + 1 = 1  c k1  ( i 1 - 3 ) k  ( i 2 - 3 ) 1 + 1 2  κ  ( i 3 - 3 ) 2 i 1 = c 11 i 2 = 1 2  ( i 1 2 - c ij  c ij ) i 3 = det   c ij  where c kl represent up to nine constants ( referred to as mooney - rivlin constants ), κ — is the bulk modulus , i i are the invariants of the cauchy - green deformation tensor c ij and n is the highest order of terms included into the series . the coefficients c kl determine the mechanical response of the material which are derived from experimental data of engineering stress versus engineering strain for various types of compression , tension and shear tests carried out over a wide range of strain values .